Blind Separation of Speech Mixtures
57
Blind Separation of Speech Mixtures Vaninirappuputhenpurayil Gopalan REJU School of Electrical and Electronic Engineering Nanyang Technological University 02:45 AM 1
description
Blind Separation of Speech Mixtures. Vaninirappuputhenpurayil Gopalan REJU School of Electrical and Electronic Engineering Nanyang Technological University. Introduction. Blind Source Separation. Convolutive. Mixing process:. s 1. s 2. Unmixing process:. Introduction. - PowerPoint PPT Presentation
Transcript of Blind Separation of Speech Mixtures
Blind Separation of Speech MixturesBlind Separation of Speech Mixtures
Vaninirappuputhenpurayil Gopalan REJU
School of Electrical and Electronic EngineeringNanyang Technological University
Vaninirappuputhenpurayil Gopalan REJU
School of Electrical and Electronic EngineeringNanyang Technological University
0510 AM 1
Introduction Introduction
Blind Source Separation Blind Source Separation
0510 AM
0
2120
1111 )()()()()(ll
ltslhltslhtx
0
2220
1212 )()()()()(ll
ltslhltslhtx
L
l
L
l
ltxlwltxlwty0
2120
1111 )()()()()(
L
l
L
l
ltxlwltxlwty0
2220
1212 )()()()()(
bull Mixing process
bull Unmixing process
ConvolutiveConvolutive
2
s1
s2
Introduction Introduction
Convolutive Blind Source Separation Convolutive Blind Source Separation Instantaneous Blind Source Separation Instantaneous Blind Source Separation
0510 AM 3
Introduction Introduction
Convolutive Blind Source Separation Convolutive Blind Source Separation Instantaneous Blind Source Separation Instantaneous Blind Source Separation
)(
)(
)(
)(
2
1
2221
1211
2
1
ts
ts
tx
tx
hh
hh
)()( tt SX H
)(
)(
)(
)(
2
1
2221
1211
2
1
ts
ts
hh
hh
tx
tx
)()( tt HSX
)(
)(
)()(
)()(
)(
)(
2
1
2221
1211
2
1
tfS
tfS
fHfH
fHfH
tfX
tfX
)()()( tfftf SX H
bull In frequency domain
Difficu
lt to
separa
te
Difficu
lt to
separa
te
Easy to
separa
te
Easy to
separa
te
0510 AM 4
Introduction Introduction
No of sources lt No of sensorNo of sources lt No of sensor1s
2s
3s
4s
1x2x3x
1s
2s1x2x3x
3s
1s
2s 1x2x3x
4s
No of sources = No of sensorNo of sources = No of sensor
No of sources gt No of sensorNo of sources gt No of sensor
Overdetermined mixingOverdetermined mixing
Determined mixingDetermined mixing
Underdetermined mixingUnderdetermined mixing
Difficult to se
parate
Difficult to se
parate
Easy to se
parate
Easy to se
parate
0510 AM 5
Approaches for BSS of Speech SignalsApproaches for BSS of Speech Signals
Types of mixing
Instantaneous mixing Convolutive mixing
0510 AM 6
Approaches for BSS of Speech SignalsApproaches for BSS of Speech Signals
Instantaneous mixing
Step 1 Selection of cost function
Step 2 Minimization or maximization of the cost function
0510 AM
WHS1
S2 X2
Y1
Y2
Separated
X1
7
Approaches for BSS of Speech SignalsApproaches for BSS of Speech SignalsInstantaneous mixingInstantaneous mixing
Selection of cost function
Statistical independence
Information theoretic
Non-Gaussianity
Kurtosis
Negentropy
Nonlinear cross moments
Temporal structure of speech
Non-stationarity of speech0510 AM
i
ii ypp y is idea Basic
Central limit theoremMixture of two or more sources will be more Gaussian than their individual components
224 E3E)( yyykurt
yyy HHJ gauss
yyyy dppH logEntropy
0 ji ygyfE
used becan statsticsorder Secondlags timedifferent for usly simultaneon correlatiooutput theedioganaliz eg
eddiagonalizusly simultaneo are matricesn correlatio the
and blocks into divided are Signals
Non Gaussianity measures
Signals from two different sources are independent
8
Approaches for BSS of Speech SignalsApproaches for BSS of Speech Signals
Instantaneous mixingMinimization or maximization of the cost function
simple gradient method
Natural gradient method
Newtonrsquos method
eg Informax ICA algorithm
eg FastICA
0510 AM 9
Approaches for BSS of Speech SignalsApproaches for BSS of Speech SignalsConvolutive Mixing
Time Domain Frequency Domain
QqltxlwyP
p
L
lpqpq 1)()(
1
1
0
)()()( tfftf SHX
)()()( tfftf XWY
AdvantageNo permutation problem
DisadvantageSlow convergence High computational cost for long filter taps
AdvantageLow computational costFast convergence
DisadvantagePermutation Problem
WHS1
S2
X1
X2
Y1 Y2
Y2 Y1
0510 AM 10
or
Permutation Problem in Frequency Domain BSS
Permutation Problem in Frequency Domain BSS
f1
f2
fk
x1x2
x3
BSS
BSS
BSSMixed signals
K po
int
FFT
y1y2y3
Still signals are mixed
K po
int
IFFT
Corresponding to different sources Due to permutation problem
One frequency binInstantaneous ICA algorithm
Solv
ing
perm
utati
on
Prob
lem y1
y2y3
Separated signals
Corresponding to y3
0510 AM 11
MotivationMotivation
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
12
My Contribution - IMy Contribution - I
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
13
Algorithm for Solving the Permutation Problem
Algorithm for Solving the Permutation Problem
f1
f2
fk
x1x2
x3
BSS
BSS
BSSMixed signals
K po
int
FFT
y1y2y3
Separated signals
K po
int
IFFT
Solv
ing
perm
utati
on
Prob
lem
Permutation problem
One frequency binInstantaneous ICA algorithm
Permutation problem solved
0510 AM 14
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Direction Of Arrival (DOA) method
2
1
)sin(2 1
p
dcfjkqpkq
pkefWfU Position of the pth sensor
Velocity of sound
)(
)(
)()(
)()(
)(
)(
2
1
2221
1211
2
1
k
k
kk
kk
k
k
fX
fX
fWfW
fWfW
fY
fY
0510 AM
Direction of y1 = -30o
Direction of y2 = 20o
15
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Reasons for failure at lower freq
Lower spacing causes error in phase difference measurement
The relation is approximated for plane wave front under anechoic condition
Disadvantages
Fails at lower frequenciesFails when sources are nearRoom reverberationSensor positions must be known
Direction Of Arrival (DOA) method
0510 AM 16
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
f1
f2
fk
BSS
BSS
BSSMixed signals
K po
int
FFT
y1y2y3
Separated signals
K po
int
IFFT
Solv
ing
perm
utati
on
Prob
lem
Low correlation
High correlationLow
correlation
x1x2
x3
Adjacent bands correlation method
0510 AM 17
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
r12
r21
r11
r22 r22 r22 r22
r11 r11 r11
r12
r21
r12
r21
r12
r21r11 r12
r21 r22
s1
s2
Correlation matrix
21122211 rrrr No change
21122211 rrrr Change permutation
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Adjacent bands correlation method
0510 AM
21122211 and and rrrr
21122211 and and rrrr
With confidence Without confidence
2090
8010
8020
1090
2090
1040
1040
2090
Example Example
18
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
r12
r21
r11
r22 r22 r22 r22
r11 r11 r11
r12
r21
r12
r21
r12
r21
r11 r12
r21 r22
s1
s2
Correlation matrix
Disadvantage The method is not robust
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Adjacent bands correlation method
0510 AM 19
0510 AM
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Combination of DOA and Correlation methods method
DOA + Harmonic Correlation + Adjacent bands correlation
Advantage Increased robustness
20
Proposed algorithm Partial separation method(Parallel configuration)
Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
Proposed algorithm Partial separation method(Parallel configuration)
Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
2y
1y
1x
2x
1s
2s
0510 AM 21
Time domain stage
Frequency domain stage
Partial separation method(Parallel configuration)
Partial separation method(Parallel configuration)
0510 AM 22
Time domain stage
Frequency domain stage
Parallel configuration
Partial separation method(Cascade configuration)
Partial separation method(Cascade configuration)
0510 AM 23
Time domain stage
Frequency domain stage
Advantages of Partial Separation methodAdvantages of Partial Separation method
bull Robustness
0510 AM 24
Comparison with Adjacent Bands Correlation Method
Comparison with Adjacent Bands Correlation Method
0510 AM 25
PS - Partial Separation method with confidence check C1 - Correlation between the adjacent bins without confidence check C2 - Correlation between adjacent bins with confidence check Ha - Correlation between the harmonic components with confidence check PS1 - Partial separation method alone without confidence check
0510 AM 26
Comparison with DOA methodComparison with DOA method
My Contribution -IIMy Contribution -II
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
27
Underdetermined Blind Source Separation of Instantaneous Mixtures
Underdetermined Blind Source Separation of Instantaneous Mixtures
t
k
0)(0)( 222221 tkStkS
0)(0)( 222221 tkStkS
0)(0)( 112111 tkStkS
0)(0)( 112111 tkStkS
tkX 1
tkX 22x
1x
0510 AM 28
Mathematical Representation of Instantaneous Mixing
Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
Mathematical Representation of Instantaneous Mixing
Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
)(
)(
)(
)( 1
1
1111
tkS
tkS
hh
hh
tkX
tkX
QPQP
Q
P
)(
)(
)(
)( 1
1
1111
ts
ts
hh
hh
tx
tx
QPQP
Q
P
)()()(11
1
1
11
tkS
h
h
tkS
h
h
tkS
h
h
Q
PQ
Q
q
Pq
q
P
)()()()( 21 tkStkStkStk QhhhX
Time domain
Time-Frequency domain
0510 AM 29
P ndash No of mixturesQ ndash No of sources
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
00point at 1 Case 11211111 tkStkStk
)()()( 1122111111 tkStkStk hhX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 2222221122 tkStkStk hhX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
0510 AM
0 0
30
Q
qqq tkStk
1
hX
2Let Q
00point at 1 Case 11211111 tkStkStk
)()( 111111 tkStk hX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()( 222222 tkStk hX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
0510 AM 31
00point at 1 Case 11211111 tkStkStk
)()( 111111 tkStk hX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()( 222222 tkStk hX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
Scalar
ScalarScalar
Scalar
At single source point 1 At single source point 2
111
111
ofDirection )( ofDirection
ofDirection )( ofDirection
hX
hX
tkI
tkR 222
222
ofDirection )( ofDirection
ofDirection )( ofDirection
hX
hX
tkI
tkR
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
0510 AM
1111 ( of Direction ( of Direction tkItkR XX 2222 ( of Direction ( of Direction tkItkR XX 32
Scatter Diagram of the Mixtures When Source are Perfectly Sparse
Scatter Diagram of the Mixtures When Source are Perfectly Sparse
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
22222
11111
2221
1211
22222
11111
kSkSkSkSkS
kSkSkSkSkS
hh
hh
kXkXkXkXkX
kXkXkXkXkX
21
111 h
hh
22
122 h
hh
0 00 0 0
Example
0510 AM 33
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
22222
11111
2221
1211
22222
11111
kSkSkSkSkS
kSkSkSkSkS
hh
hh
kXkXkXkXkX
kXkXkXkXkX
21
111 h
hh
22
122 h
hh
0 00 0 00
Example
Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
0510 AM 34
Scatter Diagram of the Mixtures when Sources are Sparse
Scatter Diagram of the Mixtures when Sources are Sparse
3h
6h
5h
1h4h
2h
0510 AM
No of sources = 6No of mixtures = 2
35
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
3h
6h
5h
1h4h
2h
0510 AM
No of sources = 6No of mixtures = 2
36
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
3h
6h
5h
1h4h
2h
0510 AM
ObjectiveEstimation of the single source points
No of sources = 6No of mixtures = 2
37
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Multi source point
38
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
Multi source point
39
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
Average of 15 pairs of speech utterances of length 10 s each
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
)( ofDirection )( ofDirection tkXItkXR )( ofDirection )( ofDirection tkXItkXR
SSPMSP
40
SSPt
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)()(
)()(
112112
111111
tkXjItkXR
tkXjItkXR
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXI
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXIMSP
)( 111 tkX
)( 112 tkX
cos
)()(
)()(
tkXItkXR
tkXItkXR T
Proposed Algorithm for the Detection of Single Source Points
Proposed Algorithm for the Detection of Single Source Points
0510 AM 41
Elimination of OutliersElimination of Outliers
SSPs detection
Clus
terin
g
Outlier elimination
0510 AM 42
0510 AM
Experimental ResultsExperimental Results
dB6747NMSE
No of mixtures =2 No of sources =6
43
Detected Single Source PointsThree mixtures
Detected Single Source PointsThree mixtures
No of mixtures =3 No of sources =60510 AM 44
Comparison with Classical Algorithms for Determined Case
Comparison with Classical Algorithms for Determined Case
No of mixtures =2No of sources =2
Average of 500 experimental results
0510 AM 45
-gt
Comparison with Method Proposed in [1] Underdetermined case
Comparison with Method Proposed in [1] Underdetermined case
[1] Y Li S Amari A Cichocki D W C Ho and S Xie ldquoUnderdetermined blind source separation based on sparse representationrdquo IEEE Transactions on Signal Processing vol 54 p 423ndash437 Feb 2006
0510 AM
Nor
mal
ized
mea
n sq
uare
err
or (N
MSE
) in
mix
ing
mat
rix e
stim
ation
(dB)
Order of the mixing matrices (PxQ)
46
P ndash No of mixturesQ ndash No of sources
Advantages of the Proposed algorithmAdvantages of the Proposed algorithm
Step 1 Convert x in the time domain to the TF domain to get XStep 2 Check the condition
Step 3 If the condition is satisfied then X(k t) is a sample atthe SSP and this sample is kept for mixing matrix estimationotherwise discard the point
Step 4 Repeat Steps 2 to 3 for all the points in the TF planeor until sufficient number of SSPs are obtained
cos
)()(
)()(
tkXItkXR
tkXItkXR T
1) Much simpler constrain the algorithm does not require ldquosingle source zonerdquo
3) The algorithm is extremely simple but effective2) Separation performance is better
0510 AM 47-gt
My Contributions ndash III IV and VMy Contributions ndash III IV and V
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
48
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Mask estimation
Mic 1
Mic P
Mixture in TF domain
Separated signals in TF domain
)( tkX P
)(1 tkX
t
t
k
k
)(1 tkY
)(1 tkY
)( tkYQ
)( tkYQ
QP
0510 AM 49
Mathematical RepresentationMathematical Representation
Q
q
L
lqpqp Pplnslhnx
1
1
0
1)()()(
)()()()()()()( 11 tkSktkSktkSktk QQqq HHHX
)(
)(
)()(
)()(
)(
)( 1
1
1111
tkS
tkS
kHkH
kHkH
tkX
tkX
QPQP
Q
P
)(
)(
)(
)(
)(
)(
)(
)(
)( 11
1
1
11
tkS
kH
kH
tkS
kH
kH
tkS
kH
kH
Q
PQ
Q
q
Pq
q
P
Time domain
Frequency domain
0510 AM 50
P ndash No of mixturesQ ndash No of sources
Single source pointsSingle source pointsInstantaneous mixing
00point at 1 Case 11211111 tkStkStk
)()()(
)()()(
111111
111111
tkSIktkI
tkSRktkR
HX
HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()(
)()()(
222222
222222
tkSIktkI
tkSRktkR
HX
HX
Single source point 2
Real scalar
RealReal
Real scalarReal scalar
Real scalar
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
0510 AM 51
Basic Principle of Single Source Points Detection
Basic Principle of Single Source Points Detection
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
j
H
C
e
cos21
21
UU
UUUUU H
and 20coscos HCH
angle pseudo called is
angleHermitian called is
H The Hermitian angle between the complex
vectors u1 and u2 will remain the same even if the vectors are multiplied by any complex scalars whereas the pseudo angle will change
0510 AM 52
-gt
k
Algorithm for Single Source Points Detection
Algorithm for Single Source Points Detection
t
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)(
)(
)(111
121
111 tkSkH
kH
11
11
j
jr
)(
)(
112
111
tkX
tkX
11
11
j
jr
)(
)(
112
111
tkX
tkX
)( 111 tkX
)( 112 tkX
)(
)(
)(112
122
112 tkSkH
kH θH2
θH1
θH2
rX
rX
)(
)(cos
11
111
tk
tk H
Hq
0510 AM 53
θH1
OR
1k
1k
1t
Clean
Estimated
Mask Estimation by k-means (KM)Mask Estimation by k-means (KM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 54
Clean
Estimated
Mask Estimation by Fuzzy c-means (FCM)Mask Estimation by Fuzzy c-means (FCM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 55
Automatic Detection of Number of SourcesAutomatic Detection of Number of Sources
0510 AM 56
Cluster validation technique
For c = 2 to cmax
Cluster the data into c clustersCalculate the cluster validation index
EndTake c corresponding to the best cluster as the number of sources
-gt
Elimination of Low Energy PointsElimination of Low Energy Points
0510 AM 57
- Blind Separation of Speech Mixtures
- Introduction
- Slide 3
- Slide 4
- Slide 5
- Approaches for BSS of Speech Signals
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Permutation Problem in Frequency Domain BSS
- Motivation
- My Contribution - I
- Algorithm for Solving the Permutation Problem
- Existing Method for Solving the Permutation Problem
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Proposed algorithm Partial separation method (Parallel configuration) Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
- Partial separation method (Parallel configuration)
- Partial separation method (Cascade configuration)
- Advantages of Partial Separation method
- Comparison with Adjacent Bands Correlation Method
- Comparison with DOA method
- My Contribution -II
- Underdetermined Blind Source Separation of Instantaneous Mixtures
- Mathematical Representation of Instantaneous Mixing Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
- Single Source Points in Time-Frequency domain
- Slide 31
- Slide 32
- Scatter Diagram of the Mixtures When Source are Perfectly Sparse
- Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
- Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
- Principle of the Proposed Algorithm for the Detection of Single Source Points
- Slide 39
- Slide 40
- Proposed Algorithm for the Detection of Single Source Points
- Elimination of Outliers
- Slide 43
- Detected Single Source Points Three mixtures
- Comparison with Classical Algorithms for Determined Case
- Comparison with Method Proposed in [1] Underdetermined case
- Advantages of the Proposed algorithm
- My Contributions ndash III IV and V
- Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
- Mathematical Representation
- Single source points
- Basic Principle of Single Source Points Detection
- Algorithm for Single Source Points Detection
- Mask Estimation by k-means (KM)
- Mask Estimation by Fuzzy c-means (FCM)
- Automatic Detection of Number of Sources
- Elimination of Low Energy Points
-
Introduction Introduction
Blind Source Separation Blind Source Separation
0510 AM
0
2120
1111 )()()()()(ll
ltslhltslhtx
0
2220
1212 )()()()()(ll
ltslhltslhtx
L
l
L
l
ltxlwltxlwty0
2120
1111 )()()()()(
L
l
L
l
ltxlwltxlwty0
2220
1212 )()()()()(
bull Mixing process
bull Unmixing process
ConvolutiveConvolutive
2
s1
s2
Introduction Introduction
Convolutive Blind Source Separation Convolutive Blind Source Separation Instantaneous Blind Source Separation Instantaneous Blind Source Separation
0510 AM 3
Introduction Introduction
Convolutive Blind Source Separation Convolutive Blind Source Separation Instantaneous Blind Source Separation Instantaneous Blind Source Separation
)(
)(
)(
)(
2
1
2221
1211
2
1
ts
ts
tx
tx
hh
hh
)()( tt SX H
)(
)(
)(
)(
2
1
2221
1211
2
1
ts
ts
hh
hh
tx
tx
)()( tt HSX
)(
)(
)()(
)()(
)(
)(
2
1
2221
1211
2
1
tfS
tfS
fHfH
fHfH
tfX
tfX
)()()( tfftf SX H
bull In frequency domain
Difficu
lt to
separa
te
Difficu
lt to
separa
te
Easy to
separa
te
Easy to
separa
te
0510 AM 4
Introduction Introduction
No of sources lt No of sensorNo of sources lt No of sensor1s
2s
3s
4s
1x2x3x
1s
2s1x2x3x
3s
1s
2s 1x2x3x
4s
No of sources = No of sensorNo of sources = No of sensor
No of sources gt No of sensorNo of sources gt No of sensor
Overdetermined mixingOverdetermined mixing
Determined mixingDetermined mixing
Underdetermined mixingUnderdetermined mixing
Difficult to se
parate
Difficult to se
parate
Easy to se
parate
Easy to se
parate
0510 AM 5
Approaches for BSS of Speech SignalsApproaches for BSS of Speech Signals
Types of mixing
Instantaneous mixing Convolutive mixing
0510 AM 6
Approaches for BSS of Speech SignalsApproaches for BSS of Speech Signals
Instantaneous mixing
Step 1 Selection of cost function
Step 2 Minimization or maximization of the cost function
0510 AM
WHS1
S2 X2
Y1
Y2
Separated
X1
7
Approaches for BSS of Speech SignalsApproaches for BSS of Speech SignalsInstantaneous mixingInstantaneous mixing
Selection of cost function
Statistical independence
Information theoretic
Non-Gaussianity
Kurtosis
Negentropy
Nonlinear cross moments
Temporal structure of speech
Non-stationarity of speech0510 AM
i
ii ypp y is idea Basic
Central limit theoremMixture of two or more sources will be more Gaussian than their individual components
224 E3E)( yyykurt
yyy HHJ gauss
yyyy dppH logEntropy
0 ji ygyfE
used becan statsticsorder Secondlags timedifferent for usly simultaneon correlatiooutput theedioganaliz eg
eddiagonalizusly simultaneo are matricesn correlatio the
and blocks into divided are Signals
Non Gaussianity measures
Signals from two different sources are independent
8
Approaches for BSS of Speech SignalsApproaches for BSS of Speech Signals
Instantaneous mixingMinimization or maximization of the cost function
simple gradient method
Natural gradient method
Newtonrsquos method
eg Informax ICA algorithm
eg FastICA
0510 AM 9
Approaches for BSS of Speech SignalsApproaches for BSS of Speech SignalsConvolutive Mixing
Time Domain Frequency Domain
QqltxlwyP
p
L
lpqpq 1)()(
1
1
0
)()()( tfftf SHX
)()()( tfftf XWY
AdvantageNo permutation problem
DisadvantageSlow convergence High computational cost for long filter taps
AdvantageLow computational costFast convergence
DisadvantagePermutation Problem
WHS1
S2
X1
X2
Y1 Y2
Y2 Y1
0510 AM 10
or
Permutation Problem in Frequency Domain BSS
Permutation Problem in Frequency Domain BSS
f1
f2
fk
x1x2
x3
BSS
BSS
BSSMixed signals
K po
int
FFT
y1y2y3
Still signals are mixed
K po
int
IFFT
Corresponding to different sources Due to permutation problem
One frequency binInstantaneous ICA algorithm
Solv
ing
perm
utati
on
Prob
lem y1
y2y3
Separated signals
Corresponding to y3
0510 AM 11
MotivationMotivation
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
12
My Contribution - IMy Contribution - I
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
13
Algorithm for Solving the Permutation Problem
Algorithm for Solving the Permutation Problem
f1
f2
fk
x1x2
x3
BSS
BSS
BSSMixed signals
K po
int
FFT
y1y2y3
Separated signals
K po
int
IFFT
Solv
ing
perm
utati
on
Prob
lem
Permutation problem
One frequency binInstantaneous ICA algorithm
Permutation problem solved
0510 AM 14
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Direction Of Arrival (DOA) method
2
1
)sin(2 1
p
dcfjkqpkq
pkefWfU Position of the pth sensor
Velocity of sound
)(
)(
)()(
)()(
)(
)(
2
1
2221
1211
2
1
k
k
kk
kk
k
k
fX
fX
fWfW
fWfW
fY
fY
0510 AM
Direction of y1 = -30o
Direction of y2 = 20o
15
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Reasons for failure at lower freq
Lower spacing causes error in phase difference measurement
The relation is approximated for plane wave front under anechoic condition
Disadvantages
Fails at lower frequenciesFails when sources are nearRoom reverberationSensor positions must be known
Direction Of Arrival (DOA) method
0510 AM 16
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
f1
f2
fk
BSS
BSS
BSSMixed signals
K po
int
FFT
y1y2y3
Separated signals
K po
int
IFFT
Solv
ing
perm
utati
on
Prob
lem
Low correlation
High correlationLow
correlation
x1x2
x3
Adjacent bands correlation method
0510 AM 17
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
r12
r21
r11
r22 r22 r22 r22
r11 r11 r11
r12
r21
r12
r21
r12
r21r11 r12
r21 r22
s1
s2
Correlation matrix
21122211 rrrr No change
21122211 rrrr Change permutation
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Adjacent bands correlation method
0510 AM
21122211 and and rrrr
21122211 and and rrrr
With confidence Without confidence
2090
8010
8020
1090
2090
1040
1040
2090
Example Example
18
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
r12
r21
r11
r22 r22 r22 r22
r11 r11 r11
r12
r21
r12
r21
r12
r21
r11 r12
r21 r22
s1
s2
Correlation matrix
Disadvantage The method is not robust
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Adjacent bands correlation method
0510 AM 19
0510 AM
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Combination of DOA and Correlation methods method
DOA + Harmonic Correlation + Adjacent bands correlation
Advantage Increased robustness
20
Proposed algorithm Partial separation method(Parallel configuration)
Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
Proposed algorithm Partial separation method(Parallel configuration)
Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
2y
1y
1x
2x
1s
2s
0510 AM 21
Time domain stage
Frequency domain stage
Partial separation method(Parallel configuration)
Partial separation method(Parallel configuration)
0510 AM 22
Time domain stage
Frequency domain stage
Parallel configuration
Partial separation method(Cascade configuration)
Partial separation method(Cascade configuration)
0510 AM 23
Time domain stage
Frequency domain stage
Advantages of Partial Separation methodAdvantages of Partial Separation method
bull Robustness
0510 AM 24
Comparison with Adjacent Bands Correlation Method
Comparison with Adjacent Bands Correlation Method
0510 AM 25
PS - Partial Separation method with confidence check C1 - Correlation between the adjacent bins without confidence check C2 - Correlation between adjacent bins with confidence check Ha - Correlation between the harmonic components with confidence check PS1 - Partial separation method alone without confidence check
0510 AM 26
Comparison with DOA methodComparison with DOA method
My Contribution -IIMy Contribution -II
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
27
Underdetermined Blind Source Separation of Instantaneous Mixtures
Underdetermined Blind Source Separation of Instantaneous Mixtures
t
k
0)(0)( 222221 tkStkS
0)(0)( 222221 tkStkS
0)(0)( 112111 tkStkS
0)(0)( 112111 tkStkS
tkX 1
tkX 22x
1x
0510 AM 28
Mathematical Representation of Instantaneous Mixing
Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
Mathematical Representation of Instantaneous Mixing
Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
)(
)(
)(
)( 1
1
1111
tkS
tkS
hh
hh
tkX
tkX
QPQP
Q
P
)(
)(
)(
)( 1
1
1111
ts
ts
hh
hh
tx
tx
QPQP
Q
P
)()()(11
1
1
11
tkS
h
h
tkS
h
h
tkS
h
h
Q
PQ
Q
q
Pq
q
P
)()()()( 21 tkStkStkStk QhhhX
Time domain
Time-Frequency domain
0510 AM 29
P ndash No of mixturesQ ndash No of sources
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
00point at 1 Case 11211111 tkStkStk
)()()( 1122111111 tkStkStk hhX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 2222221122 tkStkStk hhX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
0510 AM
0 0
30
Q
qqq tkStk
1
hX
2Let Q
00point at 1 Case 11211111 tkStkStk
)()( 111111 tkStk hX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()( 222222 tkStk hX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
0510 AM 31
00point at 1 Case 11211111 tkStkStk
)()( 111111 tkStk hX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()( 222222 tkStk hX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
Scalar
ScalarScalar
Scalar
At single source point 1 At single source point 2
111
111
ofDirection )( ofDirection
ofDirection )( ofDirection
hX
hX
tkI
tkR 222
222
ofDirection )( ofDirection
ofDirection )( ofDirection
hX
hX
tkI
tkR
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
0510 AM
1111 ( of Direction ( of Direction tkItkR XX 2222 ( of Direction ( of Direction tkItkR XX 32
Scatter Diagram of the Mixtures When Source are Perfectly Sparse
Scatter Diagram of the Mixtures When Source are Perfectly Sparse
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
22222
11111
2221
1211
22222
11111
kSkSkSkSkS
kSkSkSkSkS
hh
hh
kXkXkXkXkX
kXkXkXkXkX
21
111 h
hh
22
122 h
hh
0 00 0 0
Example
0510 AM 33
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
22222
11111
2221
1211
22222
11111
kSkSkSkSkS
kSkSkSkSkS
hh
hh
kXkXkXkXkX
kXkXkXkXkX
21
111 h
hh
22
122 h
hh
0 00 0 00
Example
Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
0510 AM 34
Scatter Diagram of the Mixtures when Sources are Sparse
Scatter Diagram of the Mixtures when Sources are Sparse
3h
6h
5h
1h4h
2h
0510 AM
No of sources = 6No of mixtures = 2
35
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
3h
6h
5h
1h4h
2h
0510 AM
No of sources = 6No of mixtures = 2
36
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
3h
6h
5h
1h4h
2h
0510 AM
ObjectiveEstimation of the single source points
No of sources = 6No of mixtures = 2
37
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Multi source point
38
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
Multi source point
39
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
Average of 15 pairs of speech utterances of length 10 s each
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
)( ofDirection )( ofDirection tkXItkXR )( ofDirection )( ofDirection tkXItkXR
SSPMSP
40
SSPt
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)()(
)()(
112112
111111
tkXjItkXR
tkXjItkXR
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXI
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXIMSP
)( 111 tkX
)( 112 tkX
cos
)()(
)()(
tkXItkXR
tkXItkXR T
Proposed Algorithm for the Detection of Single Source Points
Proposed Algorithm for the Detection of Single Source Points
0510 AM 41
Elimination of OutliersElimination of Outliers
SSPs detection
Clus
terin
g
Outlier elimination
0510 AM 42
0510 AM
Experimental ResultsExperimental Results
dB6747NMSE
No of mixtures =2 No of sources =6
43
Detected Single Source PointsThree mixtures
Detected Single Source PointsThree mixtures
No of mixtures =3 No of sources =60510 AM 44
Comparison with Classical Algorithms for Determined Case
Comparison with Classical Algorithms for Determined Case
No of mixtures =2No of sources =2
Average of 500 experimental results
0510 AM 45
-gt
Comparison with Method Proposed in [1] Underdetermined case
Comparison with Method Proposed in [1] Underdetermined case
[1] Y Li S Amari A Cichocki D W C Ho and S Xie ldquoUnderdetermined blind source separation based on sparse representationrdquo IEEE Transactions on Signal Processing vol 54 p 423ndash437 Feb 2006
0510 AM
Nor
mal
ized
mea
n sq
uare
err
or (N
MSE
) in
mix
ing
mat
rix e
stim
ation
(dB)
Order of the mixing matrices (PxQ)
46
P ndash No of mixturesQ ndash No of sources
Advantages of the Proposed algorithmAdvantages of the Proposed algorithm
Step 1 Convert x in the time domain to the TF domain to get XStep 2 Check the condition
Step 3 If the condition is satisfied then X(k t) is a sample atthe SSP and this sample is kept for mixing matrix estimationotherwise discard the point
Step 4 Repeat Steps 2 to 3 for all the points in the TF planeor until sufficient number of SSPs are obtained
cos
)()(
)()(
tkXItkXR
tkXItkXR T
1) Much simpler constrain the algorithm does not require ldquosingle source zonerdquo
3) The algorithm is extremely simple but effective2) Separation performance is better
0510 AM 47-gt
My Contributions ndash III IV and VMy Contributions ndash III IV and V
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
48
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Mask estimation
Mic 1
Mic P
Mixture in TF domain
Separated signals in TF domain
)( tkX P
)(1 tkX
t
t
k
k
)(1 tkY
)(1 tkY
)( tkYQ
)( tkYQ
QP
0510 AM 49
Mathematical RepresentationMathematical Representation
Q
q
L
lqpqp Pplnslhnx
1
1
0
1)()()(
)()()()()()()( 11 tkSktkSktkSktk QQqq HHHX
)(
)(
)()(
)()(
)(
)( 1
1
1111
tkS
tkS
kHkH
kHkH
tkX
tkX
QPQP
Q
P
)(
)(
)(
)(
)(
)(
)(
)(
)( 11
1
1
11
tkS
kH
kH
tkS
kH
kH
tkS
kH
kH
Q
PQ
Q
q
Pq
q
P
Time domain
Frequency domain
0510 AM 50
P ndash No of mixturesQ ndash No of sources
Single source pointsSingle source pointsInstantaneous mixing
00point at 1 Case 11211111 tkStkStk
)()()(
)()()(
111111
111111
tkSIktkI
tkSRktkR
HX
HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()(
)()()(
222222
222222
tkSIktkI
tkSRktkR
HX
HX
Single source point 2
Real scalar
RealReal
Real scalarReal scalar
Real scalar
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
0510 AM 51
Basic Principle of Single Source Points Detection
Basic Principle of Single Source Points Detection
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
j
H
C
e
cos21
21
UU
UUUUU H
and 20coscos HCH
angle pseudo called is
angleHermitian called is
H The Hermitian angle between the complex
vectors u1 and u2 will remain the same even if the vectors are multiplied by any complex scalars whereas the pseudo angle will change
0510 AM 52
-gt
k
Algorithm for Single Source Points Detection
Algorithm for Single Source Points Detection
t
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)(
)(
)(111
121
111 tkSkH
kH
11
11
j
jr
)(
)(
112
111
tkX
tkX
11
11
j
jr
)(
)(
112
111
tkX
tkX
)( 111 tkX
)( 112 tkX
)(
)(
)(112
122
112 tkSkH
kH θH2
θH1
θH2
rX
rX
)(
)(cos
11
111
tk
tk H
Hq
0510 AM 53
θH1
OR
1k
1k
1t
Clean
Estimated
Mask Estimation by k-means (KM)Mask Estimation by k-means (KM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 54
Clean
Estimated
Mask Estimation by Fuzzy c-means (FCM)Mask Estimation by Fuzzy c-means (FCM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 55
Automatic Detection of Number of SourcesAutomatic Detection of Number of Sources
0510 AM 56
Cluster validation technique
For c = 2 to cmax
Cluster the data into c clustersCalculate the cluster validation index
EndTake c corresponding to the best cluster as the number of sources
-gt
Elimination of Low Energy PointsElimination of Low Energy Points
0510 AM 57
- Blind Separation of Speech Mixtures
- Introduction
- Slide 3
- Slide 4
- Slide 5
- Approaches for BSS of Speech Signals
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Permutation Problem in Frequency Domain BSS
- Motivation
- My Contribution - I
- Algorithm for Solving the Permutation Problem
- Existing Method for Solving the Permutation Problem
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Proposed algorithm Partial separation method (Parallel configuration) Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
- Partial separation method (Parallel configuration)
- Partial separation method (Cascade configuration)
- Advantages of Partial Separation method
- Comparison with Adjacent Bands Correlation Method
- Comparison with DOA method
- My Contribution -II
- Underdetermined Blind Source Separation of Instantaneous Mixtures
- Mathematical Representation of Instantaneous Mixing Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
- Single Source Points in Time-Frequency domain
- Slide 31
- Slide 32
- Scatter Diagram of the Mixtures When Source are Perfectly Sparse
- Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
- Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
- Principle of the Proposed Algorithm for the Detection of Single Source Points
- Slide 39
- Slide 40
- Proposed Algorithm for the Detection of Single Source Points
- Elimination of Outliers
- Slide 43
- Detected Single Source Points Three mixtures
- Comparison with Classical Algorithms for Determined Case
- Comparison with Method Proposed in [1] Underdetermined case
- Advantages of the Proposed algorithm
- My Contributions ndash III IV and V
- Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
- Mathematical Representation
- Single source points
- Basic Principle of Single Source Points Detection
- Algorithm for Single Source Points Detection
- Mask Estimation by k-means (KM)
- Mask Estimation by Fuzzy c-means (FCM)
- Automatic Detection of Number of Sources
- Elimination of Low Energy Points
-
Introduction Introduction
Convolutive Blind Source Separation Convolutive Blind Source Separation Instantaneous Blind Source Separation Instantaneous Blind Source Separation
0510 AM 3
Introduction Introduction
Convolutive Blind Source Separation Convolutive Blind Source Separation Instantaneous Blind Source Separation Instantaneous Blind Source Separation
)(
)(
)(
)(
2
1
2221
1211
2
1
ts
ts
tx
tx
hh
hh
)()( tt SX H
)(
)(
)(
)(
2
1
2221
1211
2
1
ts
ts
hh
hh
tx
tx
)()( tt HSX
)(
)(
)()(
)()(
)(
)(
2
1
2221
1211
2
1
tfS
tfS
fHfH
fHfH
tfX
tfX
)()()( tfftf SX H
bull In frequency domain
Difficu
lt to
separa
te
Difficu
lt to
separa
te
Easy to
separa
te
Easy to
separa
te
0510 AM 4
Introduction Introduction
No of sources lt No of sensorNo of sources lt No of sensor1s
2s
3s
4s
1x2x3x
1s
2s1x2x3x
3s
1s
2s 1x2x3x
4s
No of sources = No of sensorNo of sources = No of sensor
No of sources gt No of sensorNo of sources gt No of sensor
Overdetermined mixingOverdetermined mixing
Determined mixingDetermined mixing
Underdetermined mixingUnderdetermined mixing
Difficult to se
parate
Difficult to se
parate
Easy to se
parate
Easy to se
parate
0510 AM 5
Approaches for BSS of Speech SignalsApproaches for BSS of Speech Signals
Types of mixing
Instantaneous mixing Convolutive mixing
0510 AM 6
Approaches for BSS of Speech SignalsApproaches for BSS of Speech Signals
Instantaneous mixing
Step 1 Selection of cost function
Step 2 Minimization or maximization of the cost function
0510 AM
WHS1
S2 X2
Y1
Y2
Separated
X1
7
Approaches for BSS of Speech SignalsApproaches for BSS of Speech SignalsInstantaneous mixingInstantaneous mixing
Selection of cost function
Statistical independence
Information theoretic
Non-Gaussianity
Kurtosis
Negentropy
Nonlinear cross moments
Temporal structure of speech
Non-stationarity of speech0510 AM
i
ii ypp y is idea Basic
Central limit theoremMixture of two or more sources will be more Gaussian than their individual components
224 E3E)( yyykurt
yyy HHJ gauss
yyyy dppH logEntropy
0 ji ygyfE
used becan statsticsorder Secondlags timedifferent for usly simultaneon correlatiooutput theedioganaliz eg
eddiagonalizusly simultaneo are matricesn correlatio the
and blocks into divided are Signals
Non Gaussianity measures
Signals from two different sources are independent
8
Approaches for BSS of Speech SignalsApproaches for BSS of Speech Signals
Instantaneous mixingMinimization or maximization of the cost function
simple gradient method
Natural gradient method
Newtonrsquos method
eg Informax ICA algorithm
eg FastICA
0510 AM 9
Approaches for BSS of Speech SignalsApproaches for BSS of Speech SignalsConvolutive Mixing
Time Domain Frequency Domain
QqltxlwyP
p
L
lpqpq 1)()(
1
1
0
)()()( tfftf SHX
)()()( tfftf XWY
AdvantageNo permutation problem
DisadvantageSlow convergence High computational cost for long filter taps
AdvantageLow computational costFast convergence
DisadvantagePermutation Problem
WHS1
S2
X1
X2
Y1 Y2
Y2 Y1
0510 AM 10
or
Permutation Problem in Frequency Domain BSS
Permutation Problem in Frequency Domain BSS
f1
f2
fk
x1x2
x3
BSS
BSS
BSSMixed signals
K po
int
FFT
y1y2y3
Still signals are mixed
K po
int
IFFT
Corresponding to different sources Due to permutation problem
One frequency binInstantaneous ICA algorithm
Solv
ing
perm
utati
on
Prob
lem y1
y2y3
Separated signals
Corresponding to y3
0510 AM 11
MotivationMotivation
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
12
My Contribution - IMy Contribution - I
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
13
Algorithm for Solving the Permutation Problem
Algorithm for Solving the Permutation Problem
f1
f2
fk
x1x2
x3
BSS
BSS
BSSMixed signals
K po
int
FFT
y1y2y3
Separated signals
K po
int
IFFT
Solv
ing
perm
utati
on
Prob
lem
Permutation problem
One frequency binInstantaneous ICA algorithm
Permutation problem solved
0510 AM 14
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Direction Of Arrival (DOA) method
2
1
)sin(2 1
p
dcfjkqpkq
pkefWfU Position of the pth sensor
Velocity of sound
)(
)(
)()(
)()(
)(
)(
2
1
2221
1211
2
1
k
k
kk
kk
k
k
fX
fX
fWfW
fWfW
fY
fY
0510 AM
Direction of y1 = -30o
Direction of y2 = 20o
15
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Reasons for failure at lower freq
Lower spacing causes error in phase difference measurement
The relation is approximated for plane wave front under anechoic condition
Disadvantages
Fails at lower frequenciesFails when sources are nearRoom reverberationSensor positions must be known
Direction Of Arrival (DOA) method
0510 AM 16
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
f1
f2
fk
BSS
BSS
BSSMixed signals
K po
int
FFT
y1y2y3
Separated signals
K po
int
IFFT
Solv
ing
perm
utati
on
Prob
lem
Low correlation
High correlationLow
correlation
x1x2
x3
Adjacent bands correlation method
0510 AM 17
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
r12
r21
r11
r22 r22 r22 r22
r11 r11 r11
r12
r21
r12
r21
r12
r21r11 r12
r21 r22
s1
s2
Correlation matrix
21122211 rrrr No change
21122211 rrrr Change permutation
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Adjacent bands correlation method
0510 AM
21122211 and and rrrr
21122211 and and rrrr
With confidence Without confidence
2090
8010
8020
1090
2090
1040
1040
2090
Example Example
18
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
r12
r21
r11
r22 r22 r22 r22
r11 r11 r11
r12
r21
r12
r21
r12
r21
r11 r12
r21 r22
s1
s2
Correlation matrix
Disadvantage The method is not robust
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Adjacent bands correlation method
0510 AM 19
0510 AM
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Combination of DOA and Correlation methods method
DOA + Harmonic Correlation + Adjacent bands correlation
Advantage Increased robustness
20
Proposed algorithm Partial separation method(Parallel configuration)
Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
Proposed algorithm Partial separation method(Parallel configuration)
Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
2y
1y
1x
2x
1s
2s
0510 AM 21
Time domain stage
Frequency domain stage
Partial separation method(Parallel configuration)
Partial separation method(Parallel configuration)
0510 AM 22
Time domain stage
Frequency domain stage
Parallel configuration
Partial separation method(Cascade configuration)
Partial separation method(Cascade configuration)
0510 AM 23
Time domain stage
Frequency domain stage
Advantages of Partial Separation methodAdvantages of Partial Separation method
bull Robustness
0510 AM 24
Comparison with Adjacent Bands Correlation Method
Comparison with Adjacent Bands Correlation Method
0510 AM 25
PS - Partial Separation method with confidence check C1 - Correlation between the adjacent bins without confidence check C2 - Correlation between adjacent bins with confidence check Ha - Correlation between the harmonic components with confidence check PS1 - Partial separation method alone without confidence check
0510 AM 26
Comparison with DOA methodComparison with DOA method
My Contribution -IIMy Contribution -II
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
27
Underdetermined Blind Source Separation of Instantaneous Mixtures
Underdetermined Blind Source Separation of Instantaneous Mixtures
t
k
0)(0)( 222221 tkStkS
0)(0)( 222221 tkStkS
0)(0)( 112111 tkStkS
0)(0)( 112111 tkStkS
tkX 1
tkX 22x
1x
0510 AM 28
Mathematical Representation of Instantaneous Mixing
Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
Mathematical Representation of Instantaneous Mixing
Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
)(
)(
)(
)( 1
1
1111
tkS
tkS
hh
hh
tkX
tkX
QPQP
Q
P
)(
)(
)(
)( 1
1
1111
ts
ts
hh
hh
tx
tx
QPQP
Q
P
)()()(11
1
1
11
tkS
h
h
tkS
h
h
tkS
h
h
Q
PQ
Q
q
Pq
q
P
)()()()( 21 tkStkStkStk QhhhX
Time domain
Time-Frequency domain
0510 AM 29
P ndash No of mixturesQ ndash No of sources
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
00point at 1 Case 11211111 tkStkStk
)()()( 1122111111 tkStkStk hhX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 2222221122 tkStkStk hhX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
0510 AM
0 0
30
Q
qqq tkStk
1
hX
2Let Q
00point at 1 Case 11211111 tkStkStk
)()( 111111 tkStk hX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()( 222222 tkStk hX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
0510 AM 31
00point at 1 Case 11211111 tkStkStk
)()( 111111 tkStk hX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()( 222222 tkStk hX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
Scalar
ScalarScalar
Scalar
At single source point 1 At single source point 2
111
111
ofDirection )( ofDirection
ofDirection )( ofDirection
hX
hX
tkI
tkR 222
222
ofDirection )( ofDirection
ofDirection )( ofDirection
hX
hX
tkI
tkR
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
0510 AM
1111 ( of Direction ( of Direction tkItkR XX 2222 ( of Direction ( of Direction tkItkR XX 32
Scatter Diagram of the Mixtures When Source are Perfectly Sparse
Scatter Diagram of the Mixtures When Source are Perfectly Sparse
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
22222
11111
2221
1211
22222
11111
kSkSkSkSkS
kSkSkSkSkS
hh
hh
kXkXkXkXkX
kXkXkXkXkX
21
111 h
hh
22
122 h
hh
0 00 0 0
Example
0510 AM 33
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
22222
11111
2221
1211
22222
11111
kSkSkSkSkS
kSkSkSkSkS
hh
hh
kXkXkXkXkX
kXkXkXkXkX
21
111 h
hh
22
122 h
hh
0 00 0 00
Example
Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
0510 AM 34
Scatter Diagram of the Mixtures when Sources are Sparse
Scatter Diagram of the Mixtures when Sources are Sparse
3h
6h
5h
1h4h
2h
0510 AM
No of sources = 6No of mixtures = 2
35
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
3h
6h
5h
1h4h
2h
0510 AM
No of sources = 6No of mixtures = 2
36
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
3h
6h
5h
1h4h
2h
0510 AM
ObjectiveEstimation of the single source points
No of sources = 6No of mixtures = 2
37
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Multi source point
38
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
Multi source point
39
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
Average of 15 pairs of speech utterances of length 10 s each
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
)( ofDirection )( ofDirection tkXItkXR )( ofDirection )( ofDirection tkXItkXR
SSPMSP
40
SSPt
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)()(
)()(
112112
111111
tkXjItkXR
tkXjItkXR
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXI
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXIMSP
)( 111 tkX
)( 112 tkX
cos
)()(
)()(
tkXItkXR
tkXItkXR T
Proposed Algorithm for the Detection of Single Source Points
Proposed Algorithm for the Detection of Single Source Points
0510 AM 41
Elimination of OutliersElimination of Outliers
SSPs detection
Clus
terin
g
Outlier elimination
0510 AM 42
0510 AM
Experimental ResultsExperimental Results
dB6747NMSE
No of mixtures =2 No of sources =6
43
Detected Single Source PointsThree mixtures
Detected Single Source PointsThree mixtures
No of mixtures =3 No of sources =60510 AM 44
Comparison with Classical Algorithms for Determined Case
Comparison with Classical Algorithms for Determined Case
No of mixtures =2No of sources =2
Average of 500 experimental results
0510 AM 45
-gt
Comparison with Method Proposed in [1] Underdetermined case
Comparison with Method Proposed in [1] Underdetermined case
[1] Y Li S Amari A Cichocki D W C Ho and S Xie ldquoUnderdetermined blind source separation based on sparse representationrdquo IEEE Transactions on Signal Processing vol 54 p 423ndash437 Feb 2006
0510 AM
Nor
mal
ized
mea
n sq
uare
err
or (N
MSE
) in
mix
ing
mat
rix e
stim
ation
(dB)
Order of the mixing matrices (PxQ)
46
P ndash No of mixturesQ ndash No of sources
Advantages of the Proposed algorithmAdvantages of the Proposed algorithm
Step 1 Convert x in the time domain to the TF domain to get XStep 2 Check the condition
Step 3 If the condition is satisfied then X(k t) is a sample atthe SSP and this sample is kept for mixing matrix estimationotherwise discard the point
Step 4 Repeat Steps 2 to 3 for all the points in the TF planeor until sufficient number of SSPs are obtained
cos
)()(
)()(
tkXItkXR
tkXItkXR T
1) Much simpler constrain the algorithm does not require ldquosingle source zonerdquo
3) The algorithm is extremely simple but effective2) Separation performance is better
0510 AM 47-gt
My Contributions ndash III IV and VMy Contributions ndash III IV and V
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
48
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Mask estimation
Mic 1
Mic P
Mixture in TF domain
Separated signals in TF domain
)( tkX P
)(1 tkX
t
t
k
k
)(1 tkY
)(1 tkY
)( tkYQ
)( tkYQ
QP
0510 AM 49
Mathematical RepresentationMathematical Representation
Q
q
L
lqpqp Pplnslhnx
1
1
0
1)()()(
)()()()()()()( 11 tkSktkSktkSktk QQqq HHHX
)(
)(
)()(
)()(
)(
)( 1
1
1111
tkS
tkS
kHkH
kHkH
tkX
tkX
QPQP
Q
P
)(
)(
)(
)(
)(
)(
)(
)(
)( 11
1
1
11
tkS
kH
kH
tkS
kH
kH
tkS
kH
kH
Q
PQ
Q
q
Pq
q
P
Time domain
Frequency domain
0510 AM 50
P ndash No of mixturesQ ndash No of sources
Single source pointsSingle source pointsInstantaneous mixing
00point at 1 Case 11211111 tkStkStk
)()()(
)()()(
111111
111111
tkSIktkI
tkSRktkR
HX
HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()(
)()()(
222222
222222
tkSIktkI
tkSRktkR
HX
HX
Single source point 2
Real scalar
RealReal
Real scalarReal scalar
Real scalar
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
0510 AM 51
Basic Principle of Single Source Points Detection
Basic Principle of Single Source Points Detection
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
j
H
C
e
cos21
21
UU
UUUUU H
and 20coscos HCH
angle pseudo called is
angleHermitian called is
H The Hermitian angle between the complex
vectors u1 and u2 will remain the same even if the vectors are multiplied by any complex scalars whereas the pseudo angle will change
0510 AM 52
-gt
k
Algorithm for Single Source Points Detection
Algorithm for Single Source Points Detection
t
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)(
)(
)(111
121
111 tkSkH
kH
11
11
j
jr
)(
)(
112
111
tkX
tkX
11
11
j
jr
)(
)(
112
111
tkX
tkX
)( 111 tkX
)( 112 tkX
)(
)(
)(112
122
112 tkSkH
kH θH2
θH1
θH2
rX
rX
)(
)(cos
11
111
tk
tk H
Hq
0510 AM 53
θH1
OR
1k
1k
1t
Clean
Estimated
Mask Estimation by k-means (KM)Mask Estimation by k-means (KM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 54
Clean
Estimated
Mask Estimation by Fuzzy c-means (FCM)Mask Estimation by Fuzzy c-means (FCM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 55
Automatic Detection of Number of SourcesAutomatic Detection of Number of Sources
0510 AM 56
Cluster validation technique
For c = 2 to cmax
Cluster the data into c clustersCalculate the cluster validation index
EndTake c corresponding to the best cluster as the number of sources
-gt
Elimination of Low Energy PointsElimination of Low Energy Points
0510 AM 57
- Blind Separation of Speech Mixtures
- Introduction
- Slide 3
- Slide 4
- Slide 5
- Approaches for BSS of Speech Signals
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Permutation Problem in Frequency Domain BSS
- Motivation
- My Contribution - I
- Algorithm for Solving the Permutation Problem
- Existing Method for Solving the Permutation Problem
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Proposed algorithm Partial separation method (Parallel configuration) Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
- Partial separation method (Parallel configuration)
- Partial separation method (Cascade configuration)
- Advantages of Partial Separation method
- Comparison with Adjacent Bands Correlation Method
- Comparison with DOA method
- My Contribution -II
- Underdetermined Blind Source Separation of Instantaneous Mixtures
- Mathematical Representation of Instantaneous Mixing Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
- Single Source Points in Time-Frequency domain
- Slide 31
- Slide 32
- Scatter Diagram of the Mixtures When Source are Perfectly Sparse
- Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
- Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
- Principle of the Proposed Algorithm for the Detection of Single Source Points
- Slide 39
- Slide 40
- Proposed Algorithm for the Detection of Single Source Points
- Elimination of Outliers
- Slide 43
- Detected Single Source Points Three mixtures
- Comparison with Classical Algorithms for Determined Case
- Comparison with Method Proposed in [1] Underdetermined case
- Advantages of the Proposed algorithm
- My Contributions ndash III IV and V
- Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
- Mathematical Representation
- Single source points
- Basic Principle of Single Source Points Detection
- Algorithm for Single Source Points Detection
- Mask Estimation by k-means (KM)
- Mask Estimation by Fuzzy c-means (FCM)
- Automatic Detection of Number of Sources
- Elimination of Low Energy Points
-
Introduction Introduction
Convolutive Blind Source Separation Convolutive Blind Source Separation Instantaneous Blind Source Separation Instantaneous Blind Source Separation
)(
)(
)(
)(
2
1
2221
1211
2
1
ts
ts
tx
tx
hh
hh
)()( tt SX H
)(
)(
)(
)(
2
1
2221
1211
2
1
ts
ts
hh
hh
tx
tx
)()( tt HSX
)(
)(
)()(
)()(
)(
)(
2
1
2221
1211
2
1
tfS
tfS
fHfH
fHfH
tfX
tfX
)()()( tfftf SX H
bull In frequency domain
Difficu
lt to
separa
te
Difficu
lt to
separa
te
Easy to
separa
te
Easy to
separa
te
0510 AM 4
Introduction Introduction
No of sources lt No of sensorNo of sources lt No of sensor1s
2s
3s
4s
1x2x3x
1s
2s1x2x3x
3s
1s
2s 1x2x3x
4s
No of sources = No of sensorNo of sources = No of sensor
No of sources gt No of sensorNo of sources gt No of sensor
Overdetermined mixingOverdetermined mixing
Determined mixingDetermined mixing
Underdetermined mixingUnderdetermined mixing
Difficult to se
parate
Difficult to se
parate
Easy to se
parate
Easy to se
parate
0510 AM 5
Approaches for BSS of Speech SignalsApproaches for BSS of Speech Signals
Types of mixing
Instantaneous mixing Convolutive mixing
0510 AM 6
Approaches for BSS of Speech SignalsApproaches for BSS of Speech Signals
Instantaneous mixing
Step 1 Selection of cost function
Step 2 Minimization or maximization of the cost function
0510 AM
WHS1
S2 X2
Y1
Y2
Separated
X1
7
Approaches for BSS of Speech SignalsApproaches for BSS of Speech SignalsInstantaneous mixingInstantaneous mixing
Selection of cost function
Statistical independence
Information theoretic
Non-Gaussianity
Kurtosis
Negentropy
Nonlinear cross moments
Temporal structure of speech
Non-stationarity of speech0510 AM
i
ii ypp y is idea Basic
Central limit theoremMixture of two or more sources will be more Gaussian than their individual components
224 E3E)( yyykurt
yyy HHJ gauss
yyyy dppH logEntropy
0 ji ygyfE
used becan statsticsorder Secondlags timedifferent for usly simultaneon correlatiooutput theedioganaliz eg
eddiagonalizusly simultaneo are matricesn correlatio the
and blocks into divided are Signals
Non Gaussianity measures
Signals from two different sources are independent
8
Approaches for BSS of Speech SignalsApproaches for BSS of Speech Signals
Instantaneous mixingMinimization or maximization of the cost function
simple gradient method
Natural gradient method
Newtonrsquos method
eg Informax ICA algorithm
eg FastICA
0510 AM 9
Approaches for BSS of Speech SignalsApproaches for BSS of Speech SignalsConvolutive Mixing
Time Domain Frequency Domain
QqltxlwyP
p
L
lpqpq 1)()(
1
1
0
)()()( tfftf SHX
)()()( tfftf XWY
AdvantageNo permutation problem
DisadvantageSlow convergence High computational cost for long filter taps
AdvantageLow computational costFast convergence
DisadvantagePermutation Problem
WHS1
S2
X1
X2
Y1 Y2
Y2 Y1
0510 AM 10
or
Permutation Problem in Frequency Domain BSS
Permutation Problem in Frequency Domain BSS
f1
f2
fk
x1x2
x3
BSS
BSS
BSSMixed signals
K po
int
FFT
y1y2y3
Still signals are mixed
K po
int
IFFT
Corresponding to different sources Due to permutation problem
One frequency binInstantaneous ICA algorithm
Solv
ing
perm
utati
on
Prob
lem y1
y2y3
Separated signals
Corresponding to y3
0510 AM 11
MotivationMotivation
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
12
My Contribution - IMy Contribution - I
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
13
Algorithm for Solving the Permutation Problem
Algorithm for Solving the Permutation Problem
f1
f2
fk
x1x2
x3
BSS
BSS
BSSMixed signals
K po
int
FFT
y1y2y3
Separated signals
K po
int
IFFT
Solv
ing
perm
utati
on
Prob
lem
Permutation problem
One frequency binInstantaneous ICA algorithm
Permutation problem solved
0510 AM 14
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Direction Of Arrival (DOA) method
2
1
)sin(2 1
p
dcfjkqpkq
pkefWfU Position of the pth sensor
Velocity of sound
)(
)(
)()(
)()(
)(
)(
2
1
2221
1211
2
1
k
k
kk
kk
k
k
fX
fX
fWfW
fWfW
fY
fY
0510 AM
Direction of y1 = -30o
Direction of y2 = 20o
15
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Reasons for failure at lower freq
Lower spacing causes error in phase difference measurement
The relation is approximated for plane wave front under anechoic condition
Disadvantages
Fails at lower frequenciesFails when sources are nearRoom reverberationSensor positions must be known
Direction Of Arrival (DOA) method
0510 AM 16
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
f1
f2
fk
BSS
BSS
BSSMixed signals
K po
int
FFT
y1y2y3
Separated signals
K po
int
IFFT
Solv
ing
perm
utati
on
Prob
lem
Low correlation
High correlationLow
correlation
x1x2
x3
Adjacent bands correlation method
0510 AM 17
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
r12
r21
r11
r22 r22 r22 r22
r11 r11 r11
r12
r21
r12
r21
r12
r21r11 r12
r21 r22
s1
s2
Correlation matrix
21122211 rrrr No change
21122211 rrrr Change permutation
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Adjacent bands correlation method
0510 AM
21122211 and and rrrr
21122211 and and rrrr
With confidence Without confidence
2090
8010
8020
1090
2090
1040
1040
2090
Example Example
18
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
r12
r21
r11
r22 r22 r22 r22
r11 r11 r11
r12
r21
r12
r21
r12
r21
r11 r12
r21 r22
s1
s2
Correlation matrix
Disadvantage The method is not robust
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Adjacent bands correlation method
0510 AM 19
0510 AM
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Combination of DOA and Correlation methods method
DOA + Harmonic Correlation + Adjacent bands correlation
Advantage Increased robustness
20
Proposed algorithm Partial separation method(Parallel configuration)
Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
Proposed algorithm Partial separation method(Parallel configuration)
Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
2y
1y
1x
2x
1s
2s
0510 AM 21
Time domain stage
Frequency domain stage
Partial separation method(Parallel configuration)
Partial separation method(Parallel configuration)
0510 AM 22
Time domain stage
Frequency domain stage
Parallel configuration
Partial separation method(Cascade configuration)
Partial separation method(Cascade configuration)
0510 AM 23
Time domain stage
Frequency domain stage
Advantages of Partial Separation methodAdvantages of Partial Separation method
bull Robustness
0510 AM 24
Comparison with Adjacent Bands Correlation Method
Comparison with Adjacent Bands Correlation Method
0510 AM 25
PS - Partial Separation method with confidence check C1 - Correlation between the adjacent bins without confidence check C2 - Correlation between adjacent bins with confidence check Ha - Correlation between the harmonic components with confidence check PS1 - Partial separation method alone without confidence check
0510 AM 26
Comparison with DOA methodComparison with DOA method
My Contribution -IIMy Contribution -II
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
27
Underdetermined Blind Source Separation of Instantaneous Mixtures
Underdetermined Blind Source Separation of Instantaneous Mixtures
t
k
0)(0)( 222221 tkStkS
0)(0)( 222221 tkStkS
0)(0)( 112111 tkStkS
0)(0)( 112111 tkStkS
tkX 1
tkX 22x
1x
0510 AM 28
Mathematical Representation of Instantaneous Mixing
Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
Mathematical Representation of Instantaneous Mixing
Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
)(
)(
)(
)( 1
1
1111
tkS
tkS
hh
hh
tkX
tkX
QPQP
Q
P
)(
)(
)(
)( 1
1
1111
ts
ts
hh
hh
tx
tx
QPQP
Q
P
)()()(11
1
1
11
tkS
h
h
tkS
h
h
tkS
h
h
Q
PQ
Q
q
Pq
q
P
)()()()( 21 tkStkStkStk QhhhX
Time domain
Time-Frequency domain
0510 AM 29
P ndash No of mixturesQ ndash No of sources
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
00point at 1 Case 11211111 tkStkStk
)()()( 1122111111 tkStkStk hhX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 2222221122 tkStkStk hhX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
0510 AM
0 0
30
Q
qqq tkStk
1
hX
2Let Q
00point at 1 Case 11211111 tkStkStk
)()( 111111 tkStk hX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()( 222222 tkStk hX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
0510 AM 31
00point at 1 Case 11211111 tkStkStk
)()( 111111 tkStk hX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()( 222222 tkStk hX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
Scalar
ScalarScalar
Scalar
At single source point 1 At single source point 2
111
111
ofDirection )( ofDirection
ofDirection )( ofDirection
hX
hX
tkI
tkR 222
222
ofDirection )( ofDirection
ofDirection )( ofDirection
hX
hX
tkI
tkR
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
0510 AM
1111 ( of Direction ( of Direction tkItkR XX 2222 ( of Direction ( of Direction tkItkR XX 32
Scatter Diagram of the Mixtures When Source are Perfectly Sparse
Scatter Diagram of the Mixtures When Source are Perfectly Sparse
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
22222
11111
2221
1211
22222
11111
kSkSkSkSkS
kSkSkSkSkS
hh
hh
kXkXkXkXkX
kXkXkXkXkX
21
111 h
hh
22
122 h
hh
0 00 0 0
Example
0510 AM 33
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
22222
11111
2221
1211
22222
11111
kSkSkSkSkS
kSkSkSkSkS
hh
hh
kXkXkXkXkX
kXkXkXkXkX
21
111 h
hh
22
122 h
hh
0 00 0 00
Example
Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
0510 AM 34
Scatter Diagram of the Mixtures when Sources are Sparse
Scatter Diagram of the Mixtures when Sources are Sparse
3h
6h
5h
1h4h
2h
0510 AM
No of sources = 6No of mixtures = 2
35
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
3h
6h
5h
1h4h
2h
0510 AM
No of sources = 6No of mixtures = 2
36
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
3h
6h
5h
1h4h
2h
0510 AM
ObjectiveEstimation of the single source points
No of sources = 6No of mixtures = 2
37
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Multi source point
38
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
Multi source point
39
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
Average of 15 pairs of speech utterances of length 10 s each
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
)( ofDirection )( ofDirection tkXItkXR )( ofDirection )( ofDirection tkXItkXR
SSPMSP
40
SSPt
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)()(
)()(
112112
111111
tkXjItkXR
tkXjItkXR
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXI
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXIMSP
)( 111 tkX
)( 112 tkX
cos
)()(
)()(
tkXItkXR
tkXItkXR T
Proposed Algorithm for the Detection of Single Source Points
Proposed Algorithm for the Detection of Single Source Points
0510 AM 41
Elimination of OutliersElimination of Outliers
SSPs detection
Clus
terin
g
Outlier elimination
0510 AM 42
0510 AM
Experimental ResultsExperimental Results
dB6747NMSE
No of mixtures =2 No of sources =6
43
Detected Single Source PointsThree mixtures
Detected Single Source PointsThree mixtures
No of mixtures =3 No of sources =60510 AM 44
Comparison with Classical Algorithms for Determined Case
Comparison with Classical Algorithms for Determined Case
No of mixtures =2No of sources =2
Average of 500 experimental results
0510 AM 45
-gt
Comparison with Method Proposed in [1] Underdetermined case
Comparison with Method Proposed in [1] Underdetermined case
[1] Y Li S Amari A Cichocki D W C Ho and S Xie ldquoUnderdetermined blind source separation based on sparse representationrdquo IEEE Transactions on Signal Processing vol 54 p 423ndash437 Feb 2006
0510 AM
Nor
mal
ized
mea
n sq
uare
err
or (N
MSE
) in
mix
ing
mat
rix e
stim
ation
(dB)
Order of the mixing matrices (PxQ)
46
P ndash No of mixturesQ ndash No of sources
Advantages of the Proposed algorithmAdvantages of the Proposed algorithm
Step 1 Convert x in the time domain to the TF domain to get XStep 2 Check the condition
Step 3 If the condition is satisfied then X(k t) is a sample atthe SSP and this sample is kept for mixing matrix estimationotherwise discard the point
Step 4 Repeat Steps 2 to 3 for all the points in the TF planeor until sufficient number of SSPs are obtained
cos
)()(
)()(
tkXItkXR
tkXItkXR T
1) Much simpler constrain the algorithm does not require ldquosingle source zonerdquo
3) The algorithm is extremely simple but effective2) Separation performance is better
0510 AM 47-gt
My Contributions ndash III IV and VMy Contributions ndash III IV and V
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
48
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Mask estimation
Mic 1
Mic P
Mixture in TF domain
Separated signals in TF domain
)( tkX P
)(1 tkX
t
t
k
k
)(1 tkY
)(1 tkY
)( tkYQ
)( tkYQ
QP
0510 AM 49
Mathematical RepresentationMathematical Representation
Q
q
L
lqpqp Pplnslhnx
1
1
0
1)()()(
)()()()()()()( 11 tkSktkSktkSktk QQqq HHHX
)(
)(
)()(
)()(
)(
)( 1
1
1111
tkS
tkS
kHkH
kHkH
tkX
tkX
QPQP
Q
P
)(
)(
)(
)(
)(
)(
)(
)(
)( 11
1
1
11
tkS
kH
kH
tkS
kH
kH
tkS
kH
kH
Q
PQ
Q
q
Pq
q
P
Time domain
Frequency domain
0510 AM 50
P ndash No of mixturesQ ndash No of sources
Single source pointsSingle source pointsInstantaneous mixing
00point at 1 Case 11211111 tkStkStk
)()()(
)()()(
111111
111111
tkSIktkI
tkSRktkR
HX
HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()(
)()()(
222222
222222
tkSIktkI
tkSRktkR
HX
HX
Single source point 2
Real scalar
RealReal
Real scalarReal scalar
Real scalar
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
0510 AM 51
Basic Principle of Single Source Points Detection
Basic Principle of Single Source Points Detection
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
j
H
C
e
cos21
21
UU
UUUUU H
and 20coscos HCH
angle pseudo called is
angleHermitian called is
H The Hermitian angle between the complex
vectors u1 and u2 will remain the same even if the vectors are multiplied by any complex scalars whereas the pseudo angle will change
0510 AM 52
-gt
k
Algorithm for Single Source Points Detection
Algorithm for Single Source Points Detection
t
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)(
)(
)(111
121
111 tkSkH
kH
11
11
j
jr
)(
)(
112
111
tkX
tkX
11
11
j
jr
)(
)(
112
111
tkX
tkX
)( 111 tkX
)( 112 tkX
)(
)(
)(112
122
112 tkSkH
kH θH2
θH1
θH2
rX
rX
)(
)(cos
11
111
tk
tk H
Hq
0510 AM 53
θH1
OR
1k
1k
1t
Clean
Estimated
Mask Estimation by k-means (KM)Mask Estimation by k-means (KM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 54
Clean
Estimated
Mask Estimation by Fuzzy c-means (FCM)Mask Estimation by Fuzzy c-means (FCM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 55
Automatic Detection of Number of SourcesAutomatic Detection of Number of Sources
0510 AM 56
Cluster validation technique
For c = 2 to cmax
Cluster the data into c clustersCalculate the cluster validation index
EndTake c corresponding to the best cluster as the number of sources
-gt
Elimination of Low Energy PointsElimination of Low Energy Points
0510 AM 57
- Blind Separation of Speech Mixtures
- Introduction
- Slide 3
- Slide 4
- Slide 5
- Approaches for BSS of Speech Signals
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Permutation Problem in Frequency Domain BSS
- Motivation
- My Contribution - I
- Algorithm for Solving the Permutation Problem
- Existing Method for Solving the Permutation Problem
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Proposed algorithm Partial separation method (Parallel configuration) Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
- Partial separation method (Parallel configuration)
- Partial separation method (Cascade configuration)
- Advantages of Partial Separation method
- Comparison with Adjacent Bands Correlation Method
- Comparison with DOA method
- My Contribution -II
- Underdetermined Blind Source Separation of Instantaneous Mixtures
- Mathematical Representation of Instantaneous Mixing Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
- Single Source Points in Time-Frequency domain
- Slide 31
- Slide 32
- Scatter Diagram of the Mixtures When Source are Perfectly Sparse
- Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
- Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
- Principle of the Proposed Algorithm for the Detection of Single Source Points
- Slide 39
- Slide 40
- Proposed Algorithm for the Detection of Single Source Points
- Elimination of Outliers
- Slide 43
- Detected Single Source Points Three mixtures
- Comparison with Classical Algorithms for Determined Case
- Comparison with Method Proposed in [1] Underdetermined case
- Advantages of the Proposed algorithm
- My Contributions ndash III IV and V
- Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
- Mathematical Representation
- Single source points
- Basic Principle of Single Source Points Detection
- Algorithm for Single Source Points Detection
- Mask Estimation by k-means (KM)
- Mask Estimation by Fuzzy c-means (FCM)
- Automatic Detection of Number of Sources
- Elimination of Low Energy Points
-
Introduction Introduction
No of sources lt No of sensorNo of sources lt No of sensor1s
2s
3s
4s
1x2x3x
1s
2s1x2x3x
3s
1s
2s 1x2x3x
4s
No of sources = No of sensorNo of sources = No of sensor
No of sources gt No of sensorNo of sources gt No of sensor
Overdetermined mixingOverdetermined mixing
Determined mixingDetermined mixing
Underdetermined mixingUnderdetermined mixing
Difficult to se
parate
Difficult to se
parate
Easy to se
parate
Easy to se
parate
0510 AM 5
Approaches for BSS of Speech SignalsApproaches for BSS of Speech Signals
Types of mixing
Instantaneous mixing Convolutive mixing
0510 AM 6
Approaches for BSS of Speech SignalsApproaches for BSS of Speech Signals
Instantaneous mixing
Step 1 Selection of cost function
Step 2 Minimization or maximization of the cost function
0510 AM
WHS1
S2 X2
Y1
Y2
Separated
X1
7
Approaches for BSS of Speech SignalsApproaches for BSS of Speech SignalsInstantaneous mixingInstantaneous mixing
Selection of cost function
Statistical independence
Information theoretic
Non-Gaussianity
Kurtosis
Negentropy
Nonlinear cross moments
Temporal structure of speech
Non-stationarity of speech0510 AM
i
ii ypp y is idea Basic
Central limit theoremMixture of two or more sources will be more Gaussian than their individual components
224 E3E)( yyykurt
yyy HHJ gauss
yyyy dppH logEntropy
0 ji ygyfE
used becan statsticsorder Secondlags timedifferent for usly simultaneon correlatiooutput theedioganaliz eg
eddiagonalizusly simultaneo are matricesn correlatio the
and blocks into divided are Signals
Non Gaussianity measures
Signals from two different sources are independent
8
Approaches for BSS of Speech SignalsApproaches for BSS of Speech Signals
Instantaneous mixingMinimization or maximization of the cost function
simple gradient method
Natural gradient method
Newtonrsquos method
eg Informax ICA algorithm
eg FastICA
0510 AM 9
Approaches for BSS of Speech SignalsApproaches for BSS of Speech SignalsConvolutive Mixing
Time Domain Frequency Domain
QqltxlwyP
p
L
lpqpq 1)()(
1
1
0
)()()( tfftf SHX
)()()( tfftf XWY
AdvantageNo permutation problem
DisadvantageSlow convergence High computational cost for long filter taps
AdvantageLow computational costFast convergence
DisadvantagePermutation Problem
WHS1
S2
X1
X2
Y1 Y2
Y2 Y1
0510 AM 10
or
Permutation Problem in Frequency Domain BSS
Permutation Problem in Frequency Domain BSS
f1
f2
fk
x1x2
x3
BSS
BSS
BSSMixed signals
K po
int
FFT
y1y2y3
Still signals are mixed
K po
int
IFFT
Corresponding to different sources Due to permutation problem
One frequency binInstantaneous ICA algorithm
Solv
ing
perm
utati
on
Prob
lem y1
y2y3
Separated signals
Corresponding to y3
0510 AM 11
MotivationMotivation
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
12
My Contribution - IMy Contribution - I
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
13
Algorithm for Solving the Permutation Problem
Algorithm for Solving the Permutation Problem
f1
f2
fk
x1x2
x3
BSS
BSS
BSSMixed signals
K po
int
FFT
y1y2y3
Separated signals
K po
int
IFFT
Solv
ing
perm
utati
on
Prob
lem
Permutation problem
One frequency binInstantaneous ICA algorithm
Permutation problem solved
0510 AM 14
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Direction Of Arrival (DOA) method
2
1
)sin(2 1
p
dcfjkqpkq
pkefWfU Position of the pth sensor
Velocity of sound
)(
)(
)()(
)()(
)(
)(
2
1
2221
1211
2
1
k
k
kk
kk
k
k
fX
fX
fWfW
fWfW
fY
fY
0510 AM
Direction of y1 = -30o
Direction of y2 = 20o
15
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Reasons for failure at lower freq
Lower spacing causes error in phase difference measurement
The relation is approximated for plane wave front under anechoic condition
Disadvantages
Fails at lower frequenciesFails when sources are nearRoom reverberationSensor positions must be known
Direction Of Arrival (DOA) method
0510 AM 16
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
f1
f2
fk
BSS
BSS
BSSMixed signals
K po
int
FFT
y1y2y3
Separated signals
K po
int
IFFT
Solv
ing
perm
utati
on
Prob
lem
Low correlation
High correlationLow
correlation
x1x2
x3
Adjacent bands correlation method
0510 AM 17
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
r12
r21
r11
r22 r22 r22 r22
r11 r11 r11
r12
r21
r12
r21
r12
r21r11 r12
r21 r22
s1
s2
Correlation matrix
21122211 rrrr No change
21122211 rrrr Change permutation
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Adjacent bands correlation method
0510 AM
21122211 and and rrrr
21122211 and and rrrr
With confidence Without confidence
2090
8010
8020
1090
2090
1040
1040
2090
Example Example
18
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
r12
r21
r11
r22 r22 r22 r22
r11 r11 r11
r12
r21
r12
r21
r12
r21
r11 r12
r21 r22
s1
s2
Correlation matrix
Disadvantage The method is not robust
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Adjacent bands correlation method
0510 AM 19
0510 AM
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Combination of DOA and Correlation methods method
DOA + Harmonic Correlation + Adjacent bands correlation
Advantage Increased robustness
20
Proposed algorithm Partial separation method(Parallel configuration)
Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
Proposed algorithm Partial separation method(Parallel configuration)
Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
2y
1y
1x
2x
1s
2s
0510 AM 21
Time domain stage
Frequency domain stage
Partial separation method(Parallel configuration)
Partial separation method(Parallel configuration)
0510 AM 22
Time domain stage
Frequency domain stage
Parallel configuration
Partial separation method(Cascade configuration)
Partial separation method(Cascade configuration)
0510 AM 23
Time domain stage
Frequency domain stage
Advantages of Partial Separation methodAdvantages of Partial Separation method
bull Robustness
0510 AM 24
Comparison with Adjacent Bands Correlation Method
Comparison with Adjacent Bands Correlation Method
0510 AM 25
PS - Partial Separation method with confidence check C1 - Correlation between the adjacent bins without confidence check C2 - Correlation between adjacent bins with confidence check Ha - Correlation between the harmonic components with confidence check PS1 - Partial separation method alone without confidence check
0510 AM 26
Comparison with DOA methodComparison with DOA method
My Contribution -IIMy Contribution -II
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
27
Underdetermined Blind Source Separation of Instantaneous Mixtures
Underdetermined Blind Source Separation of Instantaneous Mixtures
t
k
0)(0)( 222221 tkStkS
0)(0)( 222221 tkStkS
0)(0)( 112111 tkStkS
0)(0)( 112111 tkStkS
tkX 1
tkX 22x
1x
0510 AM 28
Mathematical Representation of Instantaneous Mixing
Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
Mathematical Representation of Instantaneous Mixing
Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
)(
)(
)(
)( 1
1
1111
tkS
tkS
hh
hh
tkX
tkX
QPQP
Q
P
)(
)(
)(
)( 1
1
1111
ts
ts
hh
hh
tx
tx
QPQP
Q
P
)()()(11
1
1
11
tkS
h
h
tkS
h
h
tkS
h
h
Q
PQ
Q
q
Pq
q
P
)()()()( 21 tkStkStkStk QhhhX
Time domain
Time-Frequency domain
0510 AM 29
P ndash No of mixturesQ ndash No of sources
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
00point at 1 Case 11211111 tkStkStk
)()()( 1122111111 tkStkStk hhX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 2222221122 tkStkStk hhX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
0510 AM
0 0
30
Q
qqq tkStk
1
hX
2Let Q
00point at 1 Case 11211111 tkStkStk
)()( 111111 tkStk hX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()( 222222 tkStk hX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
0510 AM 31
00point at 1 Case 11211111 tkStkStk
)()( 111111 tkStk hX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()( 222222 tkStk hX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
Scalar
ScalarScalar
Scalar
At single source point 1 At single source point 2
111
111
ofDirection )( ofDirection
ofDirection )( ofDirection
hX
hX
tkI
tkR 222
222
ofDirection )( ofDirection
ofDirection )( ofDirection
hX
hX
tkI
tkR
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
0510 AM
1111 ( of Direction ( of Direction tkItkR XX 2222 ( of Direction ( of Direction tkItkR XX 32
Scatter Diagram of the Mixtures When Source are Perfectly Sparse
Scatter Diagram of the Mixtures When Source are Perfectly Sparse
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
22222
11111
2221
1211
22222
11111
kSkSkSkSkS
kSkSkSkSkS
hh
hh
kXkXkXkXkX
kXkXkXkXkX
21
111 h
hh
22
122 h
hh
0 00 0 0
Example
0510 AM 33
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
22222
11111
2221
1211
22222
11111
kSkSkSkSkS
kSkSkSkSkS
hh
hh
kXkXkXkXkX
kXkXkXkXkX
21
111 h
hh
22
122 h
hh
0 00 0 00
Example
Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
0510 AM 34
Scatter Diagram of the Mixtures when Sources are Sparse
Scatter Diagram of the Mixtures when Sources are Sparse
3h
6h
5h
1h4h
2h
0510 AM
No of sources = 6No of mixtures = 2
35
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
3h
6h
5h
1h4h
2h
0510 AM
No of sources = 6No of mixtures = 2
36
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
3h
6h
5h
1h4h
2h
0510 AM
ObjectiveEstimation of the single source points
No of sources = 6No of mixtures = 2
37
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Multi source point
38
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
Multi source point
39
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
Average of 15 pairs of speech utterances of length 10 s each
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
)( ofDirection )( ofDirection tkXItkXR )( ofDirection )( ofDirection tkXItkXR
SSPMSP
40
SSPt
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)()(
)()(
112112
111111
tkXjItkXR
tkXjItkXR
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXI
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXIMSP
)( 111 tkX
)( 112 tkX
cos
)()(
)()(
tkXItkXR
tkXItkXR T
Proposed Algorithm for the Detection of Single Source Points
Proposed Algorithm for the Detection of Single Source Points
0510 AM 41
Elimination of OutliersElimination of Outliers
SSPs detection
Clus
terin
g
Outlier elimination
0510 AM 42
0510 AM
Experimental ResultsExperimental Results
dB6747NMSE
No of mixtures =2 No of sources =6
43
Detected Single Source PointsThree mixtures
Detected Single Source PointsThree mixtures
No of mixtures =3 No of sources =60510 AM 44
Comparison with Classical Algorithms for Determined Case
Comparison with Classical Algorithms for Determined Case
No of mixtures =2No of sources =2
Average of 500 experimental results
0510 AM 45
-gt
Comparison with Method Proposed in [1] Underdetermined case
Comparison with Method Proposed in [1] Underdetermined case
[1] Y Li S Amari A Cichocki D W C Ho and S Xie ldquoUnderdetermined blind source separation based on sparse representationrdquo IEEE Transactions on Signal Processing vol 54 p 423ndash437 Feb 2006
0510 AM
Nor
mal
ized
mea
n sq
uare
err
or (N
MSE
) in
mix
ing
mat
rix e
stim
ation
(dB)
Order of the mixing matrices (PxQ)
46
P ndash No of mixturesQ ndash No of sources
Advantages of the Proposed algorithmAdvantages of the Proposed algorithm
Step 1 Convert x in the time domain to the TF domain to get XStep 2 Check the condition
Step 3 If the condition is satisfied then X(k t) is a sample atthe SSP and this sample is kept for mixing matrix estimationotherwise discard the point
Step 4 Repeat Steps 2 to 3 for all the points in the TF planeor until sufficient number of SSPs are obtained
cos
)()(
)()(
tkXItkXR
tkXItkXR T
1) Much simpler constrain the algorithm does not require ldquosingle source zonerdquo
3) The algorithm is extremely simple but effective2) Separation performance is better
0510 AM 47-gt
My Contributions ndash III IV and VMy Contributions ndash III IV and V
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
48
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Mask estimation
Mic 1
Mic P
Mixture in TF domain
Separated signals in TF domain
)( tkX P
)(1 tkX
t
t
k
k
)(1 tkY
)(1 tkY
)( tkYQ
)( tkYQ
QP
0510 AM 49
Mathematical RepresentationMathematical Representation
Q
q
L
lqpqp Pplnslhnx
1
1
0
1)()()(
)()()()()()()( 11 tkSktkSktkSktk QQqq HHHX
)(
)(
)()(
)()(
)(
)( 1
1
1111
tkS
tkS
kHkH
kHkH
tkX
tkX
QPQP
Q
P
)(
)(
)(
)(
)(
)(
)(
)(
)( 11
1
1
11
tkS
kH
kH
tkS
kH
kH
tkS
kH
kH
Q
PQ
Q
q
Pq
q
P
Time domain
Frequency domain
0510 AM 50
P ndash No of mixturesQ ndash No of sources
Single source pointsSingle source pointsInstantaneous mixing
00point at 1 Case 11211111 tkStkStk
)()()(
)()()(
111111
111111
tkSIktkI
tkSRktkR
HX
HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()(
)()()(
222222
222222
tkSIktkI
tkSRktkR
HX
HX
Single source point 2
Real scalar
RealReal
Real scalarReal scalar
Real scalar
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
0510 AM 51
Basic Principle of Single Source Points Detection
Basic Principle of Single Source Points Detection
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
j
H
C
e
cos21
21
UU
UUUUU H
and 20coscos HCH
angle pseudo called is
angleHermitian called is
H The Hermitian angle between the complex
vectors u1 and u2 will remain the same even if the vectors are multiplied by any complex scalars whereas the pseudo angle will change
0510 AM 52
-gt
k
Algorithm for Single Source Points Detection
Algorithm for Single Source Points Detection
t
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)(
)(
)(111
121
111 tkSkH
kH
11
11
j
jr
)(
)(
112
111
tkX
tkX
11
11
j
jr
)(
)(
112
111
tkX
tkX
)( 111 tkX
)( 112 tkX
)(
)(
)(112
122
112 tkSkH
kH θH2
θH1
θH2
rX
rX
)(
)(cos
11
111
tk
tk H
Hq
0510 AM 53
θH1
OR
1k
1k
1t
Clean
Estimated
Mask Estimation by k-means (KM)Mask Estimation by k-means (KM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 54
Clean
Estimated
Mask Estimation by Fuzzy c-means (FCM)Mask Estimation by Fuzzy c-means (FCM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 55
Automatic Detection of Number of SourcesAutomatic Detection of Number of Sources
0510 AM 56
Cluster validation technique
For c = 2 to cmax
Cluster the data into c clustersCalculate the cluster validation index
EndTake c corresponding to the best cluster as the number of sources
-gt
Elimination of Low Energy PointsElimination of Low Energy Points
0510 AM 57
- Blind Separation of Speech Mixtures
- Introduction
- Slide 3
- Slide 4
- Slide 5
- Approaches for BSS of Speech Signals
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Permutation Problem in Frequency Domain BSS
- Motivation
- My Contribution - I
- Algorithm for Solving the Permutation Problem
- Existing Method for Solving the Permutation Problem
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Proposed algorithm Partial separation method (Parallel configuration) Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
- Partial separation method (Parallel configuration)
- Partial separation method (Cascade configuration)
- Advantages of Partial Separation method
- Comparison with Adjacent Bands Correlation Method
- Comparison with DOA method
- My Contribution -II
- Underdetermined Blind Source Separation of Instantaneous Mixtures
- Mathematical Representation of Instantaneous Mixing Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
- Single Source Points in Time-Frequency domain
- Slide 31
- Slide 32
- Scatter Diagram of the Mixtures When Source are Perfectly Sparse
- Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
- Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
- Principle of the Proposed Algorithm for the Detection of Single Source Points
- Slide 39
- Slide 40
- Proposed Algorithm for the Detection of Single Source Points
- Elimination of Outliers
- Slide 43
- Detected Single Source Points Three mixtures
- Comparison with Classical Algorithms for Determined Case
- Comparison with Method Proposed in [1] Underdetermined case
- Advantages of the Proposed algorithm
- My Contributions ndash III IV and V
- Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
- Mathematical Representation
- Single source points
- Basic Principle of Single Source Points Detection
- Algorithm for Single Source Points Detection
- Mask Estimation by k-means (KM)
- Mask Estimation by Fuzzy c-means (FCM)
- Automatic Detection of Number of Sources
- Elimination of Low Energy Points
-
Approaches for BSS of Speech SignalsApproaches for BSS of Speech Signals
Types of mixing
Instantaneous mixing Convolutive mixing
0510 AM 6
Approaches for BSS of Speech SignalsApproaches for BSS of Speech Signals
Instantaneous mixing
Step 1 Selection of cost function
Step 2 Minimization or maximization of the cost function
0510 AM
WHS1
S2 X2
Y1
Y2
Separated
X1
7
Approaches for BSS of Speech SignalsApproaches for BSS of Speech SignalsInstantaneous mixingInstantaneous mixing
Selection of cost function
Statistical independence
Information theoretic
Non-Gaussianity
Kurtosis
Negentropy
Nonlinear cross moments
Temporal structure of speech
Non-stationarity of speech0510 AM
i
ii ypp y is idea Basic
Central limit theoremMixture of two or more sources will be more Gaussian than their individual components
224 E3E)( yyykurt
yyy HHJ gauss
yyyy dppH logEntropy
0 ji ygyfE
used becan statsticsorder Secondlags timedifferent for usly simultaneon correlatiooutput theedioganaliz eg
eddiagonalizusly simultaneo are matricesn correlatio the
and blocks into divided are Signals
Non Gaussianity measures
Signals from two different sources are independent
8
Approaches for BSS of Speech SignalsApproaches for BSS of Speech Signals
Instantaneous mixingMinimization or maximization of the cost function
simple gradient method
Natural gradient method
Newtonrsquos method
eg Informax ICA algorithm
eg FastICA
0510 AM 9
Approaches for BSS of Speech SignalsApproaches for BSS of Speech SignalsConvolutive Mixing
Time Domain Frequency Domain
QqltxlwyP
p
L
lpqpq 1)()(
1
1
0
)()()( tfftf SHX
)()()( tfftf XWY
AdvantageNo permutation problem
DisadvantageSlow convergence High computational cost for long filter taps
AdvantageLow computational costFast convergence
DisadvantagePermutation Problem
WHS1
S2
X1
X2
Y1 Y2
Y2 Y1
0510 AM 10
or
Permutation Problem in Frequency Domain BSS
Permutation Problem in Frequency Domain BSS
f1
f2
fk
x1x2
x3
BSS
BSS
BSSMixed signals
K po
int
FFT
y1y2y3
Still signals are mixed
K po
int
IFFT
Corresponding to different sources Due to permutation problem
One frequency binInstantaneous ICA algorithm
Solv
ing
perm
utati
on
Prob
lem y1
y2y3
Separated signals
Corresponding to y3
0510 AM 11
MotivationMotivation
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
12
My Contribution - IMy Contribution - I
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
13
Algorithm for Solving the Permutation Problem
Algorithm for Solving the Permutation Problem
f1
f2
fk
x1x2
x3
BSS
BSS
BSSMixed signals
K po
int
FFT
y1y2y3
Separated signals
K po
int
IFFT
Solv
ing
perm
utati
on
Prob
lem
Permutation problem
One frequency binInstantaneous ICA algorithm
Permutation problem solved
0510 AM 14
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Direction Of Arrival (DOA) method
2
1
)sin(2 1
p
dcfjkqpkq
pkefWfU Position of the pth sensor
Velocity of sound
)(
)(
)()(
)()(
)(
)(
2
1
2221
1211
2
1
k
k
kk
kk
k
k
fX
fX
fWfW
fWfW
fY
fY
0510 AM
Direction of y1 = -30o
Direction of y2 = 20o
15
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Reasons for failure at lower freq
Lower spacing causes error in phase difference measurement
The relation is approximated for plane wave front under anechoic condition
Disadvantages
Fails at lower frequenciesFails when sources are nearRoom reverberationSensor positions must be known
Direction Of Arrival (DOA) method
0510 AM 16
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
f1
f2
fk
BSS
BSS
BSSMixed signals
K po
int
FFT
y1y2y3
Separated signals
K po
int
IFFT
Solv
ing
perm
utati
on
Prob
lem
Low correlation
High correlationLow
correlation
x1x2
x3
Adjacent bands correlation method
0510 AM 17
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
r12
r21
r11
r22 r22 r22 r22
r11 r11 r11
r12
r21
r12
r21
r12
r21r11 r12
r21 r22
s1
s2
Correlation matrix
21122211 rrrr No change
21122211 rrrr Change permutation
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Adjacent bands correlation method
0510 AM
21122211 and and rrrr
21122211 and and rrrr
With confidence Without confidence
2090
8010
8020
1090
2090
1040
1040
2090
Example Example
18
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
r12
r21
r11
r22 r22 r22 r22
r11 r11 r11
r12
r21
r12
r21
r12
r21
r11 r12
r21 r22
s1
s2
Correlation matrix
Disadvantage The method is not robust
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Adjacent bands correlation method
0510 AM 19
0510 AM
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Combination of DOA and Correlation methods method
DOA + Harmonic Correlation + Adjacent bands correlation
Advantage Increased robustness
20
Proposed algorithm Partial separation method(Parallel configuration)
Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
Proposed algorithm Partial separation method(Parallel configuration)
Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
2y
1y
1x
2x
1s
2s
0510 AM 21
Time domain stage
Frequency domain stage
Partial separation method(Parallel configuration)
Partial separation method(Parallel configuration)
0510 AM 22
Time domain stage
Frequency domain stage
Parallel configuration
Partial separation method(Cascade configuration)
Partial separation method(Cascade configuration)
0510 AM 23
Time domain stage
Frequency domain stage
Advantages of Partial Separation methodAdvantages of Partial Separation method
bull Robustness
0510 AM 24
Comparison with Adjacent Bands Correlation Method
Comparison with Adjacent Bands Correlation Method
0510 AM 25
PS - Partial Separation method with confidence check C1 - Correlation between the adjacent bins without confidence check C2 - Correlation between adjacent bins with confidence check Ha - Correlation between the harmonic components with confidence check PS1 - Partial separation method alone without confidence check
0510 AM 26
Comparison with DOA methodComparison with DOA method
My Contribution -IIMy Contribution -II
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
27
Underdetermined Blind Source Separation of Instantaneous Mixtures
Underdetermined Blind Source Separation of Instantaneous Mixtures
t
k
0)(0)( 222221 tkStkS
0)(0)( 222221 tkStkS
0)(0)( 112111 tkStkS
0)(0)( 112111 tkStkS
tkX 1
tkX 22x
1x
0510 AM 28
Mathematical Representation of Instantaneous Mixing
Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
Mathematical Representation of Instantaneous Mixing
Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
)(
)(
)(
)( 1
1
1111
tkS
tkS
hh
hh
tkX
tkX
QPQP
Q
P
)(
)(
)(
)( 1
1
1111
ts
ts
hh
hh
tx
tx
QPQP
Q
P
)()()(11
1
1
11
tkS
h
h
tkS
h
h
tkS
h
h
Q
PQ
Q
q
Pq
q
P
)()()()( 21 tkStkStkStk QhhhX
Time domain
Time-Frequency domain
0510 AM 29
P ndash No of mixturesQ ndash No of sources
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
00point at 1 Case 11211111 tkStkStk
)()()( 1122111111 tkStkStk hhX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 2222221122 tkStkStk hhX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
0510 AM
0 0
30
Q
qqq tkStk
1
hX
2Let Q
00point at 1 Case 11211111 tkStkStk
)()( 111111 tkStk hX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()( 222222 tkStk hX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
0510 AM 31
00point at 1 Case 11211111 tkStkStk
)()( 111111 tkStk hX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()( 222222 tkStk hX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
Scalar
ScalarScalar
Scalar
At single source point 1 At single source point 2
111
111
ofDirection )( ofDirection
ofDirection )( ofDirection
hX
hX
tkI
tkR 222
222
ofDirection )( ofDirection
ofDirection )( ofDirection
hX
hX
tkI
tkR
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
0510 AM
1111 ( of Direction ( of Direction tkItkR XX 2222 ( of Direction ( of Direction tkItkR XX 32
Scatter Diagram of the Mixtures When Source are Perfectly Sparse
Scatter Diagram of the Mixtures When Source are Perfectly Sparse
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
22222
11111
2221
1211
22222
11111
kSkSkSkSkS
kSkSkSkSkS
hh
hh
kXkXkXkXkX
kXkXkXkXkX
21
111 h
hh
22
122 h
hh
0 00 0 0
Example
0510 AM 33
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
22222
11111
2221
1211
22222
11111
kSkSkSkSkS
kSkSkSkSkS
hh
hh
kXkXkXkXkX
kXkXkXkXkX
21
111 h
hh
22
122 h
hh
0 00 0 00
Example
Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
0510 AM 34
Scatter Diagram of the Mixtures when Sources are Sparse
Scatter Diagram of the Mixtures when Sources are Sparse
3h
6h
5h
1h4h
2h
0510 AM
No of sources = 6No of mixtures = 2
35
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
3h
6h
5h
1h4h
2h
0510 AM
No of sources = 6No of mixtures = 2
36
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
3h
6h
5h
1h4h
2h
0510 AM
ObjectiveEstimation of the single source points
No of sources = 6No of mixtures = 2
37
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Multi source point
38
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
Multi source point
39
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
Average of 15 pairs of speech utterances of length 10 s each
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
)( ofDirection )( ofDirection tkXItkXR )( ofDirection )( ofDirection tkXItkXR
SSPMSP
40
SSPt
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)()(
)()(
112112
111111
tkXjItkXR
tkXjItkXR
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXI
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXIMSP
)( 111 tkX
)( 112 tkX
cos
)()(
)()(
tkXItkXR
tkXItkXR T
Proposed Algorithm for the Detection of Single Source Points
Proposed Algorithm for the Detection of Single Source Points
0510 AM 41
Elimination of OutliersElimination of Outliers
SSPs detection
Clus
terin
g
Outlier elimination
0510 AM 42
0510 AM
Experimental ResultsExperimental Results
dB6747NMSE
No of mixtures =2 No of sources =6
43
Detected Single Source PointsThree mixtures
Detected Single Source PointsThree mixtures
No of mixtures =3 No of sources =60510 AM 44
Comparison with Classical Algorithms for Determined Case
Comparison with Classical Algorithms for Determined Case
No of mixtures =2No of sources =2
Average of 500 experimental results
0510 AM 45
-gt
Comparison with Method Proposed in [1] Underdetermined case
Comparison with Method Proposed in [1] Underdetermined case
[1] Y Li S Amari A Cichocki D W C Ho and S Xie ldquoUnderdetermined blind source separation based on sparse representationrdquo IEEE Transactions on Signal Processing vol 54 p 423ndash437 Feb 2006
0510 AM
Nor
mal
ized
mea
n sq
uare
err
or (N
MSE
) in
mix
ing
mat
rix e
stim
ation
(dB)
Order of the mixing matrices (PxQ)
46
P ndash No of mixturesQ ndash No of sources
Advantages of the Proposed algorithmAdvantages of the Proposed algorithm
Step 1 Convert x in the time domain to the TF domain to get XStep 2 Check the condition
Step 3 If the condition is satisfied then X(k t) is a sample atthe SSP and this sample is kept for mixing matrix estimationotherwise discard the point
Step 4 Repeat Steps 2 to 3 for all the points in the TF planeor until sufficient number of SSPs are obtained
cos
)()(
)()(
tkXItkXR
tkXItkXR T
1) Much simpler constrain the algorithm does not require ldquosingle source zonerdquo
3) The algorithm is extremely simple but effective2) Separation performance is better
0510 AM 47-gt
My Contributions ndash III IV and VMy Contributions ndash III IV and V
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
48
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Mask estimation
Mic 1
Mic P
Mixture in TF domain
Separated signals in TF domain
)( tkX P
)(1 tkX
t
t
k
k
)(1 tkY
)(1 tkY
)( tkYQ
)( tkYQ
QP
0510 AM 49
Mathematical RepresentationMathematical Representation
Q
q
L
lqpqp Pplnslhnx
1
1
0
1)()()(
)()()()()()()( 11 tkSktkSktkSktk QQqq HHHX
)(
)(
)()(
)()(
)(
)( 1
1
1111
tkS
tkS
kHkH
kHkH
tkX
tkX
QPQP
Q
P
)(
)(
)(
)(
)(
)(
)(
)(
)( 11
1
1
11
tkS
kH
kH
tkS
kH
kH
tkS
kH
kH
Q
PQ
Q
q
Pq
q
P
Time domain
Frequency domain
0510 AM 50
P ndash No of mixturesQ ndash No of sources
Single source pointsSingle source pointsInstantaneous mixing
00point at 1 Case 11211111 tkStkStk
)()()(
)()()(
111111
111111
tkSIktkI
tkSRktkR
HX
HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()(
)()()(
222222
222222
tkSIktkI
tkSRktkR
HX
HX
Single source point 2
Real scalar
RealReal
Real scalarReal scalar
Real scalar
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
0510 AM 51
Basic Principle of Single Source Points Detection
Basic Principle of Single Source Points Detection
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
j
H
C
e
cos21
21
UU
UUUUU H
and 20coscos HCH
angle pseudo called is
angleHermitian called is
H The Hermitian angle between the complex
vectors u1 and u2 will remain the same even if the vectors are multiplied by any complex scalars whereas the pseudo angle will change
0510 AM 52
-gt
k
Algorithm for Single Source Points Detection
Algorithm for Single Source Points Detection
t
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)(
)(
)(111
121
111 tkSkH
kH
11
11
j
jr
)(
)(
112
111
tkX
tkX
11
11
j
jr
)(
)(
112
111
tkX
tkX
)( 111 tkX
)( 112 tkX
)(
)(
)(112
122
112 tkSkH
kH θH2
θH1
θH2
rX
rX
)(
)(cos
11
111
tk
tk H
Hq
0510 AM 53
θH1
OR
1k
1k
1t
Clean
Estimated
Mask Estimation by k-means (KM)Mask Estimation by k-means (KM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 54
Clean
Estimated
Mask Estimation by Fuzzy c-means (FCM)Mask Estimation by Fuzzy c-means (FCM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 55
Automatic Detection of Number of SourcesAutomatic Detection of Number of Sources
0510 AM 56
Cluster validation technique
For c = 2 to cmax
Cluster the data into c clustersCalculate the cluster validation index
EndTake c corresponding to the best cluster as the number of sources
-gt
Elimination of Low Energy PointsElimination of Low Energy Points
0510 AM 57
- Blind Separation of Speech Mixtures
- Introduction
- Slide 3
- Slide 4
- Slide 5
- Approaches for BSS of Speech Signals
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Permutation Problem in Frequency Domain BSS
- Motivation
- My Contribution - I
- Algorithm for Solving the Permutation Problem
- Existing Method for Solving the Permutation Problem
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Proposed algorithm Partial separation method (Parallel configuration) Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
- Partial separation method (Parallel configuration)
- Partial separation method (Cascade configuration)
- Advantages of Partial Separation method
- Comparison with Adjacent Bands Correlation Method
- Comparison with DOA method
- My Contribution -II
- Underdetermined Blind Source Separation of Instantaneous Mixtures
- Mathematical Representation of Instantaneous Mixing Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
- Single Source Points in Time-Frequency domain
- Slide 31
- Slide 32
- Scatter Diagram of the Mixtures When Source are Perfectly Sparse
- Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
- Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
- Principle of the Proposed Algorithm for the Detection of Single Source Points
- Slide 39
- Slide 40
- Proposed Algorithm for the Detection of Single Source Points
- Elimination of Outliers
- Slide 43
- Detected Single Source Points Three mixtures
- Comparison with Classical Algorithms for Determined Case
- Comparison with Method Proposed in [1] Underdetermined case
- Advantages of the Proposed algorithm
- My Contributions ndash III IV and V
- Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
- Mathematical Representation
- Single source points
- Basic Principle of Single Source Points Detection
- Algorithm for Single Source Points Detection
- Mask Estimation by k-means (KM)
- Mask Estimation by Fuzzy c-means (FCM)
- Automatic Detection of Number of Sources
- Elimination of Low Energy Points
-
Approaches for BSS of Speech SignalsApproaches for BSS of Speech Signals
Instantaneous mixing
Step 1 Selection of cost function
Step 2 Minimization or maximization of the cost function
0510 AM
WHS1
S2 X2
Y1
Y2
Separated
X1
7
Approaches for BSS of Speech SignalsApproaches for BSS of Speech SignalsInstantaneous mixingInstantaneous mixing
Selection of cost function
Statistical independence
Information theoretic
Non-Gaussianity
Kurtosis
Negentropy
Nonlinear cross moments
Temporal structure of speech
Non-stationarity of speech0510 AM
i
ii ypp y is idea Basic
Central limit theoremMixture of two or more sources will be more Gaussian than their individual components
224 E3E)( yyykurt
yyy HHJ gauss
yyyy dppH logEntropy
0 ji ygyfE
used becan statsticsorder Secondlags timedifferent for usly simultaneon correlatiooutput theedioganaliz eg
eddiagonalizusly simultaneo are matricesn correlatio the
and blocks into divided are Signals
Non Gaussianity measures
Signals from two different sources are independent
8
Approaches for BSS of Speech SignalsApproaches for BSS of Speech Signals
Instantaneous mixingMinimization or maximization of the cost function
simple gradient method
Natural gradient method
Newtonrsquos method
eg Informax ICA algorithm
eg FastICA
0510 AM 9
Approaches for BSS of Speech SignalsApproaches for BSS of Speech SignalsConvolutive Mixing
Time Domain Frequency Domain
QqltxlwyP
p
L
lpqpq 1)()(
1
1
0
)()()( tfftf SHX
)()()( tfftf XWY
AdvantageNo permutation problem
DisadvantageSlow convergence High computational cost for long filter taps
AdvantageLow computational costFast convergence
DisadvantagePermutation Problem
WHS1
S2
X1
X2
Y1 Y2
Y2 Y1
0510 AM 10
or
Permutation Problem in Frequency Domain BSS
Permutation Problem in Frequency Domain BSS
f1
f2
fk
x1x2
x3
BSS
BSS
BSSMixed signals
K po
int
FFT
y1y2y3
Still signals are mixed
K po
int
IFFT
Corresponding to different sources Due to permutation problem
One frequency binInstantaneous ICA algorithm
Solv
ing
perm
utati
on
Prob
lem y1
y2y3
Separated signals
Corresponding to y3
0510 AM 11
MotivationMotivation
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
12
My Contribution - IMy Contribution - I
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
13
Algorithm for Solving the Permutation Problem
Algorithm for Solving the Permutation Problem
f1
f2
fk
x1x2
x3
BSS
BSS
BSSMixed signals
K po
int
FFT
y1y2y3
Separated signals
K po
int
IFFT
Solv
ing
perm
utati
on
Prob
lem
Permutation problem
One frequency binInstantaneous ICA algorithm
Permutation problem solved
0510 AM 14
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Direction Of Arrival (DOA) method
2
1
)sin(2 1
p
dcfjkqpkq
pkefWfU Position of the pth sensor
Velocity of sound
)(
)(
)()(
)()(
)(
)(
2
1
2221
1211
2
1
k
k
kk
kk
k
k
fX
fX
fWfW
fWfW
fY
fY
0510 AM
Direction of y1 = -30o
Direction of y2 = 20o
15
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Reasons for failure at lower freq
Lower spacing causes error in phase difference measurement
The relation is approximated for plane wave front under anechoic condition
Disadvantages
Fails at lower frequenciesFails when sources are nearRoom reverberationSensor positions must be known
Direction Of Arrival (DOA) method
0510 AM 16
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
f1
f2
fk
BSS
BSS
BSSMixed signals
K po
int
FFT
y1y2y3
Separated signals
K po
int
IFFT
Solv
ing
perm
utati
on
Prob
lem
Low correlation
High correlationLow
correlation
x1x2
x3
Adjacent bands correlation method
0510 AM 17
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
r12
r21
r11
r22 r22 r22 r22
r11 r11 r11
r12
r21
r12
r21
r12
r21r11 r12
r21 r22
s1
s2
Correlation matrix
21122211 rrrr No change
21122211 rrrr Change permutation
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Adjacent bands correlation method
0510 AM
21122211 and and rrrr
21122211 and and rrrr
With confidence Without confidence
2090
8010
8020
1090
2090
1040
1040
2090
Example Example
18
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
r12
r21
r11
r22 r22 r22 r22
r11 r11 r11
r12
r21
r12
r21
r12
r21
r11 r12
r21 r22
s1
s2
Correlation matrix
Disadvantage The method is not robust
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Adjacent bands correlation method
0510 AM 19
0510 AM
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Combination of DOA and Correlation methods method
DOA + Harmonic Correlation + Adjacent bands correlation
Advantage Increased robustness
20
Proposed algorithm Partial separation method(Parallel configuration)
Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
Proposed algorithm Partial separation method(Parallel configuration)
Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
2y
1y
1x
2x
1s
2s
0510 AM 21
Time domain stage
Frequency domain stage
Partial separation method(Parallel configuration)
Partial separation method(Parallel configuration)
0510 AM 22
Time domain stage
Frequency domain stage
Parallel configuration
Partial separation method(Cascade configuration)
Partial separation method(Cascade configuration)
0510 AM 23
Time domain stage
Frequency domain stage
Advantages of Partial Separation methodAdvantages of Partial Separation method
bull Robustness
0510 AM 24
Comparison with Adjacent Bands Correlation Method
Comparison with Adjacent Bands Correlation Method
0510 AM 25
PS - Partial Separation method with confidence check C1 - Correlation between the adjacent bins without confidence check C2 - Correlation between adjacent bins with confidence check Ha - Correlation between the harmonic components with confidence check PS1 - Partial separation method alone without confidence check
0510 AM 26
Comparison with DOA methodComparison with DOA method
My Contribution -IIMy Contribution -II
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
27
Underdetermined Blind Source Separation of Instantaneous Mixtures
Underdetermined Blind Source Separation of Instantaneous Mixtures
t
k
0)(0)( 222221 tkStkS
0)(0)( 222221 tkStkS
0)(0)( 112111 tkStkS
0)(0)( 112111 tkStkS
tkX 1
tkX 22x
1x
0510 AM 28
Mathematical Representation of Instantaneous Mixing
Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
Mathematical Representation of Instantaneous Mixing
Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
)(
)(
)(
)( 1
1
1111
tkS
tkS
hh
hh
tkX
tkX
QPQP
Q
P
)(
)(
)(
)( 1
1
1111
ts
ts
hh
hh
tx
tx
QPQP
Q
P
)()()(11
1
1
11
tkS
h
h
tkS
h
h
tkS
h
h
Q
PQ
Q
q
Pq
q
P
)()()()( 21 tkStkStkStk QhhhX
Time domain
Time-Frequency domain
0510 AM 29
P ndash No of mixturesQ ndash No of sources
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
00point at 1 Case 11211111 tkStkStk
)()()( 1122111111 tkStkStk hhX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 2222221122 tkStkStk hhX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
0510 AM
0 0
30
Q
qqq tkStk
1
hX
2Let Q
00point at 1 Case 11211111 tkStkStk
)()( 111111 tkStk hX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()( 222222 tkStk hX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
0510 AM 31
00point at 1 Case 11211111 tkStkStk
)()( 111111 tkStk hX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()( 222222 tkStk hX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
Scalar
ScalarScalar
Scalar
At single source point 1 At single source point 2
111
111
ofDirection )( ofDirection
ofDirection )( ofDirection
hX
hX
tkI
tkR 222
222
ofDirection )( ofDirection
ofDirection )( ofDirection
hX
hX
tkI
tkR
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
0510 AM
1111 ( of Direction ( of Direction tkItkR XX 2222 ( of Direction ( of Direction tkItkR XX 32
Scatter Diagram of the Mixtures When Source are Perfectly Sparse
Scatter Diagram of the Mixtures When Source are Perfectly Sparse
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
22222
11111
2221
1211
22222
11111
kSkSkSkSkS
kSkSkSkSkS
hh
hh
kXkXkXkXkX
kXkXkXkXkX
21
111 h
hh
22
122 h
hh
0 00 0 0
Example
0510 AM 33
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
22222
11111
2221
1211
22222
11111
kSkSkSkSkS
kSkSkSkSkS
hh
hh
kXkXkXkXkX
kXkXkXkXkX
21
111 h
hh
22
122 h
hh
0 00 0 00
Example
Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
0510 AM 34
Scatter Diagram of the Mixtures when Sources are Sparse
Scatter Diagram of the Mixtures when Sources are Sparse
3h
6h
5h
1h4h
2h
0510 AM
No of sources = 6No of mixtures = 2
35
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
3h
6h
5h
1h4h
2h
0510 AM
No of sources = 6No of mixtures = 2
36
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
3h
6h
5h
1h4h
2h
0510 AM
ObjectiveEstimation of the single source points
No of sources = 6No of mixtures = 2
37
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Multi source point
38
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
Multi source point
39
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
Average of 15 pairs of speech utterances of length 10 s each
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
)( ofDirection )( ofDirection tkXItkXR )( ofDirection )( ofDirection tkXItkXR
SSPMSP
40
SSPt
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)()(
)()(
112112
111111
tkXjItkXR
tkXjItkXR
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXI
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXIMSP
)( 111 tkX
)( 112 tkX
cos
)()(
)()(
tkXItkXR
tkXItkXR T
Proposed Algorithm for the Detection of Single Source Points
Proposed Algorithm for the Detection of Single Source Points
0510 AM 41
Elimination of OutliersElimination of Outliers
SSPs detection
Clus
terin
g
Outlier elimination
0510 AM 42
0510 AM
Experimental ResultsExperimental Results
dB6747NMSE
No of mixtures =2 No of sources =6
43
Detected Single Source PointsThree mixtures
Detected Single Source PointsThree mixtures
No of mixtures =3 No of sources =60510 AM 44
Comparison with Classical Algorithms for Determined Case
Comparison with Classical Algorithms for Determined Case
No of mixtures =2No of sources =2
Average of 500 experimental results
0510 AM 45
-gt
Comparison with Method Proposed in [1] Underdetermined case
Comparison with Method Proposed in [1] Underdetermined case
[1] Y Li S Amari A Cichocki D W C Ho and S Xie ldquoUnderdetermined blind source separation based on sparse representationrdquo IEEE Transactions on Signal Processing vol 54 p 423ndash437 Feb 2006
0510 AM
Nor
mal
ized
mea
n sq
uare
err
or (N
MSE
) in
mix
ing
mat
rix e
stim
ation
(dB)
Order of the mixing matrices (PxQ)
46
P ndash No of mixturesQ ndash No of sources
Advantages of the Proposed algorithmAdvantages of the Proposed algorithm
Step 1 Convert x in the time domain to the TF domain to get XStep 2 Check the condition
Step 3 If the condition is satisfied then X(k t) is a sample atthe SSP and this sample is kept for mixing matrix estimationotherwise discard the point
Step 4 Repeat Steps 2 to 3 for all the points in the TF planeor until sufficient number of SSPs are obtained
cos
)()(
)()(
tkXItkXR
tkXItkXR T
1) Much simpler constrain the algorithm does not require ldquosingle source zonerdquo
3) The algorithm is extremely simple but effective2) Separation performance is better
0510 AM 47-gt
My Contributions ndash III IV and VMy Contributions ndash III IV and V
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
48
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Mask estimation
Mic 1
Mic P
Mixture in TF domain
Separated signals in TF domain
)( tkX P
)(1 tkX
t
t
k
k
)(1 tkY
)(1 tkY
)( tkYQ
)( tkYQ
QP
0510 AM 49
Mathematical RepresentationMathematical Representation
Q
q
L
lqpqp Pplnslhnx
1
1
0
1)()()(
)()()()()()()( 11 tkSktkSktkSktk QQqq HHHX
)(
)(
)()(
)()(
)(
)( 1
1
1111
tkS
tkS
kHkH
kHkH
tkX
tkX
QPQP
Q
P
)(
)(
)(
)(
)(
)(
)(
)(
)( 11
1
1
11
tkS
kH
kH
tkS
kH
kH
tkS
kH
kH
Q
PQ
Q
q
Pq
q
P
Time domain
Frequency domain
0510 AM 50
P ndash No of mixturesQ ndash No of sources
Single source pointsSingle source pointsInstantaneous mixing
00point at 1 Case 11211111 tkStkStk
)()()(
)()()(
111111
111111
tkSIktkI
tkSRktkR
HX
HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()(
)()()(
222222
222222
tkSIktkI
tkSRktkR
HX
HX
Single source point 2
Real scalar
RealReal
Real scalarReal scalar
Real scalar
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
0510 AM 51
Basic Principle of Single Source Points Detection
Basic Principle of Single Source Points Detection
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
j
H
C
e
cos21
21
UU
UUUUU H
and 20coscos HCH
angle pseudo called is
angleHermitian called is
H The Hermitian angle between the complex
vectors u1 and u2 will remain the same even if the vectors are multiplied by any complex scalars whereas the pseudo angle will change
0510 AM 52
-gt
k
Algorithm for Single Source Points Detection
Algorithm for Single Source Points Detection
t
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)(
)(
)(111
121
111 tkSkH
kH
11
11
j
jr
)(
)(
112
111
tkX
tkX
11
11
j
jr
)(
)(
112
111
tkX
tkX
)( 111 tkX
)( 112 tkX
)(
)(
)(112
122
112 tkSkH
kH θH2
θH1
θH2
rX
rX
)(
)(cos
11
111
tk
tk H
Hq
0510 AM 53
θH1
OR
1k
1k
1t
Clean
Estimated
Mask Estimation by k-means (KM)Mask Estimation by k-means (KM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 54
Clean
Estimated
Mask Estimation by Fuzzy c-means (FCM)Mask Estimation by Fuzzy c-means (FCM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 55
Automatic Detection of Number of SourcesAutomatic Detection of Number of Sources
0510 AM 56
Cluster validation technique
For c = 2 to cmax
Cluster the data into c clustersCalculate the cluster validation index
EndTake c corresponding to the best cluster as the number of sources
-gt
Elimination of Low Energy PointsElimination of Low Energy Points
0510 AM 57
- Blind Separation of Speech Mixtures
- Introduction
- Slide 3
- Slide 4
- Slide 5
- Approaches for BSS of Speech Signals
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Permutation Problem in Frequency Domain BSS
- Motivation
- My Contribution - I
- Algorithm for Solving the Permutation Problem
- Existing Method for Solving the Permutation Problem
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Proposed algorithm Partial separation method (Parallel configuration) Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
- Partial separation method (Parallel configuration)
- Partial separation method (Cascade configuration)
- Advantages of Partial Separation method
- Comparison with Adjacent Bands Correlation Method
- Comparison with DOA method
- My Contribution -II
- Underdetermined Blind Source Separation of Instantaneous Mixtures
- Mathematical Representation of Instantaneous Mixing Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
- Single Source Points in Time-Frequency domain
- Slide 31
- Slide 32
- Scatter Diagram of the Mixtures When Source are Perfectly Sparse
- Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
- Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
- Principle of the Proposed Algorithm for the Detection of Single Source Points
- Slide 39
- Slide 40
- Proposed Algorithm for the Detection of Single Source Points
- Elimination of Outliers
- Slide 43
- Detected Single Source Points Three mixtures
- Comparison with Classical Algorithms for Determined Case
- Comparison with Method Proposed in [1] Underdetermined case
- Advantages of the Proposed algorithm
- My Contributions ndash III IV and V
- Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
- Mathematical Representation
- Single source points
- Basic Principle of Single Source Points Detection
- Algorithm for Single Source Points Detection
- Mask Estimation by k-means (KM)
- Mask Estimation by Fuzzy c-means (FCM)
- Automatic Detection of Number of Sources
- Elimination of Low Energy Points
-
Approaches for BSS of Speech SignalsApproaches for BSS of Speech SignalsInstantaneous mixingInstantaneous mixing
Selection of cost function
Statistical independence
Information theoretic
Non-Gaussianity
Kurtosis
Negentropy
Nonlinear cross moments
Temporal structure of speech
Non-stationarity of speech0510 AM
i
ii ypp y is idea Basic
Central limit theoremMixture of two or more sources will be more Gaussian than their individual components
224 E3E)( yyykurt
yyy HHJ gauss
yyyy dppH logEntropy
0 ji ygyfE
used becan statsticsorder Secondlags timedifferent for usly simultaneon correlatiooutput theedioganaliz eg
eddiagonalizusly simultaneo are matricesn correlatio the
and blocks into divided are Signals
Non Gaussianity measures
Signals from two different sources are independent
8
Approaches for BSS of Speech SignalsApproaches for BSS of Speech Signals
Instantaneous mixingMinimization or maximization of the cost function
simple gradient method
Natural gradient method
Newtonrsquos method
eg Informax ICA algorithm
eg FastICA
0510 AM 9
Approaches for BSS of Speech SignalsApproaches for BSS of Speech SignalsConvolutive Mixing
Time Domain Frequency Domain
QqltxlwyP
p
L
lpqpq 1)()(
1
1
0
)()()( tfftf SHX
)()()( tfftf XWY
AdvantageNo permutation problem
DisadvantageSlow convergence High computational cost for long filter taps
AdvantageLow computational costFast convergence
DisadvantagePermutation Problem
WHS1
S2
X1
X2
Y1 Y2
Y2 Y1
0510 AM 10
or
Permutation Problem in Frequency Domain BSS
Permutation Problem in Frequency Domain BSS
f1
f2
fk
x1x2
x3
BSS
BSS
BSSMixed signals
K po
int
FFT
y1y2y3
Still signals are mixed
K po
int
IFFT
Corresponding to different sources Due to permutation problem
One frequency binInstantaneous ICA algorithm
Solv
ing
perm
utati
on
Prob
lem y1
y2y3
Separated signals
Corresponding to y3
0510 AM 11
MotivationMotivation
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
12
My Contribution - IMy Contribution - I
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
13
Algorithm for Solving the Permutation Problem
Algorithm for Solving the Permutation Problem
f1
f2
fk
x1x2
x3
BSS
BSS
BSSMixed signals
K po
int
FFT
y1y2y3
Separated signals
K po
int
IFFT
Solv
ing
perm
utati
on
Prob
lem
Permutation problem
One frequency binInstantaneous ICA algorithm
Permutation problem solved
0510 AM 14
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Direction Of Arrival (DOA) method
2
1
)sin(2 1
p
dcfjkqpkq
pkefWfU Position of the pth sensor
Velocity of sound
)(
)(
)()(
)()(
)(
)(
2
1
2221
1211
2
1
k
k
kk
kk
k
k
fX
fX
fWfW
fWfW
fY
fY
0510 AM
Direction of y1 = -30o
Direction of y2 = 20o
15
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Reasons for failure at lower freq
Lower spacing causes error in phase difference measurement
The relation is approximated for plane wave front under anechoic condition
Disadvantages
Fails at lower frequenciesFails when sources are nearRoom reverberationSensor positions must be known
Direction Of Arrival (DOA) method
0510 AM 16
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
f1
f2
fk
BSS
BSS
BSSMixed signals
K po
int
FFT
y1y2y3
Separated signals
K po
int
IFFT
Solv
ing
perm
utati
on
Prob
lem
Low correlation
High correlationLow
correlation
x1x2
x3
Adjacent bands correlation method
0510 AM 17
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
r12
r21
r11
r22 r22 r22 r22
r11 r11 r11
r12
r21
r12
r21
r12
r21r11 r12
r21 r22
s1
s2
Correlation matrix
21122211 rrrr No change
21122211 rrrr Change permutation
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Adjacent bands correlation method
0510 AM
21122211 and and rrrr
21122211 and and rrrr
With confidence Without confidence
2090
8010
8020
1090
2090
1040
1040
2090
Example Example
18
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
r12
r21
r11
r22 r22 r22 r22
r11 r11 r11
r12
r21
r12
r21
r12
r21
r11 r12
r21 r22
s1
s2
Correlation matrix
Disadvantage The method is not robust
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Adjacent bands correlation method
0510 AM 19
0510 AM
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Combination of DOA and Correlation methods method
DOA + Harmonic Correlation + Adjacent bands correlation
Advantage Increased robustness
20
Proposed algorithm Partial separation method(Parallel configuration)
Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
Proposed algorithm Partial separation method(Parallel configuration)
Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
2y
1y
1x
2x
1s
2s
0510 AM 21
Time domain stage
Frequency domain stage
Partial separation method(Parallel configuration)
Partial separation method(Parallel configuration)
0510 AM 22
Time domain stage
Frequency domain stage
Parallel configuration
Partial separation method(Cascade configuration)
Partial separation method(Cascade configuration)
0510 AM 23
Time domain stage
Frequency domain stage
Advantages of Partial Separation methodAdvantages of Partial Separation method
bull Robustness
0510 AM 24
Comparison with Adjacent Bands Correlation Method
Comparison with Adjacent Bands Correlation Method
0510 AM 25
PS - Partial Separation method with confidence check C1 - Correlation between the adjacent bins without confidence check C2 - Correlation between adjacent bins with confidence check Ha - Correlation between the harmonic components with confidence check PS1 - Partial separation method alone without confidence check
0510 AM 26
Comparison with DOA methodComparison with DOA method
My Contribution -IIMy Contribution -II
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
27
Underdetermined Blind Source Separation of Instantaneous Mixtures
Underdetermined Blind Source Separation of Instantaneous Mixtures
t
k
0)(0)( 222221 tkStkS
0)(0)( 222221 tkStkS
0)(0)( 112111 tkStkS
0)(0)( 112111 tkStkS
tkX 1
tkX 22x
1x
0510 AM 28
Mathematical Representation of Instantaneous Mixing
Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
Mathematical Representation of Instantaneous Mixing
Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
)(
)(
)(
)( 1
1
1111
tkS
tkS
hh
hh
tkX
tkX
QPQP
Q
P
)(
)(
)(
)( 1
1
1111
ts
ts
hh
hh
tx
tx
QPQP
Q
P
)()()(11
1
1
11
tkS
h
h
tkS
h
h
tkS
h
h
Q
PQ
Q
q
Pq
q
P
)()()()( 21 tkStkStkStk QhhhX
Time domain
Time-Frequency domain
0510 AM 29
P ndash No of mixturesQ ndash No of sources
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
00point at 1 Case 11211111 tkStkStk
)()()( 1122111111 tkStkStk hhX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 2222221122 tkStkStk hhX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
0510 AM
0 0
30
Q
qqq tkStk
1
hX
2Let Q
00point at 1 Case 11211111 tkStkStk
)()( 111111 tkStk hX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()( 222222 tkStk hX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
0510 AM 31
00point at 1 Case 11211111 tkStkStk
)()( 111111 tkStk hX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()( 222222 tkStk hX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
Scalar
ScalarScalar
Scalar
At single source point 1 At single source point 2
111
111
ofDirection )( ofDirection
ofDirection )( ofDirection
hX
hX
tkI
tkR 222
222
ofDirection )( ofDirection
ofDirection )( ofDirection
hX
hX
tkI
tkR
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
0510 AM
1111 ( of Direction ( of Direction tkItkR XX 2222 ( of Direction ( of Direction tkItkR XX 32
Scatter Diagram of the Mixtures When Source are Perfectly Sparse
Scatter Diagram of the Mixtures When Source are Perfectly Sparse
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
22222
11111
2221
1211
22222
11111
kSkSkSkSkS
kSkSkSkSkS
hh
hh
kXkXkXkXkX
kXkXkXkXkX
21
111 h
hh
22
122 h
hh
0 00 0 0
Example
0510 AM 33
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
22222
11111
2221
1211
22222
11111
kSkSkSkSkS
kSkSkSkSkS
hh
hh
kXkXkXkXkX
kXkXkXkXkX
21
111 h
hh
22
122 h
hh
0 00 0 00
Example
Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
0510 AM 34
Scatter Diagram of the Mixtures when Sources are Sparse
Scatter Diagram of the Mixtures when Sources are Sparse
3h
6h
5h
1h4h
2h
0510 AM
No of sources = 6No of mixtures = 2
35
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
3h
6h
5h
1h4h
2h
0510 AM
No of sources = 6No of mixtures = 2
36
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
3h
6h
5h
1h4h
2h
0510 AM
ObjectiveEstimation of the single source points
No of sources = 6No of mixtures = 2
37
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Multi source point
38
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
Multi source point
39
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
Average of 15 pairs of speech utterances of length 10 s each
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
)( ofDirection )( ofDirection tkXItkXR )( ofDirection )( ofDirection tkXItkXR
SSPMSP
40
SSPt
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)()(
)()(
112112
111111
tkXjItkXR
tkXjItkXR
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXI
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXIMSP
)( 111 tkX
)( 112 tkX
cos
)()(
)()(
tkXItkXR
tkXItkXR T
Proposed Algorithm for the Detection of Single Source Points
Proposed Algorithm for the Detection of Single Source Points
0510 AM 41
Elimination of OutliersElimination of Outliers
SSPs detection
Clus
terin
g
Outlier elimination
0510 AM 42
0510 AM
Experimental ResultsExperimental Results
dB6747NMSE
No of mixtures =2 No of sources =6
43
Detected Single Source PointsThree mixtures
Detected Single Source PointsThree mixtures
No of mixtures =3 No of sources =60510 AM 44
Comparison with Classical Algorithms for Determined Case
Comparison with Classical Algorithms for Determined Case
No of mixtures =2No of sources =2
Average of 500 experimental results
0510 AM 45
-gt
Comparison with Method Proposed in [1] Underdetermined case
Comparison with Method Proposed in [1] Underdetermined case
[1] Y Li S Amari A Cichocki D W C Ho and S Xie ldquoUnderdetermined blind source separation based on sparse representationrdquo IEEE Transactions on Signal Processing vol 54 p 423ndash437 Feb 2006
0510 AM
Nor
mal
ized
mea
n sq
uare
err
or (N
MSE
) in
mix
ing
mat
rix e
stim
ation
(dB)
Order of the mixing matrices (PxQ)
46
P ndash No of mixturesQ ndash No of sources
Advantages of the Proposed algorithmAdvantages of the Proposed algorithm
Step 1 Convert x in the time domain to the TF domain to get XStep 2 Check the condition
Step 3 If the condition is satisfied then X(k t) is a sample atthe SSP and this sample is kept for mixing matrix estimationotherwise discard the point
Step 4 Repeat Steps 2 to 3 for all the points in the TF planeor until sufficient number of SSPs are obtained
cos
)()(
)()(
tkXItkXR
tkXItkXR T
1) Much simpler constrain the algorithm does not require ldquosingle source zonerdquo
3) The algorithm is extremely simple but effective2) Separation performance is better
0510 AM 47-gt
My Contributions ndash III IV and VMy Contributions ndash III IV and V
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
48
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Mask estimation
Mic 1
Mic P
Mixture in TF domain
Separated signals in TF domain
)( tkX P
)(1 tkX
t
t
k
k
)(1 tkY
)(1 tkY
)( tkYQ
)( tkYQ
QP
0510 AM 49
Mathematical RepresentationMathematical Representation
Q
q
L
lqpqp Pplnslhnx
1
1
0
1)()()(
)()()()()()()( 11 tkSktkSktkSktk QQqq HHHX
)(
)(
)()(
)()(
)(
)( 1
1
1111
tkS
tkS
kHkH
kHkH
tkX
tkX
QPQP
Q
P
)(
)(
)(
)(
)(
)(
)(
)(
)( 11
1
1
11
tkS
kH
kH
tkS
kH
kH
tkS
kH
kH
Q
PQ
Q
q
Pq
q
P
Time domain
Frequency domain
0510 AM 50
P ndash No of mixturesQ ndash No of sources
Single source pointsSingle source pointsInstantaneous mixing
00point at 1 Case 11211111 tkStkStk
)()()(
)()()(
111111
111111
tkSIktkI
tkSRktkR
HX
HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()(
)()()(
222222
222222
tkSIktkI
tkSRktkR
HX
HX
Single source point 2
Real scalar
RealReal
Real scalarReal scalar
Real scalar
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
0510 AM 51
Basic Principle of Single Source Points Detection
Basic Principle of Single Source Points Detection
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
j
H
C
e
cos21
21
UU
UUUUU H
and 20coscos HCH
angle pseudo called is
angleHermitian called is
H The Hermitian angle between the complex
vectors u1 and u2 will remain the same even if the vectors are multiplied by any complex scalars whereas the pseudo angle will change
0510 AM 52
-gt
k
Algorithm for Single Source Points Detection
Algorithm for Single Source Points Detection
t
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)(
)(
)(111
121
111 tkSkH
kH
11
11
j
jr
)(
)(
112
111
tkX
tkX
11
11
j
jr
)(
)(
112
111
tkX
tkX
)( 111 tkX
)( 112 tkX
)(
)(
)(112
122
112 tkSkH
kH θH2
θH1
θH2
rX
rX
)(
)(cos
11
111
tk
tk H
Hq
0510 AM 53
θH1
OR
1k
1k
1t
Clean
Estimated
Mask Estimation by k-means (KM)Mask Estimation by k-means (KM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 54
Clean
Estimated
Mask Estimation by Fuzzy c-means (FCM)Mask Estimation by Fuzzy c-means (FCM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 55
Automatic Detection of Number of SourcesAutomatic Detection of Number of Sources
0510 AM 56
Cluster validation technique
For c = 2 to cmax
Cluster the data into c clustersCalculate the cluster validation index
EndTake c corresponding to the best cluster as the number of sources
-gt
Elimination of Low Energy PointsElimination of Low Energy Points
0510 AM 57
- Blind Separation of Speech Mixtures
- Introduction
- Slide 3
- Slide 4
- Slide 5
- Approaches for BSS of Speech Signals
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Permutation Problem in Frequency Domain BSS
- Motivation
- My Contribution - I
- Algorithm for Solving the Permutation Problem
- Existing Method for Solving the Permutation Problem
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Proposed algorithm Partial separation method (Parallel configuration) Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
- Partial separation method (Parallel configuration)
- Partial separation method (Cascade configuration)
- Advantages of Partial Separation method
- Comparison with Adjacent Bands Correlation Method
- Comparison with DOA method
- My Contribution -II
- Underdetermined Blind Source Separation of Instantaneous Mixtures
- Mathematical Representation of Instantaneous Mixing Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
- Single Source Points in Time-Frequency domain
- Slide 31
- Slide 32
- Scatter Diagram of the Mixtures When Source are Perfectly Sparse
- Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
- Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
- Principle of the Proposed Algorithm for the Detection of Single Source Points
- Slide 39
- Slide 40
- Proposed Algorithm for the Detection of Single Source Points
- Elimination of Outliers
- Slide 43
- Detected Single Source Points Three mixtures
- Comparison with Classical Algorithms for Determined Case
- Comparison with Method Proposed in [1] Underdetermined case
- Advantages of the Proposed algorithm
- My Contributions ndash III IV and V
- Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
- Mathematical Representation
- Single source points
- Basic Principle of Single Source Points Detection
- Algorithm for Single Source Points Detection
- Mask Estimation by k-means (KM)
- Mask Estimation by Fuzzy c-means (FCM)
- Automatic Detection of Number of Sources
- Elimination of Low Energy Points
-
Approaches for BSS of Speech SignalsApproaches for BSS of Speech Signals
Instantaneous mixingMinimization or maximization of the cost function
simple gradient method
Natural gradient method
Newtonrsquos method
eg Informax ICA algorithm
eg FastICA
0510 AM 9
Approaches for BSS of Speech SignalsApproaches for BSS of Speech SignalsConvolutive Mixing
Time Domain Frequency Domain
QqltxlwyP
p
L
lpqpq 1)()(
1
1
0
)()()( tfftf SHX
)()()( tfftf XWY
AdvantageNo permutation problem
DisadvantageSlow convergence High computational cost for long filter taps
AdvantageLow computational costFast convergence
DisadvantagePermutation Problem
WHS1
S2
X1
X2
Y1 Y2
Y2 Y1
0510 AM 10
or
Permutation Problem in Frequency Domain BSS
Permutation Problem in Frequency Domain BSS
f1
f2
fk
x1x2
x3
BSS
BSS
BSSMixed signals
K po
int
FFT
y1y2y3
Still signals are mixed
K po
int
IFFT
Corresponding to different sources Due to permutation problem
One frequency binInstantaneous ICA algorithm
Solv
ing
perm
utati
on
Prob
lem y1
y2y3
Separated signals
Corresponding to y3
0510 AM 11
MotivationMotivation
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
12
My Contribution - IMy Contribution - I
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
13
Algorithm for Solving the Permutation Problem
Algorithm for Solving the Permutation Problem
f1
f2
fk
x1x2
x3
BSS
BSS
BSSMixed signals
K po
int
FFT
y1y2y3
Separated signals
K po
int
IFFT
Solv
ing
perm
utati
on
Prob
lem
Permutation problem
One frequency binInstantaneous ICA algorithm
Permutation problem solved
0510 AM 14
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Direction Of Arrival (DOA) method
2
1
)sin(2 1
p
dcfjkqpkq
pkefWfU Position of the pth sensor
Velocity of sound
)(
)(
)()(
)()(
)(
)(
2
1
2221
1211
2
1
k
k
kk
kk
k
k
fX
fX
fWfW
fWfW
fY
fY
0510 AM
Direction of y1 = -30o
Direction of y2 = 20o
15
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Reasons for failure at lower freq
Lower spacing causes error in phase difference measurement
The relation is approximated for plane wave front under anechoic condition
Disadvantages
Fails at lower frequenciesFails when sources are nearRoom reverberationSensor positions must be known
Direction Of Arrival (DOA) method
0510 AM 16
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
f1
f2
fk
BSS
BSS
BSSMixed signals
K po
int
FFT
y1y2y3
Separated signals
K po
int
IFFT
Solv
ing
perm
utati
on
Prob
lem
Low correlation
High correlationLow
correlation
x1x2
x3
Adjacent bands correlation method
0510 AM 17
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
r12
r21
r11
r22 r22 r22 r22
r11 r11 r11
r12
r21
r12
r21
r12
r21r11 r12
r21 r22
s1
s2
Correlation matrix
21122211 rrrr No change
21122211 rrrr Change permutation
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Adjacent bands correlation method
0510 AM
21122211 and and rrrr
21122211 and and rrrr
With confidence Without confidence
2090
8010
8020
1090
2090
1040
1040
2090
Example Example
18
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
r12
r21
r11
r22 r22 r22 r22
r11 r11 r11
r12
r21
r12
r21
r12
r21
r11 r12
r21 r22
s1
s2
Correlation matrix
Disadvantage The method is not robust
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Adjacent bands correlation method
0510 AM 19
0510 AM
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Combination of DOA and Correlation methods method
DOA + Harmonic Correlation + Adjacent bands correlation
Advantage Increased robustness
20
Proposed algorithm Partial separation method(Parallel configuration)
Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
Proposed algorithm Partial separation method(Parallel configuration)
Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
2y
1y
1x
2x
1s
2s
0510 AM 21
Time domain stage
Frequency domain stage
Partial separation method(Parallel configuration)
Partial separation method(Parallel configuration)
0510 AM 22
Time domain stage
Frequency domain stage
Parallel configuration
Partial separation method(Cascade configuration)
Partial separation method(Cascade configuration)
0510 AM 23
Time domain stage
Frequency domain stage
Advantages of Partial Separation methodAdvantages of Partial Separation method
bull Robustness
0510 AM 24
Comparison with Adjacent Bands Correlation Method
Comparison with Adjacent Bands Correlation Method
0510 AM 25
PS - Partial Separation method with confidence check C1 - Correlation between the adjacent bins without confidence check C2 - Correlation between adjacent bins with confidence check Ha - Correlation between the harmonic components with confidence check PS1 - Partial separation method alone without confidence check
0510 AM 26
Comparison with DOA methodComparison with DOA method
My Contribution -IIMy Contribution -II
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
27
Underdetermined Blind Source Separation of Instantaneous Mixtures
Underdetermined Blind Source Separation of Instantaneous Mixtures
t
k
0)(0)( 222221 tkStkS
0)(0)( 222221 tkStkS
0)(0)( 112111 tkStkS
0)(0)( 112111 tkStkS
tkX 1
tkX 22x
1x
0510 AM 28
Mathematical Representation of Instantaneous Mixing
Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
Mathematical Representation of Instantaneous Mixing
Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
)(
)(
)(
)( 1
1
1111
tkS
tkS
hh
hh
tkX
tkX
QPQP
Q
P
)(
)(
)(
)( 1
1
1111
ts
ts
hh
hh
tx
tx
QPQP
Q
P
)()()(11
1
1
11
tkS
h
h
tkS
h
h
tkS
h
h
Q
PQ
Q
q
Pq
q
P
)()()()( 21 tkStkStkStk QhhhX
Time domain
Time-Frequency domain
0510 AM 29
P ndash No of mixturesQ ndash No of sources
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
00point at 1 Case 11211111 tkStkStk
)()()( 1122111111 tkStkStk hhX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 2222221122 tkStkStk hhX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
0510 AM
0 0
30
Q
qqq tkStk
1
hX
2Let Q
00point at 1 Case 11211111 tkStkStk
)()( 111111 tkStk hX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()( 222222 tkStk hX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
0510 AM 31
00point at 1 Case 11211111 tkStkStk
)()( 111111 tkStk hX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()( 222222 tkStk hX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
Scalar
ScalarScalar
Scalar
At single source point 1 At single source point 2
111
111
ofDirection )( ofDirection
ofDirection )( ofDirection
hX
hX
tkI
tkR 222
222
ofDirection )( ofDirection
ofDirection )( ofDirection
hX
hX
tkI
tkR
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
0510 AM
1111 ( of Direction ( of Direction tkItkR XX 2222 ( of Direction ( of Direction tkItkR XX 32
Scatter Diagram of the Mixtures When Source are Perfectly Sparse
Scatter Diagram of the Mixtures When Source are Perfectly Sparse
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
22222
11111
2221
1211
22222
11111
kSkSkSkSkS
kSkSkSkSkS
hh
hh
kXkXkXkXkX
kXkXkXkXkX
21
111 h
hh
22
122 h
hh
0 00 0 0
Example
0510 AM 33
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
22222
11111
2221
1211
22222
11111
kSkSkSkSkS
kSkSkSkSkS
hh
hh
kXkXkXkXkX
kXkXkXkXkX
21
111 h
hh
22
122 h
hh
0 00 0 00
Example
Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
0510 AM 34
Scatter Diagram of the Mixtures when Sources are Sparse
Scatter Diagram of the Mixtures when Sources are Sparse
3h
6h
5h
1h4h
2h
0510 AM
No of sources = 6No of mixtures = 2
35
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
3h
6h
5h
1h4h
2h
0510 AM
No of sources = 6No of mixtures = 2
36
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
3h
6h
5h
1h4h
2h
0510 AM
ObjectiveEstimation of the single source points
No of sources = 6No of mixtures = 2
37
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Multi source point
38
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
Multi source point
39
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
Average of 15 pairs of speech utterances of length 10 s each
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
)( ofDirection )( ofDirection tkXItkXR )( ofDirection )( ofDirection tkXItkXR
SSPMSP
40
SSPt
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)()(
)()(
112112
111111
tkXjItkXR
tkXjItkXR
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXI
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXIMSP
)( 111 tkX
)( 112 tkX
cos
)()(
)()(
tkXItkXR
tkXItkXR T
Proposed Algorithm for the Detection of Single Source Points
Proposed Algorithm for the Detection of Single Source Points
0510 AM 41
Elimination of OutliersElimination of Outliers
SSPs detection
Clus
terin
g
Outlier elimination
0510 AM 42
0510 AM
Experimental ResultsExperimental Results
dB6747NMSE
No of mixtures =2 No of sources =6
43
Detected Single Source PointsThree mixtures
Detected Single Source PointsThree mixtures
No of mixtures =3 No of sources =60510 AM 44
Comparison with Classical Algorithms for Determined Case
Comparison with Classical Algorithms for Determined Case
No of mixtures =2No of sources =2
Average of 500 experimental results
0510 AM 45
-gt
Comparison with Method Proposed in [1] Underdetermined case
Comparison with Method Proposed in [1] Underdetermined case
[1] Y Li S Amari A Cichocki D W C Ho and S Xie ldquoUnderdetermined blind source separation based on sparse representationrdquo IEEE Transactions on Signal Processing vol 54 p 423ndash437 Feb 2006
0510 AM
Nor
mal
ized
mea
n sq
uare
err
or (N
MSE
) in
mix
ing
mat
rix e
stim
ation
(dB)
Order of the mixing matrices (PxQ)
46
P ndash No of mixturesQ ndash No of sources
Advantages of the Proposed algorithmAdvantages of the Proposed algorithm
Step 1 Convert x in the time domain to the TF domain to get XStep 2 Check the condition
Step 3 If the condition is satisfied then X(k t) is a sample atthe SSP and this sample is kept for mixing matrix estimationotherwise discard the point
Step 4 Repeat Steps 2 to 3 for all the points in the TF planeor until sufficient number of SSPs are obtained
cos
)()(
)()(
tkXItkXR
tkXItkXR T
1) Much simpler constrain the algorithm does not require ldquosingle source zonerdquo
3) The algorithm is extremely simple but effective2) Separation performance is better
0510 AM 47-gt
My Contributions ndash III IV and VMy Contributions ndash III IV and V
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
48
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Mask estimation
Mic 1
Mic P
Mixture in TF domain
Separated signals in TF domain
)( tkX P
)(1 tkX
t
t
k
k
)(1 tkY
)(1 tkY
)( tkYQ
)( tkYQ
QP
0510 AM 49
Mathematical RepresentationMathematical Representation
Q
q
L
lqpqp Pplnslhnx
1
1
0
1)()()(
)()()()()()()( 11 tkSktkSktkSktk QQqq HHHX
)(
)(
)()(
)()(
)(
)( 1
1
1111
tkS
tkS
kHkH
kHkH
tkX
tkX
QPQP
Q
P
)(
)(
)(
)(
)(
)(
)(
)(
)( 11
1
1
11
tkS
kH
kH
tkS
kH
kH
tkS
kH
kH
Q
PQ
Q
q
Pq
q
P
Time domain
Frequency domain
0510 AM 50
P ndash No of mixturesQ ndash No of sources
Single source pointsSingle source pointsInstantaneous mixing
00point at 1 Case 11211111 tkStkStk
)()()(
)()()(
111111
111111
tkSIktkI
tkSRktkR
HX
HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()(
)()()(
222222
222222
tkSIktkI
tkSRktkR
HX
HX
Single source point 2
Real scalar
RealReal
Real scalarReal scalar
Real scalar
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
0510 AM 51
Basic Principle of Single Source Points Detection
Basic Principle of Single Source Points Detection
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
j
H
C
e
cos21
21
UU
UUUUU H
and 20coscos HCH
angle pseudo called is
angleHermitian called is
H The Hermitian angle between the complex
vectors u1 and u2 will remain the same even if the vectors are multiplied by any complex scalars whereas the pseudo angle will change
0510 AM 52
-gt
k
Algorithm for Single Source Points Detection
Algorithm for Single Source Points Detection
t
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)(
)(
)(111
121
111 tkSkH
kH
11
11
j
jr
)(
)(
112
111
tkX
tkX
11
11
j
jr
)(
)(
112
111
tkX
tkX
)( 111 tkX
)( 112 tkX
)(
)(
)(112
122
112 tkSkH
kH θH2
θH1
θH2
rX
rX
)(
)(cos
11
111
tk
tk H
Hq
0510 AM 53
θH1
OR
1k
1k
1t
Clean
Estimated
Mask Estimation by k-means (KM)Mask Estimation by k-means (KM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 54
Clean
Estimated
Mask Estimation by Fuzzy c-means (FCM)Mask Estimation by Fuzzy c-means (FCM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 55
Automatic Detection of Number of SourcesAutomatic Detection of Number of Sources
0510 AM 56
Cluster validation technique
For c = 2 to cmax
Cluster the data into c clustersCalculate the cluster validation index
EndTake c corresponding to the best cluster as the number of sources
-gt
Elimination of Low Energy PointsElimination of Low Energy Points
0510 AM 57
- Blind Separation of Speech Mixtures
- Introduction
- Slide 3
- Slide 4
- Slide 5
- Approaches for BSS of Speech Signals
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Permutation Problem in Frequency Domain BSS
- Motivation
- My Contribution - I
- Algorithm for Solving the Permutation Problem
- Existing Method for Solving the Permutation Problem
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Proposed algorithm Partial separation method (Parallel configuration) Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
- Partial separation method (Parallel configuration)
- Partial separation method (Cascade configuration)
- Advantages of Partial Separation method
- Comparison with Adjacent Bands Correlation Method
- Comparison with DOA method
- My Contribution -II
- Underdetermined Blind Source Separation of Instantaneous Mixtures
- Mathematical Representation of Instantaneous Mixing Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
- Single Source Points in Time-Frequency domain
- Slide 31
- Slide 32
- Scatter Diagram of the Mixtures When Source are Perfectly Sparse
- Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
- Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
- Principle of the Proposed Algorithm for the Detection of Single Source Points
- Slide 39
- Slide 40
- Proposed Algorithm for the Detection of Single Source Points
- Elimination of Outliers
- Slide 43
- Detected Single Source Points Three mixtures
- Comparison with Classical Algorithms for Determined Case
- Comparison with Method Proposed in [1] Underdetermined case
- Advantages of the Proposed algorithm
- My Contributions ndash III IV and V
- Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
- Mathematical Representation
- Single source points
- Basic Principle of Single Source Points Detection
- Algorithm for Single Source Points Detection
- Mask Estimation by k-means (KM)
- Mask Estimation by Fuzzy c-means (FCM)
- Automatic Detection of Number of Sources
- Elimination of Low Energy Points
-
Approaches for BSS of Speech SignalsApproaches for BSS of Speech SignalsConvolutive Mixing
Time Domain Frequency Domain
QqltxlwyP
p
L
lpqpq 1)()(
1
1
0
)()()( tfftf SHX
)()()( tfftf XWY
AdvantageNo permutation problem
DisadvantageSlow convergence High computational cost for long filter taps
AdvantageLow computational costFast convergence
DisadvantagePermutation Problem
WHS1
S2
X1
X2
Y1 Y2
Y2 Y1
0510 AM 10
or
Permutation Problem in Frequency Domain BSS
Permutation Problem in Frequency Domain BSS
f1
f2
fk
x1x2
x3
BSS
BSS
BSSMixed signals
K po
int
FFT
y1y2y3
Still signals are mixed
K po
int
IFFT
Corresponding to different sources Due to permutation problem
One frequency binInstantaneous ICA algorithm
Solv
ing
perm
utati
on
Prob
lem y1
y2y3
Separated signals
Corresponding to y3
0510 AM 11
MotivationMotivation
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
12
My Contribution - IMy Contribution - I
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
13
Algorithm for Solving the Permutation Problem
Algorithm for Solving the Permutation Problem
f1
f2
fk
x1x2
x3
BSS
BSS
BSSMixed signals
K po
int
FFT
y1y2y3
Separated signals
K po
int
IFFT
Solv
ing
perm
utati
on
Prob
lem
Permutation problem
One frequency binInstantaneous ICA algorithm
Permutation problem solved
0510 AM 14
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Direction Of Arrival (DOA) method
2
1
)sin(2 1
p
dcfjkqpkq
pkefWfU Position of the pth sensor
Velocity of sound
)(
)(
)()(
)()(
)(
)(
2
1
2221
1211
2
1
k
k
kk
kk
k
k
fX
fX
fWfW
fWfW
fY
fY
0510 AM
Direction of y1 = -30o
Direction of y2 = 20o
15
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Reasons for failure at lower freq
Lower spacing causes error in phase difference measurement
The relation is approximated for plane wave front under anechoic condition
Disadvantages
Fails at lower frequenciesFails when sources are nearRoom reverberationSensor positions must be known
Direction Of Arrival (DOA) method
0510 AM 16
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
f1
f2
fk
BSS
BSS
BSSMixed signals
K po
int
FFT
y1y2y3
Separated signals
K po
int
IFFT
Solv
ing
perm
utati
on
Prob
lem
Low correlation
High correlationLow
correlation
x1x2
x3
Adjacent bands correlation method
0510 AM 17
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
r12
r21
r11
r22 r22 r22 r22
r11 r11 r11
r12
r21
r12
r21
r12
r21r11 r12
r21 r22
s1
s2
Correlation matrix
21122211 rrrr No change
21122211 rrrr Change permutation
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Adjacent bands correlation method
0510 AM
21122211 and and rrrr
21122211 and and rrrr
With confidence Without confidence
2090
8010
8020
1090
2090
1040
1040
2090
Example Example
18
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
r12
r21
r11
r22 r22 r22 r22
r11 r11 r11
r12
r21
r12
r21
r12
r21
r11 r12
r21 r22
s1
s2
Correlation matrix
Disadvantage The method is not robust
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Adjacent bands correlation method
0510 AM 19
0510 AM
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Combination of DOA and Correlation methods method
DOA + Harmonic Correlation + Adjacent bands correlation
Advantage Increased robustness
20
Proposed algorithm Partial separation method(Parallel configuration)
Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
Proposed algorithm Partial separation method(Parallel configuration)
Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
2y
1y
1x
2x
1s
2s
0510 AM 21
Time domain stage
Frequency domain stage
Partial separation method(Parallel configuration)
Partial separation method(Parallel configuration)
0510 AM 22
Time domain stage
Frequency domain stage
Parallel configuration
Partial separation method(Cascade configuration)
Partial separation method(Cascade configuration)
0510 AM 23
Time domain stage
Frequency domain stage
Advantages of Partial Separation methodAdvantages of Partial Separation method
bull Robustness
0510 AM 24
Comparison with Adjacent Bands Correlation Method
Comparison with Adjacent Bands Correlation Method
0510 AM 25
PS - Partial Separation method with confidence check C1 - Correlation between the adjacent bins without confidence check C2 - Correlation between adjacent bins with confidence check Ha - Correlation between the harmonic components with confidence check PS1 - Partial separation method alone without confidence check
0510 AM 26
Comparison with DOA methodComparison with DOA method
My Contribution -IIMy Contribution -II
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
27
Underdetermined Blind Source Separation of Instantaneous Mixtures
Underdetermined Blind Source Separation of Instantaneous Mixtures
t
k
0)(0)( 222221 tkStkS
0)(0)( 222221 tkStkS
0)(0)( 112111 tkStkS
0)(0)( 112111 tkStkS
tkX 1
tkX 22x
1x
0510 AM 28
Mathematical Representation of Instantaneous Mixing
Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
Mathematical Representation of Instantaneous Mixing
Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
)(
)(
)(
)( 1
1
1111
tkS
tkS
hh
hh
tkX
tkX
QPQP
Q
P
)(
)(
)(
)( 1
1
1111
ts
ts
hh
hh
tx
tx
QPQP
Q
P
)()()(11
1
1
11
tkS
h
h
tkS
h
h
tkS
h
h
Q
PQ
Q
q
Pq
q
P
)()()()( 21 tkStkStkStk QhhhX
Time domain
Time-Frequency domain
0510 AM 29
P ndash No of mixturesQ ndash No of sources
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
00point at 1 Case 11211111 tkStkStk
)()()( 1122111111 tkStkStk hhX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 2222221122 tkStkStk hhX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
0510 AM
0 0
30
Q
qqq tkStk
1
hX
2Let Q
00point at 1 Case 11211111 tkStkStk
)()( 111111 tkStk hX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()( 222222 tkStk hX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
0510 AM 31
00point at 1 Case 11211111 tkStkStk
)()( 111111 tkStk hX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()( 222222 tkStk hX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
Scalar
ScalarScalar
Scalar
At single source point 1 At single source point 2
111
111
ofDirection )( ofDirection
ofDirection )( ofDirection
hX
hX
tkI
tkR 222
222
ofDirection )( ofDirection
ofDirection )( ofDirection
hX
hX
tkI
tkR
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
0510 AM
1111 ( of Direction ( of Direction tkItkR XX 2222 ( of Direction ( of Direction tkItkR XX 32
Scatter Diagram of the Mixtures When Source are Perfectly Sparse
Scatter Diagram of the Mixtures When Source are Perfectly Sparse
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
22222
11111
2221
1211
22222
11111
kSkSkSkSkS
kSkSkSkSkS
hh
hh
kXkXkXkXkX
kXkXkXkXkX
21
111 h
hh
22
122 h
hh
0 00 0 0
Example
0510 AM 33
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
22222
11111
2221
1211
22222
11111
kSkSkSkSkS
kSkSkSkSkS
hh
hh
kXkXkXkXkX
kXkXkXkXkX
21
111 h
hh
22
122 h
hh
0 00 0 00
Example
Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
0510 AM 34
Scatter Diagram of the Mixtures when Sources are Sparse
Scatter Diagram of the Mixtures when Sources are Sparse
3h
6h
5h
1h4h
2h
0510 AM
No of sources = 6No of mixtures = 2
35
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
3h
6h
5h
1h4h
2h
0510 AM
No of sources = 6No of mixtures = 2
36
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
3h
6h
5h
1h4h
2h
0510 AM
ObjectiveEstimation of the single source points
No of sources = 6No of mixtures = 2
37
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Multi source point
38
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
Multi source point
39
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
Average of 15 pairs of speech utterances of length 10 s each
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
)( ofDirection )( ofDirection tkXItkXR )( ofDirection )( ofDirection tkXItkXR
SSPMSP
40
SSPt
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)()(
)()(
112112
111111
tkXjItkXR
tkXjItkXR
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXI
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXIMSP
)( 111 tkX
)( 112 tkX
cos
)()(
)()(
tkXItkXR
tkXItkXR T
Proposed Algorithm for the Detection of Single Source Points
Proposed Algorithm for the Detection of Single Source Points
0510 AM 41
Elimination of OutliersElimination of Outliers
SSPs detection
Clus
terin
g
Outlier elimination
0510 AM 42
0510 AM
Experimental ResultsExperimental Results
dB6747NMSE
No of mixtures =2 No of sources =6
43
Detected Single Source PointsThree mixtures
Detected Single Source PointsThree mixtures
No of mixtures =3 No of sources =60510 AM 44
Comparison with Classical Algorithms for Determined Case
Comparison with Classical Algorithms for Determined Case
No of mixtures =2No of sources =2
Average of 500 experimental results
0510 AM 45
-gt
Comparison with Method Proposed in [1] Underdetermined case
Comparison with Method Proposed in [1] Underdetermined case
[1] Y Li S Amari A Cichocki D W C Ho and S Xie ldquoUnderdetermined blind source separation based on sparse representationrdquo IEEE Transactions on Signal Processing vol 54 p 423ndash437 Feb 2006
0510 AM
Nor
mal
ized
mea
n sq
uare
err
or (N
MSE
) in
mix
ing
mat
rix e
stim
ation
(dB)
Order of the mixing matrices (PxQ)
46
P ndash No of mixturesQ ndash No of sources
Advantages of the Proposed algorithmAdvantages of the Proposed algorithm
Step 1 Convert x in the time domain to the TF domain to get XStep 2 Check the condition
Step 3 If the condition is satisfied then X(k t) is a sample atthe SSP and this sample is kept for mixing matrix estimationotherwise discard the point
Step 4 Repeat Steps 2 to 3 for all the points in the TF planeor until sufficient number of SSPs are obtained
cos
)()(
)()(
tkXItkXR
tkXItkXR T
1) Much simpler constrain the algorithm does not require ldquosingle source zonerdquo
3) The algorithm is extremely simple but effective2) Separation performance is better
0510 AM 47-gt
My Contributions ndash III IV and VMy Contributions ndash III IV and V
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
48
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Mask estimation
Mic 1
Mic P
Mixture in TF domain
Separated signals in TF domain
)( tkX P
)(1 tkX
t
t
k
k
)(1 tkY
)(1 tkY
)( tkYQ
)( tkYQ
QP
0510 AM 49
Mathematical RepresentationMathematical Representation
Q
q
L
lqpqp Pplnslhnx
1
1
0
1)()()(
)()()()()()()( 11 tkSktkSktkSktk QQqq HHHX
)(
)(
)()(
)()(
)(
)( 1
1
1111
tkS
tkS
kHkH
kHkH
tkX
tkX
QPQP
Q
P
)(
)(
)(
)(
)(
)(
)(
)(
)( 11
1
1
11
tkS
kH
kH
tkS
kH
kH
tkS
kH
kH
Q
PQ
Q
q
Pq
q
P
Time domain
Frequency domain
0510 AM 50
P ndash No of mixturesQ ndash No of sources
Single source pointsSingle source pointsInstantaneous mixing
00point at 1 Case 11211111 tkStkStk
)()()(
)()()(
111111
111111
tkSIktkI
tkSRktkR
HX
HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()(
)()()(
222222
222222
tkSIktkI
tkSRktkR
HX
HX
Single source point 2
Real scalar
RealReal
Real scalarReal scalar
Real scalar
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
0510 AM 51
Basic Principle of Single Source Points Detection
Basic Principle of Single Source Points Detection
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
j
H
C
e
cos21
21
UU
UUUUU H
and 20coscos HCH
angle pseudo called is
angleHermitian called is
H The Hermitian angle between the complex
vectors u1 and u2 will remain the same even if the vectors are multiplied by any complex scalars whereas the pseudo angle will change
0510 AM 52
-gt
k
Algorithm for Single Source Points Detection
Algorithm for Single Source Points Detection
t
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)(
)(
)(111
121
111 tkSkH
kH
11
11
j
jr
)(
)(
112
111
tkX
tkX
11
11
j
jr
)(
)(
112
111
tkX
tkX
)( 111 tkX
)( 112 tkX
)(
)(
)(112
122
112 tkSkH
kH θH2
θH1
θH2
rX
rX
)(
)(cos
11
111
tk
tk H
Hq
0510 AM 53
θH1
OR
1k
1k
1t
Clean
Estimated
Mask Estimation by k-means (KM)Mask Estimation by k-means (KM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 54
Clean
Estimated
Mask Estimation by Fuzzy c-means (FCM)Mask Estimation by Fuzzy c-means (FCM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 55
Automatic Detection of Number of SourcesAutomatic Detection of Number of Sources
0510 AM 56
Cluster validation technique
For c = 2 to cmax
Cluster the data into c clustersCalculate the cluster validation index
EndTake c corresponding to the best cluster as the number of sources
-gt
Elimination of Low Energy PointsElimination of Low Energy Points
0510 AM 57
- Blind Separation of Speech Mixtures
- Introduction
- Slide 3
- Slide 4
- Slide 5
- Approaches for BSS of Speech Signals
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Permutation Problem in Frequency Domain BSS
- Motivation
- My Contribution - I
- Algorithm for Solving the Permutation Problem
- Existing Method for Solving the Permutation Problem
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Proposed algorithm Partial separation method (Parallel configuration) Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
- Partial separation method (Parallel configuration)
- Partial separation method (Cascade configuration)
- Advantages of Partial Separation method
- Comparison with Adjacent Bands Correlation Method
- Comparison with DOA method
- My Contribution -II
- Underdetermined Blind Source Separation of Instantaneous Mixtures
- Mathematical Representation of Instantaneous Mixing Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
- Single Source Points in Time-Frequency domain
- Slide 31
- Slide 32
- Scatter Diagram of the Mixtures When Source are Perfectly Sparse
- Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
- Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
- Principle of the Proposed Algorithm for the Detection of Single Source Points
- Slide 39
- Slide 40
- Proposed Algorithm for the Detection of Single Source Points
- Elimination of Outliers
- Slide 43
- Detected Single Source Points Three mixtures
- Comparison with Classical Algorithms for Determined Case
- Comparison with Method Proposed in [1] Underdetermined case
- Advantages of the Proposed algorithm
- My Contributions ndash III IV and V
- Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
- Mathematical Representation
- Single source points
- Basic Principle of Single Source Points Detection
- Algorithm for Single Source Points Detection
- Mask Estimation by k-means (KM)
- Mask Estimation by Fuzzy c-means (FCM)
- Automatic Detection of Number of Sources
- Elimination of Low Energy Points
-
Permutation Problem in Frequency Domain BSS
Permutation Problem in Frequency Domain BSS
f1
f2
fk
x1x2
x3
BSS
BSS
BSSMixed signals
K po
int
FFT
y1y2y3
Still signals are mixed
K po
int
IFFT
Corresponding to different sources Due to permutation problem
One frequency binInstantaneous ICA algorithm
Solv
ing
perm
utati
on
Prob
lem y1
y2y3
Separated signals
Corresponding to y3
0510 AM 11
MotivationMotivation
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
12
My Contribution - IMy Contribution - I
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
13
Algorithm for Solving the Permutation Problem
Algorithm for Solving the Permutation Problem
f1
f2
fk
x1x2
x3
BSS
BSS
BSSMixed signals
K po
int
FFT
y1y2y3
Separated signals
K po
int
IFFT
Solv
ing
perm
utati
on
Prob
lem
Permutation problem
One frequency binInstantaneous ICA algorithm
Permutation problem solved
0510 AM 14
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Direction Of Arrival (DOA) method
2
1
)sin(2 1
p
dcfjkqpkq
pkefWfU Position of the pth sensor
Velocity of sound
)(
)(
)()(
)()(
)(
)(
2
1
2221
1211
2
1
k
k
kk
kk
k
k
fX
fX
fWfW
fWfW
fY
fY
0510 AM
Direction of y1 = -30o
Direction of y2 = 20o
15
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Reasons for failure at lower freq
Lower spacing causes error in phase difference measurement
The relation is approximated for plane wave front under anechoic condition
Disadvantages
Fails at lower frequenciesFails when sources are nearRoom reverberationSensor positions must be known
Direction Of Arrival (DOA) method
0510 AM 16
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
f1
f2
fk
BSS
BSS
BSSMixed signals
K po
int
FFT
y1y2y3
Separated signals
K po
int
IFFT
Solv
ing
perm
utati
on
Prob
lem
Low correlation
High correlationLow
correlation
x1x2
x3
Adjacent bands correlation method
0510 AM 17
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
r12
r21
r11
r22 r22 r22 r22
r11 r11 r11
r12
r21
r12
r21
r12
r21r11 r12
r21 r22
s1
s2
Correlation matrix
21122211 rrrr No change
21122211 rrrr Change permutation
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Adjacent bands correlation method
0510 AM
21122211 and and rrrr
21122211 and and rrrr
With confidence Without confidence
2090
8010
8020
1090
2090
1040
1040
2090
Example Example
18
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
r12
r21
r11
r22 r22 r22 r22
r11 r11 r11
r12
r21
r12
r21
r12
r21
r11 r12
r21 r22
s1
s2
Correlation matrix
Disadvantage The method is not robust
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Adjacent bands correlation method
0510 AM 19
0510 AM
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Combination of DOA and Correlation methods method
DOA + Harmonic Correlation + Adjacent bands correlation
Advantage Increased robustness
20
Proposed algorithm Partial separation method(Parallel configuration)
Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
Proposed algorithm Partial separation method(Parallel configuration)
Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
2y
1y
1x
2x
1s
2s
0510 AM 21
Time domain stage
Frequency domain stage
Partial separation method(Parallel configuration)
Partial separation method(Parallel configuration)
0510 AM 22
Time domain stage
Frequency domain stage
Parallel configuration
Partial separation method(Cascade configuration)
Partial separation method(Cascade configuration)
0510 AM 23
Time domain stage
Frequency domain stage
Advantages of Partial Separation methodAdvantages of Partial Separation method
bull Robustness
0510 AM 24
Comparison with Adjacent Bands Correlation Method
Comparison with Adjacent Bands Correlation Method
0510 AM 25
PS - Partial Separation method with confidence check C1 - Correlation between the adjacent bins without confidence check C2 - Correlation between adjacent bins with confidence check Ha - Correlation between the harmonic components with confidence check PS1 - Partial separation method alone without confidence check
0510 AM 26
Comparison with DOA methodComparison with DOA method
My Contribution -IIMy Contribution -II
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
27
Underdetermined Blind Source Separation of Instantaneous Mixtures
Underdetermined Blind Source Separation of Instantaneous Mixtures
t
k
0)(0)( 222221 tkStkS
0)(0)( 222221 tkStkS
0)(0)( 112111 tkStkS
0)(0)( 112111 tkStkS
tkX 1
tkX 22x
1x
0510 AM 28
Mathematical Representation of Instantaneous Mixing
Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
Mathematical Representation of Instantaneous Mixing
Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
)(
)(
)(
)( 1
1
1111
tkS
tkS
hh
hh
tkX
tkX
QPQP
Q
P
)(
)(
)(
)( 1
1
1111
ts
ts
hh
hh
tx
tx
QPQP
Q
P
)()()(11
1
1
11
tkS
h
h
tkS
h
h
tkS
h
h
Q
PQ
Q
q
Pq
q
P
)()()()( 21 tkStkStkStk QhhhX
Time domain
Time-Frequency domain
0510 AM 29
P ndash No of mixturesQ ndash No of sources
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
00point at 1 Case 11211111 tkStkStk
)()()( 1122111111 tkStkStk hhX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 2222221122 tkStkStk hhX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
0510 AM
0 0
30
Q
qqq tkStk
1
hX
2Let Q
00point at 1 Case 11211111 tkStkStk
)()( 111111 tkStk hX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()( 222222 tkStk hX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
0510 AM 31
00point at 1 Case 11211111 tkStkStk
)()( 111111 tkStk hX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()( 222222 tkStk hX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
Scalar
ScalarScalar
Scalar
At single source point 1 At single source point 2
111
111
ofDirection )( ofDirection
ofDirection )( ofDirection
hX
hX
tkI
tkR 222
222
ofDirection )( ofDirection
ofDirection )( ofDirection
hX
hX
tkI
tkR
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
0510 AM
1111 ( of Direction ( of Direction tkItkR XX 2222 ( of Direction ( of Direction tkItkR XX 32
Scatter Diagram of the Mixtures When Source are Perfectly Sparse
Scatter Diagram of the Mixtures When Source are Perfectly Sparse
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
22222
11111
2221
1211
22222
11111
kSkSkSkSkS
kSkSkSkSkS
hh
hh
kXkXkXkXkX
kXkXkXkXkX
21
111 h
hh
22
122 h
hh
0 00 0 0
Example
0510 AM 33
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
22222
11111
2221
1211
22222
11111
kSkSkSkSkS
kSkSkSkSkS
hh
hh
kXkXkXkXkX
kXkXkXkXkX
21
111 h
hh
22
122 h
hh
0 00 0 00
Example
Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
0510 AM 34
Scatter Diagram of the Mixtures when Sources are Sparse
Scatter Diagram of the Mixtures when Sources are Sparse
3h
6h
5h
1h4h
2h
0510 AM
No of sources = 6No of mixtures = 2
35
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
3h
6h
5h
1h4h
2h
0510 AM
No of sources = 6No of mixtures = 2
36
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
3h
6h
5h
1h4h
2h
0510 AM
ObjectiveEstimation of the single source points
No of sources = 6No of mixtures = 2
37
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Multi source point
38
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
Multi source point
39
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
Average of 15 pairs of speech utterances of length 10 s each
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
)( ofDirection )( ofDirection tkXItkXR )( ofDirection )( ofDirection tkXItkXR
SSPMSP
40
SSPt
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)()(
)()(
112112
111111
tkXjItkXR
tkXjItkXR
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXI
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXIMSP
)( 111 tkX
)( 112 tkX
cos
)()(
)()(
tkXItkXR
tkXItkXR T
Proposed Algorithm for the Detection of Single Source Points
Proposed Algorithm for the Detection of Single Source Points
0510 AM 41
Elimination of OutliersElimination of Outliers
SSPs detection
Clus
terin
g
Outlier elimination
0510 AM 42
0510 AM
Experimental ResultsExperimental Results
dB6747NMSE
No of mixtures =2 No of sources =6
43
Detected Single Source PointsThree mixtures
Detected Single Source PointsThree mixtures
No of mixtures =3 No of sources =60510 AM 44
Comparison with Classical Algorithms for Determined Case
Comparison with Classical Algorithms for Determined Case
No of mixtures =2No of sources =2
Average of 500 experimental results
0510 AM 45
-gt
Comparison with Method Proposed in [1] Underdetermined case
Comparison with Method Proposed in [1] Underdetermined case
[1] Y Li S Amari A Cichocki D W C Ho and S Xie ldquoUnderdetermined blind source separation based on sparse representationrdquo IEEE Transactions on Signal Processing vol 54 p 423ndash437 Feb 2006
0510 AM
Nor
mal
ized
mea
n sq
uare
err
or (N
MSE
) in
mix
ing
mat
rix e
stim
ation
(dB)
Order of the mixing matrices (PxQ)
46
P ndash No of mixturesQ ndash No of sources
Advantages of the Proposed algorithmAdvantages of the Proposed algorithm
Step 1 Convert x in the time domain to the TF domain to get XStep 2 Check the condition
Step 3 If the condition is satisfied then X(k t) is a sample atthe SSP and this sample is kept for mixing matrix estimationotherwise discard the point
Step 4 Repeat Steps 2 to 3 for all the points in the TF planeor until sufficient number of SSPs are obtained
cos
)()(
)()(
tkXItkXR
tkXItkXR T
1) Much simpler constrain the algorithm does not require ldquosingle source zonerdquo
3) The algorithm is extremely simple but effective2) Separation performance is better
0510 AM 47-gt
My Contributions ndash III IV and VMy Contributions ndash III IV and V
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
48
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Mask estimation
Mic 1
Mic P
Mixture in TF domain
Separated signals in TF domain
)( tkX P
)(1 tkX
t
t
k
k
)(1 tkY
)(1 tkY
)( tkYQ
)( tkYQ
QP
0510 AM 49
Mathematical RepresentationMathematical Representation
Q
q
L
lqpqp Pplnslhnx
1
1
0
1)()()(
)()()()()()()( 11 tkSktkSktkSktk QQqq HHHX
)(
)(
)()(
)()(
)(
)( 1
1
1111
tkS
tkS
kHkH
kHkH
tkX
tkX
QPQP
Q
P
)(
)(
)(
)(
)(
)(
)(
)(
)( 11
1
1
11
tkS
kH
kH
tkS
kH
kH
tkS
kH
kH
Q
PQ
Q
q
Pq
q
P
Time domain
Frequency domain
0510 AM 50
P ndash No of mixturesQ ndash No of sources
Single source pointsSingle source pointsInstantaneous mixing
00point at 1 Case 11211111 tkStkStk
)()()(
)()()(
111111
111111
tkSIktkI
tkSRktkR
HX
HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()(
)()()(
222222
222222
tkSIktkI
tkSRktkR
HX
HX
Single source point 2
Real scalar
RealReal
Real scalarReal scalar
Real scalar
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
0510 AM 51
Basic Principle of Single Source Points Detection
Basic Principle of Single Source Points Detection
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
j
H
C
e
cos21
21
UU
UUUUU H
and 20coscos HCH
angle pseudo called is
angleHermitian called is
H The Hermitian angle between the complex
vectors u1 and u2 will remain the same even if the vectors are multiplied by any complex scalars whereas the pseudo angle will change
0510 AM 52
-gt
k
Algorithm for Single Source Points Detection
Algorithm for Single Source Points Detection
t
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)(
)(
)(111
121
111 tkSkH
kH
11
11
j
jr
)(
)(
112
111
tkX
tkX
11
11
j
jr
)(
)(
112
111
tkX
tkX
)( 111 tkX
)( 112 tkX
)(
)(
)(112
122
112 tkSkH
kH θH2
θH1
θH2
rX
rX
)(
)(cos
11
111
tk
tk H
Hq
0510 AM 53
θH1
OR
1k
1k
1t
Clean
Estimated
Mask Estimation by k-means (KM)Mask Estimation by k-means (KM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 54
Clean
Estimated
Mask Estimation by Fuzzy c-means (FCM)Mask Estimation by Fuzzy c-means (FCM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 55
Automatic Detection of Number of SourcesAutomatic Detection of Number of Sources
0510 AM 56
Cluster validation technique
For c = 2 to cmax
Cluster the data into c clustersCalculate the cluster validation index
EndTake c corresponding to the best cluster as the number of sources
-gt
Elimination of Low Energy PointsElimination of Low Energy Points
0510 AM 57
- Blind Separation of Speech Mixtures
- Introduction
- Slide 3
- Slide 4
- Slide 5
- Approaches for BSS of Speech Signals
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Permutation Problem in Frequency Domain BSS
- Motivation
- My Contribution - I
- Algorithm for Solving the Permutation Problem
- Existing Method for Solving the Permutation Problem
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Proposed algorithm Partial separation method (Parallel configuration) Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
- Partial separation method (Parallel configuration)
- Partial separation method (Cascade configuration)
- Advantages of Partial Separation method
- Comparison with Adjacent Bands Correlation Method
- Comparison with DOA method
- My Contribution -II
- Underdetermined Blind Source Separation of Instantaneous Mixtures
- Mathematical Representation of Instantaneous Mixing Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
- Single Source Points in Time-Frequency domain
- Slide 31
- Slide 32
- Scatter Diagram of the Mixtures When Source are Perfectly Sparse
- Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
- Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
- Principle of the Proposed Algorithm for the Detection of Single Source Points
- Slide 39
- Slide 40
- Proposed Algorithm for the Detection of Single Source Points
- Elimination of Outliers
- Slide 43
- Detected Single Source Points Three mixtures
- Comparison with Classical Algorithms for Determined Case
- Comparison with Method Proposed in [1] Underdetermined case
- Advantages of the Proposed algorithm
- My Contributions ndash III IV and V
- Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
- Mathematical Representation
- Single source points
- Basic Principle of Single Source Points Detection
- Algorithm for Single Source Points Detection
- Mask Estimation by k-means (KM)
- Mask Estimation by Fuzzy c-means (FCM)
- Automatic Detection of Number of Sources
- Elimination of Low Energy Points
-
MotivationMotivation
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
12
My Contribution - IMy Contribution - I
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
13
Algorithm for Solving the Permutation Problem
Algorithm for Solving the Permutation Problem
f1
f2
fk
x1x2
x3
BSS
BSS
BSSMixed signals
K po
int
FFT
y1y2y3
Separated signals
K po
int
IFFT
Solv
ing
perm
utati
on
Prob
lem
Permutation problem
One frequency binInstantaneous ICA algorithm
Permutation problem solved
0510 AM 14
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Direction Of Arrival (DOA) method
2
1
)sin(2 1
p
dcfjkqpkq
pkefWfU Position of the pth sensor
Velocity of sound
)(
)(
)()(
)()(
)(
)(
2
1
2221
1211
2
1
k
k
kk
kk
k
k
fX
fX
fWfW
fWfW
fY
fY
0510 AM
Direction of y1 = -30o
Direction of y2 = 20o
15
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Reasons for failure at lower freq
Lower spacing causes error in phase difference measurement
The relation is approximated for plane wave front under anechoic condition
Disadvantages
Fails at lower frequenciesFails when sources are nearRoom reverberationSensor positions must be known
Direction Of Arrival (DOA) method
0510 AM 16
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
f1
f2
fk
BSS
BSS
BSSMixed signals
K po
int
FFT
y1y2y3
Separated signals
K po
int
IFFT
Solv
ing
perm
utati
on
Prob
lem
Low correlation
High correlationLow
correlation
x1x2
x3
Adjacent bands correlation method
0510 AM 17
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
r12
r21
r11
r22 r22 r22 r22
r11 r11 r11
r12
r21
r12
r21
r12
r21r11 r12
r21 r22
s1
s2
Correlation matrix
21122211 rrrr No change
21122211 rrrr Change permutation
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Adjacent bands correlation method
0510 AM
21122211 and and rrrr
21122211 and and rrrr
With confidence Without confidence
2090
8010
8020
1090
2090
1040
1040
2090
Example Example
18
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
r12
r21
r11
r22 r22 r22 r22
r11 r11 r11
r12
r21
r12
r21
r12
r21
r11 r12
r21 r22
s1
s2
Correlation matrix
Disadvantage The method is not robust
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Adjacent bands correlation method
0510 AM 19
0510 AM
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Combination of DOA and Correlation methods method
DOA + Harmonic Correlation + Adjacent bands correlation
Advantage Increased robustness
20
Proposed algorithm Partial separation method(Parallel configuration)
Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
Proposed algorithm Partial separation method(Parallel configuration)
Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
2y
1y
1x
2x
1s
2s
0510 AM 21
Time domain stage
Frequency domain stage
Partial separation method(Parallel configuration)
Partial separation method(Parallel configuration)
0510 AM 22
Time domain stage
Frequency domain stage
Parallel configuration
Partial separation method(Cascade configuration)
Partial separation method(Cascade configuration)
0510 AM 23
Time domain stage
Frequency domain stage
Advantages of Partial Separation methodAdvantages of Partial Separation method
bull Robustness
0510 AM 24
Comparison with Adjacent Bands Correlation Method
Comparison with Adjacent Bands Correlation Method
0510 AM 25
PS - Partial Separation method with confidence check C1 - Correlation between the adjacent bins without confidence check C2 - Correlation between adjacent bins with confidence check Ha - Correlation between the harmonic components with confidence check PS1 - Partial separation method alone without confidence check
0510 AM 26
Comparison with DOA methodComparison with DOA method
My Contribution -IIMy Contribution -II
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
27
Underdetermined Blind Source Separation of Instantaneous Mixtures
Underdetermined Blind Source Separation of Instantaneous Mixtures
t
k
0)(0)( 222221 tkStkS
0)(0)( 222221 tkStkS
0)(0)( 112111 tkStkS
0)(0)( 112111 tkStkS
tkX 1
tkX 22x
1x
0510 AM 28
Mathematical Representation of Instantaneous Mixing
Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
Mathematical Representation of Instantaneous Mixing
Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
)(
)(
)(
)( 1
1
1111
tkS
tkS
hh
hh
tkX
tkX
QPQP
Q
P
)(
)(
)(
)( 1
1
1111
ts
ts
hh
hh
tx
tx
QPQP
Q
P
)()()(11
1
1
11
tkS
h
h
tkS
h
h
tkS
h
h
Q
PQ
Q
q
Pq
q
P
)()()()( 21 tkStkStkStk QhhhX
Time domain
Time-Frequency domain
0510 AM 29
P ndash No of mixturesQ ndash No of sources
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
00point at 1 Case 11211111 tkStkStk
)()()( 1122111111 tkStkStk hhX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 2222221122 tkStkStk hhX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
0510 AM
0 0
30
Q
qqq tkStk
1
hX
2Let Q
00point at 1 Case 11211111 tkStkStk
)()( 111111 tkStk hX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()( 222222 tkStk hX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
0510 AM 31
00point at 1 Case 11211111 tkStkStk
)()( 111111 tkStk hX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()( 222222 tkStk hX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
Scalar
ScalarScalar
Scalar
At single source point 1 At single source point 2
111
111
ofDirection )( ofDirection
ofDirection )( ofDirection
hX
hX
tkI
tkR 222
222
ofDirection )( ofDirection
ofDirection )( ofDirection
hX
hX
tkI
tkR
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
0510 AM
1111 ( of Direction ( of Direction tkItkR XX 2222 ( of Direction ( of Direction tkItkR XX 32
Scatter Diagram of the Mixtures When Source are Perfectly Sparse
Scatter Diagram of the Mixtures When Source are Perfectly Sparse
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
22222
11111
2221
1211
22222
11111
kSkSkSkSkS
kSkSkSkSkS
hh
hh
kXkXkXkXkX
kXkXkXkXkX
21
111 h
hh
22
122 h
hh
0 00 0 0
Example
0510 AM 33
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
22222
11111
2221
1211
22222
11111
kSkSkSkSkS
kSkSkSkSkS
hh
hh
kXkXkXkXkX
kXkXkXkXkX
21
111 h
hh
22
122 h
hh
0 00 0 00
Example
Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
0510 AM 34
Scatter Diagram of the Mixtures when Sources are Sparse
Scatter Diagram of the Mixtures when Sources are Sparse
3h
6h
5h
1h4h
2h
0510 AM
No of sources = 6No of mixtures = 2
35
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
3h
6h
5h
1h4h
2h
0510 AM
No of sources = 6No of mixtures = 2
36
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
3h
6h
5h
1h4h
2h
0510 AM
ObjectiveEstimation of the single source points
No of sources = 6No of mixtures = 2
37
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Multi source point
38
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
Multi source point
39
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
Average of 15 pairs of speech utterances of length 10 s each
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
)( ofDirection )( ofDirection tkXItkXR )( ofDirection )( ofDirection tkXItkXR
SSPMSP
40
SSPt
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)()(
)()(
112112
111111
tkXjItkXR
tkXjItkXR
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXI
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXIMSP
)( 111 tkX
)( 112 tkX
cos
)()(
)()(
tkXItkXR
tkXItkXR T
Proposed Algorithm for the Detection of Single Source Points
Proposed Algorithm for the Detection of Single Source Points
0510 AM 41
Elimination of OutliersElimination of Outliers
SSPs detection
Clus
terin
g
Outlier elimination
0510 AM 42
0510 AM
Experimental ResultsExperimental Results
dB6747NMSE
No of mixtures =2 No of sources =6
43
Detected Single Source PointsThree mixtures
Detected Single Source PointsThree mixtures
No of mixtures =3 No of sources =60510 AM 44
Comparison with Classical Algorithms for Determined Case
Comparison with Classical Algorithms for Determined Case
No of mixtures =2No of sources =2
Average of 500 experimental results
0510 AM 45
-gt
Comparison with Method Proposed in [1] Underdetermined case
Comparison with Method Proposed in [1] Underdetermined case
[1] Y Li S Amari A Cichocki D W C Ho and S Xie ldquoUnderdetermined blind source separation based on sparse representationrdquo IEEE Transactions on Signal Processing vol 54 p 423ndash437 Feb 2006
0510 AM
Nor
mal
ized
mea
n sq
uare
err
or (N
MSE
) in
mix
ing
mat
rix e
stim
ation
(dB)
Order of the mixing matrices (PxQ)
46
P ndash No of mixturesQ ndash No of sources
Advantages of the Proposed algorithmAdvantages of the Proposed algorithm
Step 1 Convert x in the time domain to the TF domain to get XStep 2 Check the condition
Step 3 If the condition is satisfied then X(k t) is a sample atthe SSP and this sample is kept for mixing matrix estimationotherwise discard the point
Step 4 Repeat Steps 2 to 3 for all the points in the TF planeor until sufficient number of SSPs are obtained
cos
)()(
)()(
tkXItkXR
tkXItkXR T
1) Much simpler constrain the algorithm does not require ldquosingle source zonerdquo
3) The algorithm is extremely simple but effective2) Separation performance is better
0510 AM 47-gt
My Contributions ndash III IV and VMy Contributions ndash III IV and V
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
48
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Mask estimation
Mic 1
Mic P
Mixture in TF domain
Separated signals in TF domain
)( tkX P
)(1 tkX
t
t
k
k
)(1 tkY
)(1 tkY
)( tkYQ
)( tkYQ
QP
0510 AM 49
Mathematical RepresentationMathematical Representation
Q
q
L
lqpqp Pplnslhnx
1
1
0
1)()()(
)()()()()()()( 11 tkSktkSktkSktk QQqq HHHX
)(
)(
)()(
)()(
)(
)( 1
1
1111
tkS
tkS
kHkH
kHkH
tkX
tkX
QPQP
Q
P
)(
)(
)(
)(
)(
)(
)(
)(
)( 11
1
1
11
tkS
kH
kH
tkS
kH
kH
tkS
kH
kH
Q
PQ
Q
q
Pq
q
P
Time domain
Frequency domain
0510 AM 50
P ndash No of mixturesQ ndash No of sources
Single source pointsSingle source pointsInstantaneous mixing
00point at 1 Case 11211111 tkStkStk
)()()(
)()()(
111111
111111
tkSIktkI
tkSRktkR
HX
HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()(
)()()(
222222
222222
tkSIktkI
tkSRktkR
HX
HX
Single source point 2
Real scalar
RealReal
Real scalarReal scalar
Real scalar
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
0510 AM 51
Basic Principle of Single Source Points Detection
Basic Principle of Single Source Points Detection
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
j
H
C
e
cos21
21
UU
UUUUU H
and 20coscos HCH
angle pseudo called is
angleHermitian called is
H The Hermitian angle between the complex
vectors u1 and u2 will remain the same even if the vectors are multiplied by any complex scalars whereas the pseudo angle will change
0510 AM 52
-gt
k
Algorithm for Single Source Points Detection
Algorithm for Single Source Points Detection
t
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)(
)(
)(111
121
111 tkSkH
kH
11
11
j
jr
)(
)(
112
111
tkX
tkX
11
11
j
jr
)(
)(
112
111
tkX
tkX
)( 111 tkX
)( 112 tkX
)(
)(
)(112
122
112 tkSkH
kH θH2
θH1
θH2
rX
rX
)(
)(cos
11
111
tk
tk H
Hq
0510 AM 53
θH1
OR
1k
1k
1t
Clean
Estimated
Mask Estimation by k-means (KM)Mask Estimation by k-means (KM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 54
Clean
Estimated
Mask Estimation by Fuzzy c-means (FCM)Mask Estimation by Fuzzy c-means (FCM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 55
Automatic Detection of Number of SourcesAutomatic Detection of Number of Sources
0510 AM 56
Cluster validation technique
For c = 2 to cmax
Cluster the data into c clustersCalculate the cluster validation index
EndTake c corresponding to the best cluster as the number of sources
-gt
Elimination of Low Energy PointsElimination of Low Energy Points
0510 AM 57
- Blind Separation of Speech Mixtures
- Introduction
- Slide 3
- Slide 4
- Slide 5
- Approaches for BSS of Speech Signals
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Permutation Problem in Frequency Domain BSS
- Motivation
- My Contribution - I
- Algorithm for Solving the Permutation Problem
- Existing Method for Solving the Permutation Problem
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Proposed algorithm Partial separation method (Parallel configuration) Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
- Partial separation method (Parallel configuration)
- Partial separation method (Cascade configuration)
- Advantages of Partial Separation method
- Comparison with Adjacent Bands Correlation Method
- Comparison with DOA method
- My Contribution -II
- Underdetermined Blind Source Separation of Instantaneous Mixtures
- Mathematical Representation of Instantaneous Mixing Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
- Single Source Points in Time-Frequency domain
- Slide 31
- Slide 32
- Scatter Diagram of the Mixtures When Source are Perfectly Sparse
- Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
- Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
- Principle of the Proposed Algorithm for the Detection of Single Source Points
- Slide 39
- Slide 40
- Proposed Algorithm for the Detection of Single Source Points
- Elimination of Outliers
- Slide 43
- Detected Single Source Points Three mixtures
- Comparison with Classical Algorithms for Determined Case
- Comparison with Method Proposed in [1] Underdetermined case
- Advantages of the Proposed algorithm
- My Contributions ndash III IV and V
- Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
- Mathematical Representation
- Single source points
- Basic Principle of Single Source Points Detection
- Algorithm for Single Source Points Detection
- Mask Estimation by k-means (KM)
- Mask Estimation by Fuzzy c-means (FCM)
- Automatic Detection of Number of Sources
- Elimination of Low Energy Points
-
My Contribution - IMy Contribution - I
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
13
Algorithm for Solving the Permutation Problem
Algorithm for Solving the Permutation Problem
f1
f2
fk
x1x2
x3
BSS
BSS
BSSMixed signals
K po
int
FFT
y1y2y3
Separated signals
K po
int
IFFT
Solv
ing
perm
utati
on
Prob
lem
Permutation problem
One frequency binInstantaneous ICA algorithm
Permutation problem solved
0510 AM 14
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Direction Of Arrival (DOA) method
2
1
)sin(2 1
p
dcfjkqpkq
pkefWfU Position of the pth sensor
Velocity of sound
)(
)(
)()(
)()(
)(
)(
2
1
2221
1211
2
1
k
k
kk
kk
k
k
fX
fX
fWfW
fWfW
fY
fY
0510 AM
Direction of y1 = -30o
Direction of y2 = 20o
15
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Reasons for failure at lower freq
Lower spacing causes error in phase difference measurement
The relation is approximated for plane wave front under anechoic condition
Disadvantages
Fails at lower frequenciesFails when sources are nearRoom reverberationSensor positions must be known
Direction Of Arrival (DOA) method
0510 AM 16
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
f1
f2
fk
BSS
BSS
BSSMixed signals
K po
int
FFT
y1y2y3
Separated signals
K po
int
IFFT
Solv
ing
perm
utati
on
Prob
lem
Low correlation
High correlationLow
correlation
x1x2
x3
Adjacent bands correlation method
0510 AM 17
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
r12
r21
r11
r22 r22 r22 r22
r11 r11 r11
r12
r21
r12
r21
r12
r21r11 r12
r21 r22
s1
s2
Correlation matrix
21122211 rrrr No change
21122211 rrrr Change permutation
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Adjacent bands correlation method
0510 AM
21122211 and and rrrr
21122211 and and rrrr
With confidence Without confidence
2090
8010
8020
1090
2090
1040
1040
2090
Example Example
18
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
r12
r21
r11
r22 r22 r22 r22
r11 r11 r11
r12
r21
r12
r21
r12
r21
r11 r12
r21 r22
s1
s2
Correlation matrix
Disadvantage The method is not robust
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Adjacent bands correlation method
0510 AM 19
0510 AM
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Combination of DOA and Correlation methods method
DOA + Harmonic Correlation + Adjacent bands correlation
Advantage Increased robustness
20
Proposed algorithm Partial separation method(Parallel configuration)
Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
Proposed algorithm Partial separation method(Parallel configuration)
Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
2y
1y
1x
2x
1s
2s
0510 AM 21
Time domain stage
Frequency domain stage
Partial separation method(Parallel configuration)
Partial separation method(Parallel configuration)
0510 AM 22
Time domain stage
Frequency domain stage
Parallel configuration
Partial separation method(Cascade configuration)
Partial separation method(Cascade configuration)
0510 AM 23
Time domain stage
Frequency domain stage
Advantages of Partial Separation methodAdvantages of Partial Separation method
bull Robustness
0510 AM 24
Comparison with Adjacent Bands Correlation Method
Comparison with Adjacent Bands Correlation Method
0510 AM 25
PS - Partial Separation method with confidence check C1 - Correlation between the adjacent bins without confidence check C2 - Correlation between adjacent bins with confidence check Ha - Correlation between the harmonic components with confidence check PS1 - Partial separation method alone without confidence check
0510 AM 26
Comparison with DOA methodComparison with DOA method
My Contribution -IIMy Contribution -II
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
27
Underdetermined Blind Source Separation of Instantaneous Mixtures
Underdetermined Blind Source Separation of Instantaneous Mixtures
t
k
0)(0)( 222221 tkStkS
0)(0)( 222221 tkStkS
0)(0)( 112111 tkStkS
0)(0)( 112111 tkStkS
tkX 1
tkX 22x
1x
0510 AM 28
Mathematical Representation of Instantaneous Mixing
Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
Mathematical Representation of Instantaneous Mixing
Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
)(
)(
)(
)( 1
1
1111
tkS
tkS
hh
hh
tkX
tkX
QPQP
Q
P
)(
)(
)(
)( 1
1
1111
ts
ts
hh
hh
tx
tx
QPQP
Q
P
)()()(11
1
1
11
tkS
h
h
tkS
h
h
tkS
h
h
Q
PQ
Q
q
Pq
q
P
)()()()( 21 tkStkStkStk QhhhX
Time domain
Time-Frequency domain
0510 AM 29
P ndash No of mixturesQ ndash No of sources
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
00point at 1 Case 11211111 tkStkStk
)()()( 1122111111 tkStkStk hhX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 2222221122 tkStkStk hhX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
0510 AM
0 0
30
Q
qqq tkStk
1
hX
2Let Q
00point at 1 Case 11211111 tkStkStk
)()( 111111 tkStk hX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()( 222222 tkStk hX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
0510 AM 31
00point at 1 Case 11211111 tkStkStk
)()( 111111 tkStk hX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()( 222222 tkStk hX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
Scalar
ScalarScalar
Scalar
At single source point 1 At single source point 2
111
111
ofDirection )( ofDirection
ofDirection )( ofDirection
hX
hX
tkI
tkR 222
222
ofDirection )( ofDirection
ofDirection )( ofDirection
hX
hX
tkI
tkR
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
0510 AM
1111 ( of Direction ( of Direction tkItkR XX 2222 ( of Direction ( of Direction tkItkR XX 32
Scatter Diagram of the Mixtures When Source are Perfectly Sparse
Scatter Diagram of the Mixtures When Source are Perfectly Sparse
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
22222
11111
2221
1211
22222
11111
kSkSkSkSkS
kSkSkSkSkS
hh
hh
kXkXkXkXkX
kXkXkXkXkX
21
111 h
hh
22
122 h
hh
0 00 0 0
Example
0510 AM 33
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
22222
11111
2221
1211
22222
11111
kSkSkSkSkS
kSkSkSkSkS
hh
hh
kXkXkXkXkX
kXkXkXkXkX
21
111 h
hh
22
122 h
hh
0 00 0 00
Example
Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
0510 AM 34
Scatter Diagram of the Mixtures when Sources are Sparse
Scatter Diagram of the Mixtures when Sources are Sparse
3h
6h
5h
1h4h
2h
0510 AM
No of sources = 6No of mixtures = 2
35
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
3h
6h
5h
1h4h
2h
0510 AM
No of sources = 6No of mixtures = 2
36
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
3h
6h
5h
1h4h
2h
0510 AM
ObjectiveEstimation of the single source points
No of sources = 6No of mixtures = 2
37
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Multi source point
38
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
Multi source point
39
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
Average of 15 pairs of speech utterances of length 10 s each
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
)( ofDirection )( ofDirection tkXItkXR )( ofDirection )( ofDirection tkXItkXR
SSPMSP
40
SSPt
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)()(
)()(
112112
111111
tkXjItkXR
tkXjItkXR
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXI
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXIMSP
)( 111 tkX
)( 112 tkX
cos
)()(
)()(
tkXItkXR
tkXItkXR T
Proposed Algorithm for the Detection of Single Source Points
Proposed Algorithm for the Detection of Single Source Points
0510 AM 41
Elimination of OutliersElimination of Outliers
SSPs detection
Clus
terin
g
Outlier elimination
0510 AM 42
0510 AM
Experimental ResultsExperimental Results
dB6747NMSE
No of mixtures =2 No of sources =6
43
Detected Single Source PointsThree mixtures
Detected Single Source PointsThree mixtures
No of mixtures =3 No of sources =60510 AM 44
Comparison with Classical Algorithms for Determined Case
Comparison with Classical Algorithms for Determined Case
No of mixtures =2No of sources =2
Average of 500 experimental results
0510 AM 45
-gt
Comparison with Method Proposed in [1] Underdetermined case
Comparison with Method Proposed in [1] Underdetermined case
[1] Y Li S Amari A Cichocki D W C Ho and S Xie ldquoUnderdetermined blind source separation based on sparse representationrdquo IEEE Transactions on Signal Processing vol 54 p 423ndash437 Feb 2006
0510 AM
Nor
mal
ized
mea
n sq
uare
err
or (N
MSE
) in
mix
ing
mat
rix e
stim
ation
(dB)
Order of the mixing matrices (PxQ)
46
P ndash No of mixturesQ ndash No of sources
Advantages of the Proposed algorithmAdvantages of the Proposed algorithm
Step 1 Convert x in the time domain to the TF domain to get XStep 2 Check the condition
Step 3 If the condition is satisfied then X(k t) is a sample atthe SSP and this sample is kept for mixing matrix estimationotherwise discard the point
Step 4 Repeat Steps 2 to 3 for all the points in the TF planeor until sufficient number of SSPs are obtained
cos
)()(
)()(
tkXItkXR
tkXItkXR T
1) Much simpler constrain the algorithm does not require ldquosingle source zonerdquo
3) The algorithm is extremely simple but effective2) Separation performance is better
0510 AM 47-gt
My Contributions ndash III IV and VMy Contributions ndash III IV and V
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
48
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Mask estimation
Mic 1
Mic P
Mixture in TF domain
Separated signals in TF domain
)( tkX P
)(1 tkX
t
t
k
k
)(1 tkY
)(1 tkY
)( tkYQ
)( tkYQ
QP
0510 AM 49
Mathematical RepresentationMathematical Representation
Q
q
L
lqpqp Pplnslhnx
1
1
0
1)()()(
)()()()()()()( 11 tkSktkSktkSktk QQqq HHHX
)(
)(
)()(
)()(
)(
)( 1
1
1111
tkS
tkS
kHkH
kHkH
tkX
tkX
QPQP
Q
P
)(
)(
)(
)(
)(
)(
)(
)(
)( 11
1
1
11
tkS
kH
kH
tkS
kH
kH
tkS
kH
kH
Q
PQ
Q
q
Pq
q
P
Time domain
Frequency domain
0510 AM 50
P ndash No of mixturesQ ndash No of sources
Single source pointsSingle source pointsInstantaneous mixing
00point at 1 Case 11211111 tkStkStk
)()()(
)()()(
111111
111111
tkSIktkI
tkSRktkR
HX
HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()(
)()()(
222222
222222
tkSIktkI
tkSRktkR
HX
HX
Single source point 2
Real scalar
RealReal
Real scalarReal scalar
Real scalar
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
0510 AM 51
Basic Principle of Single Source Points Detection
Basic Principle of Single Source Points Detection
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
j
H
C
e
cos21
21
UU
UUUUU H
and 20coscos HCH
angle pseudo called is
angleHermitian called is
H The Hermitian angle between the complex
vectors u1 and u2 will remain the same even if the vectors are multiplied by any complex scalars whereas the pseudo angle will change
0510 AM 52
-gt
k
Algorithm for Single Source Points Detection
Algorithm for Single Source Points Detection
t
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)(
)(
)(111
121
111 tkSkH
kH
11
11
j
jr
)(
)(
112
111
tkX
tkX
11
11
j
jr
)(
)(
112
111
tkX
tkX
)( 111 tkX
)( 112 tkX
)(
)(
)(112
122
112 tkSkH
kH θH2
θH1
θH2
rX
rX
)(
)(cos
11
111
tk
tk H
Hq
0510 AM 53
θH1
OR
1k
1k
1t
Clean
Estimated
Mask Estimation by k-means (KM)Mask Estimation by k-means (KM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 54
Clean
Estimated
Mask Estimation by Fuzzy c-means (FCM)Mask Estimation by Fuzzy c-means (FCM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 55
Automatic Detection of Number of SourcesAutomatic Detection of Number of Sources
0510 AM 56
Cluster validation technique
For c = 2 to cmax
Cluster the data into c clustersCalculate the cluster validation index
EndTake c corresponding to the best cluster as the number of sources
-gt
Elimination of Low Energy PointsElimination of Low Energy Points
0510 AM 57
- Blind Separation of Speech Mixtures
- Introduction
- Slide 3
- Slide 4
- Slide 5
- Approaches for BSS of Speech Signals
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Permutation Problem in Frequency Domain BSS
- Motivation
- My Contribution - I
- Algorithm for Solving the Permutation Problem
- Existing Method for Solving the Permutation Problem
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Proposed algorithm Partial separation method (Parallel configuration) Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
- Partial separation method (Parallel configuration)
- Partial separation method (Cascade configuration)
- Advantages of Partial Separation method
- Comparison with Adjacent Bands Correlation Method
- Comparison with DOA method
- My Contribution -II
- Underdetermined Blind Source Separation of Instantaneous Mixtures
- Mathematical Representation of Instantaneous Mixing Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
- Single Source Points in Time-Frequency domain
- Slide 31
- Slide 32
- Scatter Diagram of the Mixtures When Source are Perfectly Sparse
- Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
- Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
- Principle of the Proposed Algorithm for the Detection of Single Source Points
- Slide 39
- Slide 40
- Proposed Algorithm for the Detection of Single Source Points
- Elimination of Outliers
- Slide 43
- Detected Single Source Points Three mixtures
- Comparison with Classical Algorithms for Determined Case
- Comparison with Method Proposed in [1] Underdetermined case
- Advantages of the Proposed algorithm
- My Contributions ndash III IV and V
- Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
- Mathematical Representation
- Single source points
- Basic Principle of Single Source Points Detection
- Algorithm for Single Source Points Detection
- Mask Estimation by k-means (KM)
- Mask Estimation by Fuzzy c-means (FCM)
- Automatic Detection of Number of Sources
- Elimination of Low Energy Points
-
Algorithm for Solving the Permutation Problem
Algorithm for Solving the Permutation Problem
f1
f2
fk
x1x2
x3
BSS
BSS
BSSMixed signals
K po
int
FFT
y1y2y3
Separated signals
K po
int
IFFT
Solv
ing
perm
utati
on
Prob
lem
Permutation problem
One frequency binInstantaneous ICA algorithm
Permutation problem solved
0510 AM 14
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Direction Of Arrival (DOA) method
2
1
)sin(2 1
p
dcfjkqpkq
pkefWfU Position of the pth sensor
Velocity of sound
)(
)(
)()(
)()(
)(
)(
2
1
2221
1211
2
1
k
k
kk
kk
k
k
fX
fX
fWfW
fWfW
fY
fY
0510 AM
Direction of y1 = -30o
Direction of y2 = 20o
15
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Reasons for failure at lower freq
Lower spacing causes error in phase difference measurement
The relation is approximated for plane wave front under anechoic condition
Disadvantages
Fails at lower frequenciesFails when sources are nearRoom reverberationSensor positions must be known
Direction Of Arrival (DOA) method
0510 AM 16
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
f1
f2
fk
BSS
BSS
BSSMixed signals
K po
int
FFT
y1y2y3
Separated signals
K po
int
IFFT
Solv
ing
perm
utati
on
Prob
lem
Low correlation
High correlationLow
correlation
x1x2
x3
Adjacent bands correlation method
0510 AM 17
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
r12
r21
r11
r22 r22 r22 r22
r11 r11 r11
r12
r21
r12
r21
r12
r21r11 r12
r21 r22
s1
s2
Correlation matrix
21122211 rrrr No change
21122211 rrrr Change permutation
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Adjacent bands correlation method
0510 AM
21122211 and and rrrr
21122211 and and rrrr
With confidence Without confidence
2090
8010
8020
1090
2090
1040
1040
2090
Example Example
18
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
r12
r21
r11
r22 r22 r22 r22
r11 r11 r11
r12
r21
r12
r21
r12
r21
r11 r12
r21 r22
s1
s2
Correlation matrix
Disadvantage The method is not robust
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Adjacent bands correlation method
0510 AM 19
0510 AM
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Combination of DOA and Correlation methods method
DOA + Harmonic Correlation + Adjacent bands correlation
Advantage Increased robustness
20
Proposed algorithm Partial separation method(Parallel configuration)
Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
Proposed algorithm Partial separation method(Parallel configuration)
Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
2y
1y
1x
2x
1s
2s
0510 AM 21
Time domain stage
Frequency domain stage
Partial separation method(Parallel configuration)
Partial separation method(Parallel configuration)
0510 AM 22
Time domain stage
Frequency domain stage
Parallel configuration
Partial separation method(Cascade configuration)
Partial separation method(Cascade configuration)
0510 AM 23
Time domain stage
Frequency domain stage
Advantages of Partial Separation methodAdvantages of Partial Separation method
bull Robustness
0510 AM 24
Comparison with Adjacent Bands Correlation Method
Comparison with Adjacent Bands Correlation Method
0510 AM 25
PS - Partial Separation method with confidence check C1 - Correlation between the adjacent bins without confidence check C2 - Correlation between adjacent bins with confidence check Ha - Correlation between the harmonic components with confidence check PS1 - Partial separation method alone without confidence check
0510 AM 26
Comparison with DOA methodComparison with DOA method
My Contribution -IIMy Contribution -II
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
27
Underdetermined Blind Source Separation of Instantaneous Mixtures
Underdetermined Blind Source Separation of Instantaneous Mixtures
t
k
0)(0)( 222221 tkStkS
0)(0)( 222221 tkStkS
0)(0)( 112111 tkStkS
0)(0)( 112111 tkStkS
tkX 1
tkX 22x
1x
0510 AM 28
Mathematical Representation of Instantaneous Mixing
Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
Mathematical Representation of Instantaneous Mixing
Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
)(
)(
)(
)( 1
1
1111
tkS
tkS
hh
hh
tkX
tkX
QPQP
Q
P
)(
)(
)(
)( 1
1
1111
ts
ts
hh
hh
tx
tx
QPQP
Q
P
)()()(11
1
1
11
tkS
h
h
tkS
h
h
tkS
h
h
Q
PQ
Q
q
Pq
q
P
)()()()( 21 tkStkStkStk QhhhX
Time domain
Time-Frequency domain
0510 AM 29
P ndash No of mixturesQ ndash No of sources
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
00point at 1 Case 11211111 tkStkStk
)()()( 1122111111 tkStkStk hhX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 2222221122 tkStkStk hhX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
0510 AM
0 0
30
Q
qqq tkStk
1
hX
2Let Q
00point at 1 Case 11211111 tkStkStk
)()( 111111 tkStk hX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()( 222222 tkStk hX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
0510 AM 31
00point at 1 Case 11211111 tkStkStk
)()( 111111 tkStk hX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()( 222222 tkStk hX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
Scalar
ScalarScalar
Scalar
At single source point 1 At single source point 2
111
111
ofDirection )( ofDirection
ofDirection )( ofDirection
hX
hX
tkI
tkR 222
222
ofDirection )( ofDirection
ofDirection )( ofDirection
hX
hX
tkI
tkR
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
0510 AM
1111 ( of Direction ( of Direction tkItkR XX 2222 ( of Direction ( of Direction tkItkR XX 32
Scatter Diagram of the Mixtures When Source are Perfectly Sparse
Scatter Diagram of the Mixtures When Source are Perfectly Sparse
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
22222
11111
2221
1211
22222
11111
kSkSkSkSkS
kSkSkSkSkS
hh
hh
kXkXkXkXkX
kXkXkXkXkX
21
111 h
hh
22
122 h
hh
0 00 0 0
Example
0510 AM 33
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
22222
11111
2221
1211
22222
11111
kSkSkSkSkS
kSkSkSkSkS
hh
hh
kXkXkXkXkX
kXkXkXkXkX
21
111 h
hh
22
122 h
hh
0 00 0 00
Example
Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
0510 AM 34
Scatter Diagram of the Mixtures when Sources are Sparse
Scatter Diagram of the Mixtures when Sources are Sparse
3h
6h
5h
1h4h
2h
0510 AM
No of sources = 6No of mixtures = 2
35
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
3h
6h
5h
1h4h
2h
0510 AM
No of sources = 6No of mixtures = 2
36
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
3h
6h
5h
1h4h
2h
0510 AM
ObjectiveEstimation of the single source points
No of sources = 6No of mixtures = 2
37
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Multi source point
38
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
Multi source point
39
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
Average of 15 pairs of speech utterances of length 10 s each
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
)( ofDirection )( ofDirection tkXItkXR )( ofDirection )( ofDirection tkXItkXR
SSPMSP
40
SSPt
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)()(
)()(
112112
111111
tkXjItkXR
tkXjItkXR
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXI
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXIMSP
)( 111 tkX
)( 112 tkX
cos
)()(
)()(
tkXItkXR
tkXItkXR T
Proposed Algorithm for the Detection of Single Source Points
Proposed Algorithm for the Detection of Single Source Points
0510 AM 41
Elimination of OutliersElimination of Outliers
SSPs detection
Clus
terin
g
Outlier elimination
0510 AM 42
0510 AM
Experimental ResultsExperimental Results
dB6747NMSE
No of mixtures =2 No of sources =6
43
Detected Single Source PointsThree mixtures
Detected Single Source PointsThree mixtures
No of mixtures =3 No of sources =60510 AM 44
Comparison with Classical Algorithms for Determined Case
Comparison with Classical Algorithms for Determined Case
No of mixtures =2No of sources =2
Average of 500 experimental results
0510 AM 45
-gt
Comparison with Method Proposed in [1] Underdetermined case
Comparison with Method Proposed in [1] Underdetermined case
[1] Y Li S Amari A Cichocki D W C Ho and S Xie ldquoUnderdetermined blind source separation based on sparse representationrdquo IEEE Transactions on Signal Processing vol 54 p 423ndash437 Feb 2006
0510 AM
Nor
mal
ized
mea
n sq
uare
err
or (N
MSE
) in
mix
ing
mat
rix e
stim
ation
(dB)
Order of the mixing matrices (PxQ)
46
P ndash No of mixturesQ ndash No of sources
Advantages of the Proposed algorithmAdvantages of the Proposed algorithm
Step 1 Convert x in the time domain to the TF domain to get XStep 2 Check the condition
Step 3 If the condition is satisfied then X(k t) is a sample atthe SSP and this sample is kept for mixing matrix estimationotherwise discard the point
Step 4 Repeat Steps 2 to 3 for all the points in the TF planeor until sufficient number of SSPs are obtained
cos
)()(
)()(
tkXItkXR
tkXItkXR T
1) Much simpler constrain the algorithm does not require ldquosingle source zonerdquo
3) The algorithm is extremely simple but effective2) Separation performance is better
0510 AM 47-gt
My Contributions ndash III IV and VMy Contributions ndash III IV and V
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
48
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Mask estimation
Mic 1
Mic P
Mixture in TF domain
Separated signals in TF domain
)( tkX P
)(1 tkX
t
t
k
k
)(1 tkY
)(1 tkY
)( tkYQ
)( tkYQ
QP
0510 AM 49
Mathematical RepresentationMathematical Representation
Q
q
L
lqpqp Pplnslhnx
1
1
0
1)()()(
)()()()()()()( 11 tkSktkSktkSktk QQqq HHHX
)(
)(
)()(
)()(
)(
)( 1
1
1111
tkS
tkS
kHkH
kHkH
tkX
tkX
QPQP
Q
P
)(
)(
)(
)(
)(
)(
)(
)(
)( 11
1
1
11
tkS
kH
kH
tkS
kH
kH
tkS
kH
kH
Q
PQ
Q
q
Pq
q
P
Time domain
Frequency domain
0510 AM 50
P ndash No of mixturesQ ndash No of sources
Single source pointsSingle source pointsInstantaneous mixing
00point at 1 Case 11211111 tkStkStk
)()()(
)()()(
111111
111111
tkSIktkI
tkSRktkR
HX
HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()(
)()()(
222222
222222
tkSIktkI
tkSRktkR
HX
HX
Single source point 2
Real scalar
RealReal
Real scalarReal scalar
Real scalar
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
0510 AM 51
Basic Principle of Single Source Points Detection
Basic Principle of Single Source Points Detection
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
j
H
C
e
cos21
21
UU
UUUUU H
and 20coscos HCH
angle pseudo called is
angleHermitian called is
H The Hermitian angle between the complex
vectors u1 and u2 will remain the same even if the vectors are multiplied by any complex scalars whereas the pseudo angle will change
0510 AM 52
-gt
k
Algorithm for Single Source Points Detection
Algorithm for Single Source Points Detection
t
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)(
)(
)(111
121
111 tkSkH
kH
11
11
j
jr
)(
)(
112
111
tkX
tkX
11
11
j
jr
)(
)(
112
111
tkX
tkX
)( 111 tkX
)( 112 tkX
)(
)(
)(112
122
112 tkSkH
kH θH2
θH1
θH2
rX
rX
)(
)(cos
11
111
tk
tk H
Hq
0510 AM 53
θH1
OR
1k
1k
1t
Clean
Estimated
Mask Estimation by k-means (KM)Mask Estimation by k-means (KM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 54
Clean
Estimated
Mask Estimation by Fuzzy c-means (FCM)Mask Estimation by Fuzzy c-means (FCM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 55
Automatic Detection of Number of SourcesAutomatic Detection of Number of Sources
0510 AM 56
Cluster validation technique
For c = 2 to cmax
Cluster the data into c clustersCalculate the cluster validation index
EndTake c corresponding to the best cluster as the number of sources
-gt
Elimination of Low Energy PointsElimination of Low Energy Points
0510 AM 57
- Blind Separation of Speech Mixtures
- Introduction
- Slide 3
- Slide 4
- Slide 5
- Approaches for BSS of Speech Signals
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Permutation Problem in Frequency Domain BSS
- Motivation
- My Contribution - I
- Algorithm for Solving the Permutation Problem
- Existing Method for Solving the Permutation Problem
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Proposed algorithm Partial separation method (Parallel configuration) Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
- Partial separation method (Parallel configuration)
- Partial separation method (Cascade configuration)
- Advantages of Partial Separation method
- Comparison with Adjacent Bands Correlation Method
- Comparison with DOA method
- My Contribution -II
- Underdetermined Blind Source Separation of Instantaneous Mixtures
- Mathematical Representation of Instantaneous Mixing Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
- Single Source Points in Time-Frequency domain
- Slide 31
- Slide 32
- Scatter Diagram of the Mixtures When Source are Perfectly Sparse
- Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
- Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
- Principle of the Proposed Algorithm for the Detection of Single Source Points
- Slide 39
- Slide 40
- Proposed Algorithm for the Detection of Single Source Points
- Elimination of Outliers
- Slide 43
- Detected Single Source Points Three mixtures
- Comparison with Classical Algorithms for Determined Case
- Comparison with Method Proposed in [1] Underdetermined case
- Advantages of the Proposed algorithm
- My Contributions ndash III IV and V
- Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
- Mathematical Representation
- Single source points
- Basic Principle of Single Source Points Detection
- Algorithm for Single Source Points Detection
- Mask Estimation by k-means (KM)
- Mask Estimation by Fuzzy c-means (FCM)
- Automatic Detection of Number of Sources
- Elimination of Low Energy Points
-
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Direction Of Arrival (DOA) method
2
1
)sin(2 1
p
dcfjkqpkq
pkefWfU Position of the pth sensor
Velocity of sound
)(
)(
)()(
)()(
)(
)(
2
1
2221
1211
2
1
k
k
kk
kk
k
k
fX
fX
fWfW
fWfW
fY
fY
0510 AM
Direction of y1 = -30o
Direction of y2 = 20o
15
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Reasons for failure at lower freq
Lower spacing causes error in phase difference measurement
The relation is approximated for plane wave front under anechoic condition
Disadvantages
Fails at lower frequenciesFails when sources are nearRoom reverberationSensor positions must be known
Direction Of Arrival (DOA) method
0510 AM 16
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
f1
f2
fk
BSS
BSS
BSSMixed signals
K po
int
FFT
y1y2y3
Separated signals
K po
int
IFFT
Solv
ing
perm
utati
on
Prob
lem
Low correlation
High correlationLow
correlation
x1x2
x3
Adjacent bands correlation method
0510 AM 17
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
r12
r21
r11
r22 r22 r22 r22
r11 r11 r11
r12
r21
r12
r21
r12
r21r11 r12
r21 r22
s1
s2
Correlation matrix
21122211 rrrr No change
21122211 rrrr Change permutation
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Adjacent bands correlation method
0510 AM
21122211 and and rrrr
21122211 and and rrrr
With confidence Without confidence
2090
8010
8020
1090
2090
1040
1040
2090
Example Example
18
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
r12
r21
r11
r22 r22 r22 r22
r11 r11 r11
r12
r21
r12
r21
r12
r21
r11 r12
r21 r22
s1
s2
Correlation matrix
Disadvantage The method is not robust
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Adjacent bands correlation method
0510 AM 19
0510 AM
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Combination of DOA and Correlation methods method
DOA + Harmonic Correlation + Adjacent bands correlation
Advantage Increased robustness
20
Proposed algorithm Partial separation method(Parallel configuration)
Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
Proposed algorithm Partial separation method(Parallel configuration)
Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
2y
1y
1x
2x
1s
2s
0510 AM 21
Time domain stage
Frequency domain stage
Partial separation method(Parallel configuration)
Partial separation method(Parallel configuration)
0510 AM 22
Time domain stage
Frequency domain stage
Parallel configuration
Partial separation method(Cascade configuration)
Partial separation method(Cascade configuration)
0510 AM 23
Time domain stage
Frequency domain stage
Advantages of Partial Separation methodAdvantages of Partial Separation method
bull Robustness
0510 AM 24
Comparison with Adjacent Bands Correlation Method
Comparison with Adjacent Bands Correlation Method
0510 AM 25
PS - Partial Separation method with confidence check C1 - Correlation between the adjacent bins without confidence check C2 - Correlation between adjacent bins with confidence check Ha - Correlation between the harmonic components with confidence check PS1 - Partial separation method alone without confidence check
0510 AM 26
Comparison with DOA methodComparison with DOA method
My Contribution -IIMy Contribution -II
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
27
Underdetermined Blind Source Separation of Instantaneous Mixtures
Underdetermined Blind Source Separation of Instantaneous Mixtures
t
k
0)(0)( 222221 tkStkS
0)(0)( 222221 tkStkS
0)(0)( 112111 tkStkS
0)(0)( 112111 tkStkS
tkX 1
tkX 22x
1x
0510 AM 28
Mathematical Representation of Instantaneous Mixing
Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
Mathematical Representation of Instantaneous Mixing
Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
)(
)(
)(
)( 1
1
1111
tkS
tkS
hh
hh
tkX
tkX
QPQP
Q
P
)(
)(
)(
)( 1
1
1111
ts
ts
hh
hh
tx
tx
QPQP
Q
P
)()()(11
1
1
11
tkS
h
h
tkS
h
h
tkS
h
h
Q
PQ
Q
q
Pq
q
P
)()()()( 21 tkStkStkStk QhhhX
Time domain
Time-Frequency domain
0510 AM 29
P ndash No of mixturesQ ndash No of sources
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
00point at 1 Case 11211111 tkStkStk
)()()( 1122111111 tkStkStk hhX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 2222221122 tkStkStk hhX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
0510 AM
0 0
30
Q
qqq tkStk
1
hX
2Let Q
00point at 1 Case 11211111 tkStkStk
)()( 111111 tkStk hX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()( 222222 tkStk hX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
0510 AM 31
00point at 1 Case 11211111 tkStkStk
)()( 111111 tkStk hX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()( 222222 tkStk hX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
Scalar
ScalarScalar
Scalar
At single source point 1 At single source point 2
111
111
ofDirection )( ofDirection
ofDirection )( ofDirection
hX
hX
tkI
tkR 222
222
ofDirection )( ofDirection
ofDirection )( ofDirection
hX
hX
tkI
tkR
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
0510 AM
1111 ( of Direction ( of Direction tkItkR XX 2222 ( of Direction ( of Direction tkItkR XX 32
Scatter Diagram of the Mixtures When Source are Perfectly Sparse
Scatter Diagram of the Mixtures When Source are Perfectly Sparse
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
22222
11111
2221
1211
22222
11111
kSkSkSkSkS
kSkSkSkSkS
hh
hh
kXkXkXkXkX
kXkXkXkXkX
21
111 h
hh
22
122 h
hh
0 00 0 0
Example
0510 AM 33
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
22222
11111
2221
1211
22222
11111
kSkSkSkSkS
kSkSkSkSkS
hh
hh
kXkXkXkXkX
kXkXkXkXkX
21
111 h
hh
22
122 h
hh
0 00 0 00
Example
Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
0510 AM 34
Scatter Diagram of the Mixtures when Sources are Sparse
Scatter Diagram of the Mixtures when Sources are Sparse
3h
6h
5h
1h4h
2h
0510 AM
No of sources = 6No of mixtures = 2
35
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
3h
6h
5h
1h4h
2h
0510 AM
No of sources = 6No of mixtures = 2
36
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
3h
6h
5h
1h4h
2h
0510 AM
ObjectiveEstimation of the single source points
No of sources = 6No of mixtures = 2
37
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Multi source point
38
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
Multi source point
39
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
Average of 15 pairs of speech utterances of length 10 s each
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
)( ofDirection )( ofDirection tkXItkXR )( ofDirection )( ofDirection tkXItkXR
SSPMSP
40
SSPt
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)()(
)()(
112112
111111
tkXjItkXR
tkXjItkXR
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXI
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXIMSP
)( 111 tkX
)( 112 tkX
cos
)()(
)()(
tkXItkXR
tkXItkXR T
Proposed Algorithm for the Detection of Single Source Points
Proposed Algorithm for the Detection of Single Source Points
0510 AM 41
Elimination of OutliersElimination of Outliers
SSPs detection
Clus
terin
g
Outlier elimination
0510 AM 42
0510 AM
Experimental ResultsExperimental Results
dB6747NMSE
No of mixtures =2 No of sources =6
43
Detected Single Source PointsThree mixtures
Detected Single Source PointsThree mixtures
No of mixtures =3 No of sources =60510 AM 44
Comparison with Classical Algorithms for Determined Case
Comparison with Classical Algorithms for Determined Case
No of mixtures =2No of sources =2
Average of 500 experimental results
0510 AM 45
-gt
Comparison with Method Proposed in [1] Underdetermined case
Comparison with Method Proposed in [1] Underdetermined case
[1] Y Li S Amari A Cichocki D W C Ho and S Xie ldquoUnderdetermined blind source separation based on sparse representationrdquo IEEE Transactions on Signal Processing vol 54 p 423ndash437 Feb 2006
0510 AM
Nor
mal
ized
mea
n sq
uare
err
or (N
MSE
) in
mix
ing
mat
rix e
stim
ation
(dB)
Order of the mixing matrices (PxQ)
46
P ndash No of mixturesQ ndash No of sources
Advantages of the Proposed algorithmAdvantages of the Proposed algorithm
Step 1 Convert x in the time domain to the TF domain to get XStep 2 Check the condition
Step 3 If the condition is satisfied then X(k t) is a sample atthe SSP and this sample is kept for mixing matrix estimationotherwise discard the point
Step 4 Repeat Steps 2 to 3 for all the points in the TF planeor until sufficient number of SSPs are obtained
cos
)()(
)()(
tkXItkXR
tkXItkXR T
1) Much simpler constrain the algorithm does not require ldquosingle source zonerdquo
3) The algorithm is extremely simple but effective2) Separation performance is better
0510 AM 47-gt
My Contributions ndash III IV and VMy Contributions ndash III IV and V
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
48
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Mask estimation
Mic 1
Mic P
Mixture in TF domain
Separated signals in TF domain
)( tkX P
)(1 tkX
t
t
k
k
)(1 tkY
)(1 tkY
)( tkYQ
)( tkYQ
QP
0510 AM 49
Mathematical RepresentationMathematical Representation
Q
q
L
lqpqp Pplnslhnx
1
1
0
1)()()(
)()()()()()()( 11 tkSktkSktkSktk QQqq HHHX
)(
)(
)()(
)()(
)(
)( 1
1
1111
tkS
tkS
kHkH
kHkH
tkX
tkX
QPQP
Q
P
)(
)(
)(
)(
)(
)(
)(
)(
)( 11
1
1
11
tkS
kH
kH
tkS
kH
kH
tkS
kH
kH
Q
PQ
Q
q
Pq
q
P
Time domain
Frequency domain
0510 AM 50
P ndash No of mixturesQ ndash No of sources
Single source pointsSingle source pointsInstantaneous mixing
00point at 1 Case 11211111 tkStkStk
)()()(
)()()(
111111
111111
tkSIktkI
tkSRktkR
HX
HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()(
)()()(
222222
222222
tkSIktkI
tkSRktkR
HX
HX
Single source point 2
Real scalar
RealReal
Real scalarReal scalar
Real scalar
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
0510 AM 51
Basic Principle of Single Source Points Detection
Basic Principle of Single Source Points Detection
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
j
H
C
e
cos21
21
UU
UUUUU H
and 20coscos HCH
angle pseudo called is
angleHermitian called is
H The Hermitian angle between the complex
vectors u1 and u2 will remain the same even if the vectors are multiplied by any complex scalars whereas the pseudo angle will change
0510 AM 52
-gt
k
Algorithm for Single Source Points Detection
Algorithm for Single Source Points Detection
t
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)(
)(
)(111
121
111 tkSkH
kH
11
11
j
jr
)(
)(
112
111
tkX
tkX
11
11
j
jr
)(
)(
112
111
tkX
tkX
)( 111 tkX
)( 112 tkX
)(
)(
)(112
122
112 tkSkH
kH θH2
θH1
θH2
rX
rX
)(
)(cos
11
111
tk
tk H
Hq
0510 AM 53
θH1
OR
1k
1k
1t
Clean
Estimated
Mask Estimation by k-means (KM)Mask Estimation by k-means (KM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 54
Clean
Estimated
Mask Estimation by Fuzzy c-means (FCM)Mask Estimation by Fuzzy c-means (FCM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 55
Automatic Detection of Number of SourcesAutomatic Detection of Number of Sources
0510 AM 56
Cluster validation technique
For c = 2 to cmax
Cluster the data into c clustersCalculate the cluster validation index
EndTake c corresponding to the best cluster as the number of sources
-gt
Elimination of Low Energy PointsElimination of Low Energy Points
0510 AM 57
- Blind Separation of Speech Mixtures
- Introduction
- Slide 3
- Slide 4
- Slide 5
- Approaches for BSS of Speech Signals
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Permutation Problem in Frequency Domain BSS
- Motivation
- My Contribution - I
- Algorithm for Solving the Permutation Problem
- Existing Method for Solving the Permutation Problem
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Proposed algorithm Partial separation method (Parallel configuration) Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
- Partial separation method (Parallel configuration)
- Partial separation method (Cascade configuration)
- Advantages of Partial Separation method
- Comparison with Adjacent Bands Correlation Method
- Comparison with DOA method
- My Contribution -II
- Underdetermined Blind Source Separation of Instantaneous Mixtures
- Mathematical Representation of Instantaneous Mixing Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
- Single Source Points in Time-Frequency domain
- Slide 31
- Slide 32
- Scatter Diagram of the Mixtures When Source are Perfectly Sparse
- Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
- Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
- Principle of the Proposed Algorithm for the Detection of Single Source Points
- Slide 39
- Slide 40
- Proposed Algorithm for the Detection of Single Source Points
- Elimination of Outliers
- Slide 43
- Detected Single Source Points Three mixtures
- Comparison with Classical Algorithms for Determined Case
- Comparison with Method Proposed in [1] Underdetermined case
- Advantages of the Proposed algorithm
- My Contributions ndash III IV and V
- Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
- Mathematical Representation
- Single source points
- Basic Principle of Single Source Points Detection
- Algorithm for Single Source Points Detection
- Mask Estimation by k-means (KM)
- Mask Estimation by Fuzzy c-means (FCM)
- Automatic Detection of Number of Sources
- Elimination of Low Energy Points
-
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Reasons for failure at lower freq
Lower spacing causes error in phase difference measurement
The relation is approximated for plane wave front under anechoic condition
Disadvantages
Fails at lower frequenciesFails when sources are nearRoom reverberationSensor positions must be known
Direction Of Arrival (DOA) method
0510 AM 16
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
f1
f2
fk
BSS
BSS
BSSMixed signals
K po
int
FFT
y1y2y3
Separated signals
K po
int
IFFT
Solv
ing
perm
utati
on
Prob
lem
Low correlation
High correlationLow
correlation
x1x2
x3
Adjacent bands correlation method
0510 AM 17
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
r12
r21
r11
r22 r22 r22 r22
r11 r11 r11
r12
r21
r12
r21
r12
r21r11 r12
r21 r22
s1
s2
Correlation matrix
21122211 rrrr No change
21122211 rrrr Change permutation
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Adjacent bands correlation method
0510 AM
21122211 and and rrrr
21122211 and and rrrr
With confidence Without confidence
2090
8010
8020
1090
2090
1040
1040
2090
Example Example
18
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
r12
r21
r11
r22 r22 r22 r22
r11 r11 r11
r12
r21
r12
r21
r12
r21
r11 r12
r21 r22
s1
s2
Correlation matrix
Disadvantage The method is not robust
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Adjacent bands correlation method
0510 AM 19
0510 AM
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Combination of DOA and Correlation methods method
DOA + Harmonic Correlation + Adjacent bands correlation
Advantage Increased robustness
20
Proposed algorithm Partial separation method(Parallel configuration)
Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
Proposed algorithm Partial separation method(Parallel configuration)
Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
2y
1y
1x
2x
1s
2s
0510 AM 21
Time domain stage
Frequency domain stage
Partial separation method(Parallel configuration)
Partial separation method(Parallel configuration)
0510 AM 22
Time domain stage
Frequency domain stage
Parallel configuration
Partial separation method(Cascade configuration)
Partial separation method(Cascade configuration)
0510 AM 23
Time domain stage
Frequency domain stage
Advantages of Partial Separation methodAdvantages of Partial Separation method
bull Robustness
0510 AM 24
Comparison with Adjacent Bands Correlation Method
Comparison with Adjacent Bands Correlation Method
0510 AM 25
PS - Partial Separation method with confidence check C1 - Correlation between the adjacent bins without confidence check C2 - Correlation between adjacent bins with confidence check Ha - Correlation between the harmonic components with confidence check PS1 - Partial separation method alone without confidence check
0510 AM 26
Comparison with DOA methodComparison with DOA method
My Contribution -IIMy Contribution -II
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
27
Underdetermined Blind Source Separation of Instantaneous Mixtures
Underdetermined Blind Source Separation of Instantaneous Mixtures
t
k
0)(0)( 222221 tkStkS
0)(0)( 222221 tkStkS
0)(0)( 112111 tkStkS
0)(0)( 112111 tkStkS
tkX 1
tkX 22x
1x
0510 AM 28
Mathematical Representation of Instantaneous Mixing
Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
Mathematical Representation of Instantaneous Mixing
Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
)(
)(
)(
)( 1
1
1111
tkS
tkS
hh
hh
tkX
tkX
QPQP
Q
P
)(
)(
)(
)( 1
1
1111
ts
ts
hh
hh
tx
tx
QPQP
Q
P
)()()(11
1
1
11
tkS
h
h
tkS
h
h
tkS
h
h
Q
PQ
Q
q
Pq
q
P
)()()()( 21 tkStkStkStk QhhhX
Time domain
Time-Frequency domain
0510 AM 29
P ndash No of mixturesQ ndash No of sources
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
00point at 1 Case 11211111 tkStkStk
)()()( 1122111111 tkStkStk hhX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 2222221122 tkStkStk hhX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
0510 AM
0 0
30
Q
qqq tkStk
1
hX
2Let Q
00point at 1 Case 11211111 tkStkStk
)()( 111111 tkStk hX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()( 222222 tkStk hX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
0510 AM 31
00point at 1 Case 11211111 tkStkStk
)()( 111111 tkStk hX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()( 222222 tkStk hX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
Scalar
ScalarScalar
Scalar
At single source point 1 At single source point 2
111
111
ofDirection )( ofDirection
ofDirection )( ofDirection
hX
hX
tkI
tkR 222
222
ofDirection )( ofDirection
ofDirection )( ofDirection
hX
hX
tkI
tkR
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
0510 AM
1111 ( of Direction ( of Direction tkItkR XX 2222 ( of Direction ( of Direction tkItkR XX 32
Scatter Diagram of the Mixtures When Source are Perfectly Sparse
Scatter Diagram of the Mixtures When Source are Perfectly Sparse
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
22222
11111
2221
1211
22222
11111
kSkSkSkSkS
kSkSkSkSkS
hh
hh
kXkXkXkXkX
kXkXkXkXkX
21
111 h
hh
22
122 h
hh
0 00 0 0
Example
0510 AM 33
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
22222
11111
2221
1211
22222
11111
kSkSkSkSkS
kSkSkSkSkS
hh
hh
kXkXkXkXkX
kXkXkXkXkX
21
111 h
hh
22
122 h
hh
0 00 0 00
Example
Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
0510 AM 34
Scatter Diagram of the Mixtures when Sources are Sparse
Scatter Diagram of the Mixtures when Sources are Sparse
3h
6h
5h
1h4h
2h
0510 AM
No of sources = 6No of mixtures = 2
35
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
3h
6h
5h
1h4h
2h
0510 AM
No of sources = 6No of mixtures = 2
36
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
3h
6h
5h
1h4h
2h
0510 AM
ObjectiveEstimation of the single source points
No of sources = 6No of mixtures = 2
37
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Multi source point
38
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
Multi source point
39
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
Average of 15 pairs of speech utterances of length 10 s each
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
)( ofDirection )( ofDirection tkXItkXR )( ofDirection )( ofDirection tkXItkXR
SSPMSP
40
SSPt
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)()(
)()(
112112
111111
tkXjItkXR
tkXjItkXR
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXI
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXIMSP
)( 111 tkX
)( 112 tkX
cos
)()(
)()(
tkXItkXR
tkXItkXR T
Proposed Algorithm for the Detection of Single Source Points
Proposed Algorithm for the Detection of Single Source Points
0510 AM 41
Elimination of OutliersElimination of Outliers
SSPs detection
Clus
terin
g
Outlier elimination
0510 AM 42
0510 AM
Experimental ResultsExperimental Results
dB6747NMSE
No of mixtures =2 No of sources =6
43
Detected Single Source PointsThree mixtures
Detected Single Source PointsThree mixtures
No of mixtures =3 No of sources =60510 AM 44
Comparison with Classical Algorithms for Determined Case
Comparison with Classical Algorithms for Determined Case
No of mixtures =2No of sources =2
Average of 500 experimental results
0510 AM 45
-gt
Comparison with Method Proposed in [1] Underdetermined case
Comparison with Method Proposed in [1] Underdetermined case
[1] Y Li S Amari A Cichocki D W C Ho and S Xie ldquoUnderdetermined blind source separation based on sparse representationrdquo IEEE Transactions on Signal Processing vol 54 p 423ndash437 Feb 2006
0510 AM
Nor
mal
ized
mea
n sq
uare
err
or (N
MSE
) in
mix
ing
mat
rix e
stim
ation
(dB)
Order of the mixing matrices (PxQ)
46
P ndash No of mixturesQ ndash No of sources
Advantages of the Proposed algorithmAdvantages of the Proposed algorithm
Step 1 Convert x in the time domain to the TF domain to get XStep 2 Check the condition
Step 3 If the condition is satisfied then X(k t) is a sample atthe SSP and this sample is kept for mixing matrix estimationotherwise discard the point
Step 4 Repeat Steps 2 to 3 for all the points in the TF planeor until sufficient number of SSPs are obtained
cos
)()(
)()(
tkXItkXR
tkXItkXR T
1) Much simpler constrain the algorithm does not require ldquosingle source zonerdquo
3) The algorithm is extremely simple but effective2) Separation performance is better
0510 AM 47-gt
My Contributions ndash III IV and VMy Contributions ndash III IV and V
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
48
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Mask estimation
Mic 1
Mic P
Mixture in TF domain
Separated signals in TF domain
)( tkX P
)(1 tkX
t
t
k
k
)(1 tkY
)(1 tkY
)( tkYQ
)( tkYQ
QP
0510 AM 49
Mathematical RepresentationMathematical Representation
Q
q
L
lqpqp Pplnslhnx
1
1
0
1)()()(
)()()()()()()( 11 tkSktkSktkSktk QQqq HHHX
)(
)(
)()(
)()(
)(
)( 1
1
1111
tkS
tkS
kHkH
kHkH
tkX
tkX
QPQP
Q
P
)(
)(
)(
)(
)(
)(
)(
)(
)( 11
1
1
11
tkS
kH
kH
tkS
kH
kH
tkS
kH
kH
Q
PQ
Q
q
Pq
q
P
Time domain
Frequency domain
0510 AM 50
P ndash No of mixturesQ ndash No of sources
Single source pointsSingle source pointsInstantaneous mixing
00point at 1 Case 11211111 tkStkStk
)()()(
)()()(
111111
111111
tkSIktkI
tkSRktkR
HX
HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()(
)()()(
222222
222222
tkSIktkI
tkSRktkR
HX
HX
Single source point 2
Real scalar
RealReal
Real scalarReal scalar
Real scalar
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
0510 AM 51
Basic Principle of Single Source Points Detection
Basic Principle of Single Source Points Detection
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
j
H
C
e
cos21
21
UU
UUUUU H
and 20coscos HCH
angle pseudo called is
angleHermitian called is
H The Hermitian angle between the complex
vectors u1 and u2 will remain the same even if the vectors are multiplied by any complex scalars whereas the pseudo angle will change
0510 AM 52
-gt
k
Algorithm for Single Source Points Detection
Algorithm for Single Source Points Detection
t
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)(
)(
)(111
121
111 tkSkH
kH
11
11
j
jr
)(
)(
112
111
tkX
tkX
11
11
j
jr
)(
)(
112
111
tkX
tkX
)( 111 tkX
)( 112 tkX
)(
)(
)(112
122
112 tkSkH
kH θH2
θH1
θH2
rX
rX
)(
)(cos
11
111
tk
tk H
Hq
0510 AM 53
θH1
OR
1k
1k
1t
Clean
Estimated
Mask Estimation by k-means (KM)Mask Estimation by k-means (KM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 54
Clean
Estimated
Mask Estimation by Fuzzy c-means (FCM)Mask Estimation by Fuzzy c-means (FCM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 55
Automatic Detection of Number of SourcesAutomatic Detection of Number of Sources
0510 AM 56
Cluster validation technique
For c = 2 to cmax
Cluster the data into c clustersCalculate the cluster validation index
EndTake c corresponding to the best cluster as the number of sources
-gt
Elimination of Low Energy PointsElimination of Low Energy Points
0510 AM 57
- Blind Separation of Speech Mixtures
- Introduction
- Slide 3
- Slide 4
- Slide 5
- Approaches for BSS of Speech Signals
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Permutation Problem in Frequency Domain BSS
- Motivation
- My Contribution - I
- Algorithm for Solving the Permutation Problem
- Existing Method for Solving the Permutation Problem
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Proposed algorithm Partial separation method (Parallel configuration) Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
- Partial separation method (Parallel configuration)
- Partial separation method (Cascade configuration)
- Advantages of Partial Separation method
- Comparison with Adjacent Bands Correlation Method
- Comparison with DOA method
- My Contribution -II
- Underdetermined Blind Source Separation of Instantaneous Mixtures
- Mathematical Representation of Instantaneous Mixing Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
- Single Source Points in Time-Frequency domain
- Slide 31
- Slide 32
- Scatter Diagram of the Mixtures When Source are Perfectly Sparse
- Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
- Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
- Principle of the Proposed Algorithm for the Detection of Single Source Points
- Slide 39
- Slide 40
- Proposed Algorithm for the Detection of Single Source Points
- Elimination of Outliers
- Slide 43
- Detected Single Source Points Three mixtures
- Comparison with Classical Algorithms for Determined Case
- Comparison with Method Proposed in [1] Underdetermined case
- Advantages of the Proposed algorithm
- My Contributions ndash III IV and V
- Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
- Mathematical Representation
- Single source points
- Basic Principle of Single Source Points Detection
- Algorithm for Single Source Points Detection
- Mask Estimation by k-means (KM)
- Mask Estimation by Fuzzy c-means (FCM)
- Automatic Detection of Number of Sources
- Elimination of Low Energy Points
-
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
f1
f2
fk
BSS
BSS
BSSMixed signals
K po
int
FFT
y1y2y3
Separated signals
K po
int
IFFT
Solv
ing
perm
utati
on
Prob
lem
Low correlation
High correlationLow
correlation
x1x2
x3
Adjacent bands correlation method
0510 AM 17
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
r12
r21
r11
r22 r22 r22 r22
r11 r11 r11
r12
r21
r12
r21
r12
r21r11 r12
r21 r22
s1
s2
Correlation matrix
21122211 rrrr No change
21122211 rrrr Change permutation
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Adjacent bands correlation method
0510 AM
21122211 and and rrrr
21122211 and and rrrr
With confidence Without confidence
2090
8010
8020
1090
2090
1040
1040
2090
Example Example
18
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
r12
r21
r11
r22 r22 r22 r22
r11 r11 r11
r12
r21
r12
r21
r12
r21
r11 r12
r21 r22
s1
s2
Correlation matrix
Disadvantage The method is not robust
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Adjacent bands correlation method
0510 AM 19
0510 AM
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Combination of DOA and Correlation methods method
DOA + Harmonic Correlation + Adjacent bands correlation
Advantage Increased robustness
20
Proposed algorithm Partial separation method(Parallel configuration)
Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
Proposed algorithm Partial separation method(Parallel configuration)
Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
2y
1y
1x
2x
1s
2s
0510 AM 21
Time domain stage
Frequency domain stage
Partial separation method(Parallel configuration)
Partial separation method(Parallel configuration)
0510 AM 22
Time domain stage
Frequency domain stage
Parallel configuration
Partial separation method(Cascade configuration)
Partial separation method(Cascade configuration)
0510 AM 23
Time domain stage
Frequency domain stage
Advantages of Partial Separation methodAdvantages of Partial Separation method
bull Robustness
0510 AM 24
Comparison with Adjacent Bands Correlation Method
Comparison with Adjacent Bands Correlation Method
0510 AM 25
PS - Partial Separation method with confidence check C1 - Correlation between the adjacent bins without confidence check C2 - Correlation between adjacent bins with confidence check Ha - Correlation between the harmonic components with confidence check PS1 - Partial separation method alone without confidence check
0510 AM 26
Comparison with DOA methodComparison with DOA method
My Contribution -IIMy Contribution -II
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
27
Underdetermined Blind Source Separation of Instantaneous Mixtures
Underdetermined Blind Source Separation of Instantaneous Mixtures
t
k
0)(0)( 222221 tkStkS
0)(0)( 222221 tkStkS
0)(0)( 112111 tkStkS
0)(0)( 112111 tkStkS
tkX 1
tkX 22x
1x
0510 AM 28
Mathematical Representation of Instantaneous Mixing
Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
Mathematical Representation of Instantaneous Mixing
Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
)(
)(
)(
)( 1
1
1111
tkS
tkS
hh
hh
tkX
tkX
QPQP
Q
P
)(
)(
)(
)( 1
1
1111
ts
ts
hh
hh
tx
tx
QPQP
Q
P
)()()(11
1
1
11
tkS
h
h
tkS
h
h
tkS
h
h
Q
PQ
Q
q
Pq
q
P
)()()()( 21 tkStkStkStk QhhhX
Time domain
Time-Frequency domain
0510 AM 29
P ndash No of mixturesQ ndash No of sources
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
00point at 1 Case 11211111 tkStkStk
)()()( 1122111111 tkStkStk hhX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 2222221122 tkStkStk hhX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
0510 AM
0 0
30
Q
qqq tkStk
1
hX
2Let Q
00point at 1 Case 11211111 tkStkStk
)()( 111111 tkStk hX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()( 222222 tkStk hX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
0510 AM 31
00point at 1 Case 11211111 tkStkStk
)()( 111111 tkStk hX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()( 222222 tkStk hX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
Scalar
ScalarScalar
Scalar
At single source point 1 At single source point 2
111
111
ofDirection )( ofDirection
ofDirection )( ofDirection
hX
hX
tkI
tkR 222
222
ofDirection )( ofDirection
ofDirection )( ofDirection
hX
hX
tkI
tkR
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
0510 AM
1111 ( of Direction ( of Direction tkItkR XX 2222 ( of Direction ( of Direction tkItkR XX 32
Scatter Diagram of the Mixtures When Source are Perfectly Sparse
Scatter Diagram of the Mixtures When Source are Perfectly Sparse
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
22222
11111
2221
1211
22222
11111
kSkSkSkSkS
kSkSkSkSkS
hh
hh
kXkXkXkXkX
kXkXkXkXkX
21
111 h
hh
22
122 h
hh
0 00 0 0
Example
0510 AM 33
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
22222
11111
2221
1211
22222
11111
kSkSkSkSkS
kSkSkSkSkS
hh
hh
kXkXkXkXkX
kXkXkXkXkX
21
111 h
hh
22
122 h
hh
0 00 0 00
Example
Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
0510 AM 34
Scatter Diagram of the Mixtures when Sources are Sparse
Scatter Diagram of the Mixtures when Sources are Sparse
3h
6h
5h
1h4h
2h
0510 AM
No of sources = 6No of mixtures = 2
35
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
3h
6h
5h
1h4h
2h
0510 AM
No of sources = 6No of mixtures = 2
36
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
3h
6h
5h
1h4h
2h
0510 AM
ObjectiveEstimation of the single source points
No of sources = 6No of mixtures = 2
37
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Multi source point
38
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
Multi source point
39
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
Average of 15 pairs of speech utterances of length 10 s each
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
)( ofDirection )( ofDirection tkXItkXR )( ofDirection )( ofDirection tkXItkXR
SSPMSP
40
SSPt
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)()(
)()(
112112
111111
tkXjItkXR
tkXjItkXR
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXI
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXIMSP
)( 111 tkX
)( 112 tkX
cos
)()(
)()(
tkXItkXR
tkXItkXR T
Proposed Algorithm for the Detection of Single Source Points
Proposed Algorithm for the Detection of Single Source Points
0510 AM 41
Elimination of OutliersElimination of Outliers
SSPs detection
Clus
terin
g
Outlier elimination
0510 AM 42
0510 AM
Experimental ResultsExperimental Results
dB6747NMSE
No of mixtures =2 No of sources =6
43
Detected Single Source PointsThree mixtures
Detected Single Source PointsThree mixtures
No of mixtures =3 No of sources =60510 AM 44
Comparison with Classical Algorithms for Determined Case
Comparison with Classical Algorithms for Determined Case
No of mixtures =2No of sources =2
Average of 500 experimental results
0510 AM 45
-gt
Comparison with Method Proposed in [1] Underdetermined case
Comparison with Method Proposed in [1] Underdetermined case
[1] Y Li S Amari A Cichocki D W C Ho and S Xie ldquoUnderdetermined blind source separation based on sparse representationrdquo IEEE Transactions on Signal Processing vol 54 p 423ndash437 Feb 2006
0510 AM
Nor
mal
ized
mea
n sq
uare
err
or (N
MSE
) in
mix
ing
mat
rix e
stim
ation
(dB)
Order of the mixing matrices (PxQ)
46
P ndash No of mixturesQ ndash No of sources
Advantages of the Proposed algorithmAdvantages of the Proposed algorithm
Step 1 Convert x in the time domain to the TF domain to get XStep 2 Check the condition
Step 3 If the condition is satisfied then X(k t) is a sample atthe SSP and this sample is kept for mixing matrix estimationotherwise discard the point
Step 4 Repeat Steps 2 to 3 for all the points in the TF planeor until sufficient number of SSPs are obtained
cos
)()(
)()(
tkXItkXR
tkXItkXR T
1) Much simpler constrain the algorithm does not require ldquosingle source zonerdquo
3) The algorithm is extremely simple but effective2) Separation performance is better
0510 AM 47-gt
My Contributions ndash III IV and VMy Contributions ndash III IV and V
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
48
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Mask estimation
Mic 1
Mic P
Mixture in TF domain
Separated signals in TF domain
)( tkX P
)(1 tkX
t
t
k
k
)(1 tkY
)(1 tkY
)( tkYQ
)( tkYQ
QP
0510 AM 49
Mathematical RepresentationMathematical Representation
Q
q
L
lqpqp Pplnslhnx
1
1
0
1)()()(
)()()()()()()( 11 tkSktkSktkSktk QQqq HHHX
)(
)(
)()(
)()(
)(
)( 1
1
1111
tkS
tkS
kHkH
kHkH
tkX
tkX
QPQP
Q
P
)(
)(
)(
)(
)(
)(
)(
)(
)( 11
1
1
11
tkS
kH
kH
tkS
kH
kH
tkS
kH
kH
Q
PQ
Q
q
Pq
q
P
Time domain
Frequency domain
0510 AM 50
P ndash No of mixturesQ ndash No of sources
Single source pointsSingle source pointsInstantaneous mixing
00point at 1 Case 11211111 tkStkStk
)()()(
)()()(
111111
111111
tkSIktkI
tkSRktkR
HX
HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()(
)()()(
222222
222222
tkSIktkI
tkSRktkR
HX
HX
Single source point 2
Real scalar
RealReal
Real scalarReal scalar
Real scalar
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
0510 AM 51
Basic Principle of Single Source Points Detection
Basic Principle of Single Source Points Detection
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
j
H
C
e
cos21
21
UU
UUUUU H
and 20coscos HCH
angle pseudo called is
angleHermitian called is
H The Hermitian angle between the complex
vectors u1 and u2 will remain the same even if the vectors are multiplied by any complex scalars whereas the pseudo angle will change
0510 AM 52
-gt
k
Algorithm for Single Source Points Detection
Algorithm for Single Source Points Detection
t
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)(
)(
)(111
121
111 tkSkH
kH
11
11
j
jr
)(
)(
112
111
tkX
tkX
11
11
j
jr
)(
)(
112
111
tkX
tkX
)( 111 tkX
)( 112 tkX
)(
)(
)(112
122
112 tkSkH
kH θH2
θH1
θH2
rX
rX
)(
)(cos
11
111
tk
tk H
Hq
0510 AM 53
θH1
OR
1k
1k
1t
Clean
Estimated
Mask Estimation by k-means (KM)Mask Estimation by k-means (KM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 54
Clean
Estimated
Mask Estimation by Fuzzy c-means (FCM)Mask Estimation by Fuzzy c-means (FCM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 55
Automatic Detection of Number of SourcesAutomatic Detection of Number of Sources
0510 AM 56
Cluster validation technique
For c = 2 to cmax
Cluster the data into c clustersCalculate the cluster validation index
EndTake c corresponding to the best cluster as the number of sources
-gt
Elimination of Low Energy PointsElimination of Low Energy Points
0510 AM 57
- Blind Separation of Speech Mixtures
- Introduction
- Slide 3
- Slide 4
- Slide 5
- Approaches for BSS of Speech Signals
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Permutation Problem in Frequency Domain BSS
- Motivation
- My Contribution - I
- Algorithm for Solving the Permutation Problem
- Existing Method for Solving the Permutation Problem
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Proposed algorithm Partial separation method (Parallel configuration) Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
- Partial separation method (Parallel configuration)
- Partial separation method (Cascade configuration)
- Advantages of Partial Separation method
- Comparison with Adjacent Bands Correlation Method
- Comparison with DOA method
- My Contribution -II
- Underdetermined Blind Source Separation of Instantaneous Mixtures
- Mathematical Representation of Instantaneous Mixing Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
- Single Source Points in Time-Frequency domain
- Slide 31
- Slide 32
- Scatter Diagram of the Mixtures When Source are Perfectly Sparse
- Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
- Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
- Principle of the Proposed Algorithm for the Detection of Single Source Points
- Slide 39
- Slide 40
- Proposed Algorithm for the Detection of Single Source Points
- Elimination of Outliers
- Slide 43
- Detected Single Source Points Three mixtures
- Comparison with Classical Algorithms for Determined Case
- Comparison with Method Proposed in [1] Underdetermined case
- Advantages of the Proposed algorithm
- My Contributions ndash III IV and V
- Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
- Mathematical Representation
- Single source points
- Basic Principle of Single Source Points Detection
- Algorithm for Single Source Points Detection
- Mask Estimation by k-means (KM)
- Mask Estimation by Fuzzy c-means (FCM)
- Automatic Detection of Number of Sources
- Elimination of Low Energy Points
-
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
r12
r21
r11
r22 r22 r22 r22
r11 r11 r11
r12
r21
r12
r21
r12
r21r11 r12
r21 r22
s1
s2
Correlation matrix
21122211 rrrr No change
21122211 rrrr Change permutation
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Adjacent bands correlation method
0510 AM
21122211 and and rrrr
21122211 and and rrrr
With confidence Without confidence
2090
8010
8020
1090
2090
1040
1040
2090
Example Example
18
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
r12
r21
r11
r22 r22 r22 r22
r11 r11 r11
r12
r21
r12
r21
r12
r21
r11 r12
r21 r22
s1
s2
Correlation matrix
Disadvantage The method is not robust
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Adjacent bands correlation method
0510 AM 19
0510 AM
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Combination of DOA and Correlation methods method
DOA + Harmonic Correlation + Adjacent bands correlation
Advantage Increased robustness
20
Proposed algorithm Partial separation method(Parallel configuration)
Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
Proposed algorithm Partial separation method(Parallel configuration)
Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
2y
1y
1x
2x
1s
2s
0510 AM 21
Time domain stage
Frequency domain stage
Partial separation method(Parallel configuration)
Partial separation method(Parallel configuration)
0510 AM 22
Time domain stage
Frequency domain stage
Parallel configuration
Partial separation method(Cascade configuration)
Partial separation method(Cascade configuration)
0510 AM 23
Time domain stage
Frequency domain stage
Advantages of Partial Separation methodAdvantages of Partial Separation method
bull Robustness
0510 AM 24
Comparison with Adjacent Bands Correlation Method
Comparison with Adjacent Bands Correlation Method
0510 AM 25
PS - Partial Separation method with confidence check C1 - Correlation between the adjacent bins without confidence check C2 - Correlation between adjacent bins with confidence check Ha - Correlation between the harmonic components with confidence check PS1 - Partial separation method alone without confidence check
0510 AM 26
Comparison with DOA methodComparison with DOA method
My Contribution -IIMy Contribution -II
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
27
Underdetermined Blind Source Separation of Instantaneous Mixtures
Underdetermined Blind Source Separation of Instantaneous Mixtures
t
k
0)(0)( 222221 tkStkS
0)(0)( 222221 tkStkS
0)(0)( 112111 tkStkS
0)(0)( 112111 tkStkS
tkX 1
tkX 22x
1x
0510 AM 28
Mathematical Representation of Instantaneous Mixing
Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
Mathematical Representation of Instantaneous Mixing
Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
)(
)(
)(
)( 1
1
1111
tkS
tkS
hh
hh
tkX
tkX
QPQP
Q
P
)(
)(
)(
)( 1
1
1111
ts
ts
hh
hh
tx
tx
QPQP
Q
P
)()()(11
1
1
11
tkS
h
h
tkS
h
h
tkS
h
h
Q
PQ
Q
q
Pq
q
P
)()()()( 21 tkStkStkStk QhhhX
Time domain
Time-Frequency domain
0510 AM 29
P ndash No of mixturesQ ndash No of sources
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
00point at 1 Case 11211111 tkStkStk
)()()( 1122111111 tkStkStk hhX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 2222221122 tkStkStk hhX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
0510 AM
0 0
30
Q
qqq tkStk
1
hX
2Let Q
00point at 1 Case 11211111 tkStkStk
)()( 111111 tkStk hX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()( 222222 tkStk hX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
0510 AM 31
00point at 1 Case 11211111 tkStkStk
)()( 111111 tkStk hX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()( 222222 tkStk hX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
Scalar
ScalarScalar
Scalar
At single source point 1 At single source point 2
111
111
ofDirection )( ofDirection
ofDirection )( ofDirection
hX
hX
tkI
tkR 222
222
ofDirection )( ofDirection
ofDirection )( ofDirection
hX
hX
tkI
tkR
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
0510 AM
1111 ( of Direction ( of Direction tkItkR XX 2222 ( of Direction ( of Direction tkItkR XX 32
Scatter Diagram of the Mixtures When Source are Perfectly Sparse
Scatter Diagram of the Mixtures When Source are Perfectly Sparse
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
22222
11111
2221
1211
22222
11111
kSkSkSkSkS
kSkSkSkSkS
hh
hh
kXkXkXkXkX
kXkXkXkXkX
21
111 h
hh
22
122 h
hh
0 00 0 0
Example
0510 AM 33
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
22222
11111
2221
1211
22222
11111
kSkSkSkSkS
kSkSkSkSkS
hh
hh
kXkXkXkXkX
kXkXkXkXkX
21
111 h
hh
22
122 h
hh
0 00 0 00
Example
Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
0510 AM 34
Scatter Diagram of the Mixtures when Sources are Sparse
Scatter Diagram of the Mixtures when Sources are Sparse
3h
6h
5h
1h4h
2h
0510 AM
No of sources = 6No of mixtures = 2
35
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
3h
6h
5h
1h4h
2h
0510 AM
No of sources = 6No of mixtures = 2
36
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
3h
6h
5h
1h4h
2h
0510 AM
ObjectiveEstimation of the single source points
No of sources = 6No of mixtures = 2
37
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Multi source point
38
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
Multi source point
39
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
Average of 15 pairs of speech utterances of length 10 s each
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
)( ofDirection )( ofDirection tkXItkXR )( ofDirection )( ofDirection tkXItkXR
SSPMSP
40
SSPt
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)()(
)()(
112112
111111
tkXjItkXR
tkXjItkXR
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXI
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXIMSP
)( 111 tkX
)( 112 tkX
cos
)()(
)()(
tkXItkXR
tkXItkXR T
Proposed Algorithm for the Detection of Single Source Points
Proposed Algorithm for the Detection of Single Source Points
0510 AM 41
Elimination of OutliersElimination of Outliers
SSPs detection
Clus
terin
g
Outlier elimination
0510 AM 42
0510 AM
Experimental ResultsExperimental Results
dB6747NMSE
No of mixtures =2 No of sources =6
43
Detected Single Source PointsThree mixtures
Detected Single Source PointsThree mixtures
No of mixtures =3 No of sources =60510 AM 44
Comparison with Classical Algorithms for Determined Case
Comparison with Classical Algorithms for Determined Case
No of mixtures =2No of sources =2
Average of 500 experimental results
0510 AM 45
-gt
Comparison with Method Proposed in [1] Underdetermined case
Comparison with Method Proposed in [1] Underdetermined case
[1] Y Li S Amari A Cichocki D W C Ho and S Xie ldquoUnderdetermined blind source separation based on sparse representationrdquo IEEE Transactions on Signal Processing vol 54 p 423ndash437 Feb 2006
0510 AM
Nor
mal
ized
mea
n sq
uare
err
or (N
MSE
) in
mix
ing
mat
rix e
stim
ation
(dB)
Order of the mixing matrices (PxQ)
46
P ndash No of mixturesQ ndash No of sources
Advantages of the Proposed algorithmAdvantages of the Proposed algorithm
Step 1 Convert x in the time domain to the TF domain to get XStep 2 Check the condition
Step 3 If the condition is satisfied then X(k t) is a sample atthe SSP and this sample is kept for mixing matrix estimationotherwise discard the point
Step 4 Repeat Steps 2 to 3 for all the points in the TF planeor until sufficient number of SSPs are obtained
cos
)()(
)()(
tkXItkXR
tkXItkXR T
1) Much simpler constrain the algorithm does not require ldquosingle source zonerdquo
3) The algorithm is extremely simple but effective2) Separation performance is better
0510 AM 47-gt
My Contributions ndash III IV and VMy Contributions ndash III IV and V
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
48
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Mask estimation
Mic 1
Mic P
Mixture in TF domain
Separated signals in TF domain
)( tkX P
)(1 tkX
t
t
k
k
)(1 tkY
)(1 tkY
)( tkYQ
)( tkYQ
QP
0510 AM 49
Mathematical RepresentationMathematical Representation
Q
q
L
lqpqp Pplnslhnx
1
1
0
1)()()(
)()()()()()()( 11 tkSktkSktkSktk QQqq HHHX
)(
)(
)()(
)()(
)(
)( 1
1
1111
tkS
tkS
kHkH
kHkH
tkX
tkX
QPQP
Q
P
)(
)(
)(
)(
)(
)(
)(
)(
)( 11
1
1
11
tkS
kH
kH
tkS
kH
kH
tkS
kH
kH
Q
PQ
Q
q
Pq
q
P
Time domain
Frequency domain
0510 AM 50
P ndash No of mixturesQ ndash No of sources
Single source pointsSingle source pointsInstantaneous mixing
00point at 1 Case 11211111 tkStkStk
)()()(
)()()(
111111
111111
tkSIktkI
tkSRktkR
HX
HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()(
)()()(
222222
222222
tkSIktkI
tkSRktkR
HX
HX
Single source point 2
Real scalar
RealReal
Real scalarReal scalar
Real scalar
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
0510 AM 51
Basic Principle of Single Source Points Detection
Basic Principle of Single Source Points Detection
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
j
H
C
e
cos21
21
UU
UUUUU H
and 20coscos HCH
angle pseudo called is
angleHermitian called is
H The Hermitian angle between the complex
vectors u1 and u2 will remain the same even if the vectors are multiplied by any complex scalars whereas the pseudo angle will change
0510 AM 52
-gt
k
Algorithm for Single Source Points Detection
Algorithm for Single Source Points Detection
t
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)(
)(
)(111
121
111 tkSkH
kH
11
11
j
jr
)(
)(
112
111
tkX
tkX
11
11
j
jr
)(
)(
112
111
tkX
tkX
)( 111 tkX
)( 112 tkX
)(
)(
)(112
122
112 tkSkH
kH θH2
θH1
θH2
rX
rX
)(
)(cos
11
111
tk
tk H
Hq
0510 AM 53
θH1
OR
1k
1k
1t
Clean
Estimated
Mask Estimation by k-means (KM)Mask Estimation by k-means (KM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 54
Clean
Estimated
Mask Estimation by Fuzzy c-means (FCM)Mask Estimation by Fuzzy c-means (FCM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 55
Automatic Detection of Number of SourcesAutomatic Detection of Number of Sources
0510 AM 56
Cluster validation technique
For c = 2 to cmax
Cluster the data into c clustersCalculate the cluster validation index
EndTake c corresponding to the best cluster as the number of sources
-gt
Elimination of Low Energy PointsElimination of Low Energy Points
0510 AM 57
- Blind Separation of Speech Mixtures
- Introduction
- Slide 3
- Slide 4
- Slide 5
- Approaches for BSS of Speech Signals
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Permutation Problem in Frequency Domain BSS
- Motivation
- My Contribution - I
- Algorithm for Solving the Permutation Problem
- Existing Method for Solving the Permutation Problem
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Proposed algorithm Partial separation method (Parallel configuration) Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
- Partial separation method (Parallel configuration)
- Partial separation method (Cascade configuration)
- Advantages of Partial Separation method
- Comparison with Adjacent Bands Correlation Method
- Comparison with DOA method
- My Contribution -II
- Underdetermined Blind Source Separation of Instantaneous Mixtures
- Mathematical Representation of Instantaneous Mixing Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
- Single Source Points in Time-Frequency domain
- Slide 31
- Slide 32
- Scatter Diagram of the Mixtures When Source are Perfectly Sparse
- Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
- Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
- Principle of the Proposed Algorithm for the Detection of Single Source Points
- Slide 39
- Slide 40
- Proposed Algorithm for the Detection of Single Source Points
- Elimination of Outliers
- Slide 43
- Detected Single Source Points Three mixtures
- Comparison with Classical Algorithms for Determined Case
- Comparison with Method Proposed in [1] Underdetermined case
- Advantages of the Proposed algorithm
- My Contributions ndash III IV and V
- Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
- Mathematical Representation
- Single source points
- Basic Principle of Single Source Points Detection
- Algorithm for Single Source Points Detection
- Mask Estimation by k-means (KM)
- Mask Estimation by Fuzzy c-means (FCM)
- Automatic Detection of Number of Sources
- Elimination of Low Energy Points
-
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
K-1
K
K+1 K+2
K+3
helliphelliphelliphellip
r12
r21
r11
r22 r22 r22 r22
r11 r11 r11
r12
r21
r12
r21
r12
r21
r11 r12
r21 r22
s1
s2
Correlation matrix
Disadvantage The method is not robust
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Adjacent bands correlation method
0510 AM 19
0510 AM
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Combination of DOA and Correlation methods method
DOA + Harmonic Correlation + Adjacent bands correlation
Advantage Increased robustness
20
Proposed algorithm Partial separation method(Parallel configuration)
Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
Proposed algorithm Partial separation method(Parallel configuration)
Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
2y
1y
1x
2x
1s
2s
0510 AM 21
Time domain stage
Frequency domain stage
Partial separation method(Parallel configuration)
Partial separation method(Parallel configuration)
0510 AM 22
Time domain stage
Frequency domain stage
Parallel configuration
Partial separation method(Cascade configuration)
Partial separation method(Cascade configuration)
0510 AM 23
Time domain stage
Frequency domain stage
Advantages of Partial Separation methodAdvantages of Partial Separation method
bull Robustness
0510 AM 24
Comparison with Adjacent Bands Correlation Method
Comparison with Adjacent Bands Correlation Method
0510 AM 25
PS - Partial Separation method with confidence check C1 - Correlation between the adjacent bins without confidence check C2 - Correlation between adjacent bins with confidence check Ha - Correlation between the harmonic components with confidence check PS1 - Partial separation method alone without confidence check
0510 AM 26
Comparison with DOA methodComparison with DOA method
My Contribution -IIMy Contribution -II
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
27
Underdetermined Blind Source Separation of Instantaneous Mixtures
Underdetermined Blind Source Separation of Instantaneous Mixtures
t
k
0)(0)( 222221 tkStkS
0)(0)( 222221 tkStkS
0)(0)( 112111 tkStkS
0)(0)( 112111 tkStkS
tkX 1
tkX 22x
1x
0510 AM 28
Mathematical Representation of Instantaneous Mixing
Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
Mathematical Representation of Instantaneous Mixing
Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
)(
)(
)(
)( 1
1
1111
tkS
tkS
hh
hh
tkX
tkX
QPQP
Q
P
)(
)(
)(
)( 1
1
1111
ts
ts
hh
hh
tx
tx
QPQP
Q
P
)()()(11
1
1
11
tkS
h
h
tkS
h
h
tkS
h
h
Q
PQ
Q
q
Pq
q
P
)()()()( 21 tkStkStkStk QhhhX
Time domain
Time-Frequency domain
0510 AM 29
P ndash No of mixturesQ ndash No of sources
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
00point at 1 Case 11211111 tkStkStk
)()()( 1122111111 tkStkStk hhX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 2222221122 tkStkStk hhX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
0510 AM
0 0
30
Q
qqq tkStk
1
hX
2Let Q
00point at 1 Case 11211111 tkStkStk
)()( 111111 tkStk hX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()( 222222 tkStk hX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
0510 AM 31
00point at 1 Case 11211111 tkStkStk
)()( 111111 tkStk hX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()( 222222 tkStk hX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
Scalar
ScalarScalar
Scalar
At single source point 1 At single source point 2
111
111
ofDirection )( ofDirection
ofDirection )( ofDirection
hX
hX
tkI
tkR 222
222
ofDirection )( ofDirection
ofDirection )( ofDirection
hX
hX
tkI
tkR
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
0510 AM
1111 ( of Direction ( of Direction tkItkR XX 2222 ( of Direction ( of Direction tkItkR XX 32
Scatter Diagram of the Mixtures When Source are Perfectly Sparse
Scatter Diagram of the Mixtures When Source are Perfectly Sparse
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
22222
11111
2221
1211
22222
11111
kSkSkSkSkS
kSkSkSkSkS
hh
hh
kXkXkXkXkX
kXkXkXkXkX
21
111 h
hh
22
122 h
hh
0 00 0 0
Example
0510 AM 33
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
22222
11111
2221
1211
22222
11111
kSkSkSkSkS
kSkSkSkSkS
hh
hh
kXkXkXkXkX
kXkXkXkXkX
21
111 h
hh
22
122 h
hh
0 00 0 00
Example
Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
0510 AM 34
Scatter Diagram of the Mixtures when Sources are Sparse
Scatter Diagram of the Mixtures when Sources are Sparse
3h
6h
5h
1h4h
2h
0510 AM
No of sources = 6No of mixtures = 2
35
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
3h
6h
5h
1h4h
2h
0510 AM
No of sources = 6No of mixtures = 2
36
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
3h
6h
5h
1h4h
2h
0510 AM
ObjectiveEstimation of the single source points
No of sources = 6No of mixtures = 2
37
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Multi source point
38
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
Multi source point
39
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
Average of 15 pairs of speech utterances of length 10 s each
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
)( ofDirection )( ofDirection tkXItkXR )( ofDirection )( ofDirection tkXItkXR
SSPMSP
40
SSPt
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)()(
)()(
112112
111111
tkXjItkXR
tkXjItkXR
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXI
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXIMSP
)( 111 tkX
)( 112 tkX
cos
)()(
)()(
tkXItkXR
tkXItkXR T
Proposed Algorithm for the Detection of Single Source Points
Proposed Algorithm for the Detection of Single Source Points
0510 AM 41
Elimination of OutliersElimination of Outliers
SSPs detection
Clus
terin
g
Outlier elimination
0510 AM 42
0510 AM
Experimental ResultsExperimental Results
dB6747NMSE
No of mixtures =2 No of sources =6
43
Detected Single Source PointsThree mixtures
Detected Single Source PointsThree mixtures
No of mixtures =3 No of sources =60510 AM 44
Comparison with Classical Algorithms for Determined Case
Comparison with Classical Algorithms for Determined Case
No of mixtures =2No of sources =2
Average of 500 experimental results
0510 AM 45
-gt
Comparison with Method Proposed in [1] Underdetermined case
Comparison with Method Proposed in [1] Underdetermined case
[1] Y Li S Amari A Cichocki D W C Ho and S Xie ldquoUnderdetermined blind source separation based on sparse representationrdquo IEEE Transactions on Signal Processing vol 54 p 423ndash437 Feb 2006
0510 AM
Nor
mal
ized
mea
n sq
uare
err
or (N
MSE
) in
mix
ing
mat
rix e
stim
ation
(dB)
Order of the mixing matrices (PxQ)
46
P ndash No of mixturesQ ndash No of sources
Advantages of the Proposed algorithmAdvantages of the Proposed algorithm
Step 1 Convert x in the time domain to the TF domain to get XStep 2 Check the condition
Step 3 If the condition is satisfied then X(k t) is a sample atthe SSP and this sample is kept for mixing matrix estimationotherwise discard the point
Step 4 Repeat Steps 2 to 3 for all the points in the TF planeor until sufficient number of SSPs are obtained
cos
)()(
)()(
tkXItkXR
tkXItkXR T
1) Much simpler constrain the algorithm does not require ldquosingle source zonerdquo
3) The algorithm is extremely simple but effective2) Separation performance is better
0510 AM 47-gt
My Contributions ndash III IV and VMy Contributions ndash III IV and V
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
48
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Mask estimation
Mic 1
Mic P
Mixture in TF domain
Separated signals in TF domain
)( tkX P
)(1 tkX
t
t
k
k
)(1 tkY
)(1 tkY
)( tkYQ
)( tkYQ
QP
0510 AM 49
Mathematical RepresentationMathematical Representation
Q
q
L
lqpqp Pplnslhnx
1
1
0
1)()()(
)()()()()()()( 11 tkSktkSktkSktk QQqq HHHX
)(
)(
)()(
)()(
)(
)( 1
1
1111
tkS
tkS
kHkH
kHkH
tkX
tkX
QPQP
Q
P
)(
)(
)(
)(
)(
)(
)(
)(
)( 11
1
1
11
tkS
kH
kH
tkS
kH
kH
tkS
kH
kH
Q
PQ
Q
q
Pq
q
P
Time domain
Frequency domain
0510 AM 50
P ndash No of mixturesQ ndash No of sources
Single source pointsSingle source pointsInstantaneous mixing
00point at 1 Case 11211111 tkStkStk
)()()(
)()()(
111111
111111
tkSIktkI
tkSRktkR
HX
HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()(
)()()(
222222
222222
tkSIktkI
tkSRktkR
HX
HX
Single source point 2
Real scalar
RealReal
Real scalarReal scalar
Real scalar
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
0510 AM 51
Basic Principle of Single Source Points Detection
Basic Principle of Single Source Points Detection
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
j
H
C
e
cos21
21
UU
UUUUU H
and 20coscos HCH
angle pseudo called is
angleHermitian called is
H The Hermitian angle between the complex
vectors u1 and u2 will remain the same even if the vectors are multiplied by any complex scalars whereas the pseudo angle will change
0510 AM 52
-gt
k
Algorithm for Single Source Points Detection
Algorithm for Single Source Points Detection
t
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)(
)(
)(111
121
111 tkSkH
kH
11
11
j
jr
)(
)(
112
111
tkX
tkX
11
11
j
jr
)(
)(
112
111
tkX
tkX
)( 111 tkX
)( 112 tkX
)(
)(
)(112
122
112 tkSkH
kH θH2
θH1
θH2
rX
rX
)(
)(cos
11
111
tk
tk H
Hq
0510 AM 53
θH1
OR
1k
1k
1t
Clean
Estimated
Mask Estimation by k-means (KM)Mask Estimation by k-means (KM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 54
Clean
Estimated
Mask Estimation by Fuzzy c-means (FCM)Mask Estimation by Fuzzy c-means (FCM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 55
Automatic Detection of Number of SourcesAutomatic Detection of Number of Sources
0510 AM 56
Cluster validation technique
For c = 2 to cmax
Cluster the data into c clustersCalculate the cluster validation index
EndTake c corresponding to the best cluster as the number of sources
-gt
Elimination of Low Energy PointsElimination of Low Energy Points
0510 AM 57
- Blind Separation of Speech Mixtures
- Introduction
- Slide 3
- Slide 4
- Slide 5
- Approaches for BSS of Speech Signals
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Permutation Problem in Frequency Domain BSS
- Motivation
- My Contribution - I
- Algorithm for Solving the Permutation Problem
- Existing Method for Solving the Permutation Problem
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Proposed algorithm Partial separation method (Parallel configuration) Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
- Partial separation method (Parallel configuration)
- Partial separation method (Cascade configuration)
- Advantages of Partial Separation method
- Comparison with Adjacent Bands Correlation Method
- Comparison with DOA method
- My Contribution -II
- Underdetermined Blind Source Separation of Instantaneous Mixtures
- Mathematical Representation of Instantaneous Mixing Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
- Single Source Points in Time-Frequency domain
- Slide 31
- Slide 32
- Scatter Diagram of the Mixtures When Source are Perfectly Sparse
- Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
- Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
- Principle of the Proposed Algorithm for the Detection of Single Source Points
- Slide 39
- Slide 40
- Proposed Algorithm for the Detection of Single Source Points
- Elimination of Outliers
- Slide 43
- Detected Single Source Points Three mixtures
- Comparison with Classical Algorithms for Determined Case
- Comparison with Method Proposed in [1] Underdetermined case
- Advantages of the Proposed algorithm
- My Contributions ndash III IV and V
- Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
- Mathematical Representation
- Single source points
- Basic Principle of Single Source Points Detection
- Algorithm for Single Source Points Detection
- Mask Estimation by k-means (KM)
- Mask Estimation by Fuzzy c-means (FCM)
- Automatic Detection of Number of Sources
- Elimination of Low Energy Points
-
0510 AM
Existing Method forSolving the Permutation Problem
Existing Method forSolving the Permutation Problem
Combination of DOA and Correlation methods method
DOA + Harmonic Correlation + Adjacent bands correlation
Advantage Increased robustness
20
Proposed algorithm Partial separation method(Parallel configuration)
Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
Proposed algorithm Partial separation method(Parallel configuration)
Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
2y
1y
1x
2x
1s
2s
0510 AM 21
Time domain stage
Frequency domain stage
Partial separation method(Parallel configuration)
Partial separation method(Parallel configuration)
0510 AM 22
Time domain stage
Frequency domain stage
Parallel configuration
Partial separation method(Cascade configuration)
Partial separation method(Cascade configuration)
0510 AM 23
Time domain stage
Frequency domain stage
Advantages of Partial Separation methodAdvantages of Partial Separation method
bull Robustness
0510 AM 24
Comparison with Adjacent Bands Correlation Method
Comparison with Adjacent Bands Correlation Method
0510 AM 25
PS - Partial Separation method with confidence check C1 - Correlation between the adjacent bins without confidence check C2 - Correlation between adjacent bins with confidence check Ha - Correlation between the harmonic components with confidence check PS1 - Partial separation method alone without confidence check
0510 AM 26
Comparison with DOA methodComparison with DOA method
My Contribution -IIMy Contribution -II
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
27
Underdetermined Blind Source Separation of Instantaneous Mixtures
Underdetermined Blind Source Separation of Instantaneous Mixtures
t
k
0)(0)( 222221 tkStkS
0)(0)( 222221 tkStkS
0)(0)( 112111 tkStkS
0)(0)( 112111 tkStkS
tkX 1
tkX 22x
1x
0510 AM 28
Mathematical Representation of Instantaneous Mixing
Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
Mathematical Representation of Instantaneous Mixing
Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
)(
)(
)(
)( 1
1
1111
tkS
tkS
hh
hh
tkX
tkX
QPQP
Q
P
)(
)(
)(
)( 1
1
1111
ts
ts
hh
hh
tx
tx
QPQP
Q
P
)()()(11
1
1
11
tkS
h
h
tkS
h
h
tkS
h
h
Q
PQ
Q
q
Pq
q
P
)()()()( 21 tkStkStkStk QhhhX
Time domain
Time-Frequency domain
0510 AM 29
P ndash No of mixturesQ ndash No of sources
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
00point at 1 Case 11211111 tkStkStk
)()()( 1122111111 tkStkStk hhX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 2222221122 tkStkStk hhX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
0510 AM
0 0
30
Q
qqq tkStk
1
hX
2Let Q
00point at 1 Case 11211111 tkStkStk
)()( 111111 tkStk hX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()( 222222 tkStk hX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
0510 AM 31
00point at 1 Case 11211111 tkStkStk
)()( 111111 tkStk hX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()( 222222 tkStk hX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
Scalar
ScalarScalar
Scalar
At single source point 1 At single source point 2
111
111
ofDirection )( ofDirection
ofDirection )( ofDirection
hX
hX
tkI
tkR 222
222
ofDirection )( ofDirection
ofDirection )( ofDirection
hX
hX
tkI
tkR
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
0510 AM
1111 ( of Direction ( of Direction tkItkR XX 2222 ( of Direction ( of Direction tkItkR XX 32
Scatter Diagram of the Mixtures When Source are Perfectly Sparse
Scatter Diagram of the Mixtures When Source are Perfectly Sparse
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
22222
11111
2221
1211
22222
11111
kSkSkSkSkS
kSkSkSkSkS
hh
hh
kXkXkXkXkX
kXkXkXkXkX
21
111 h
hh
22
122 h
hh
0 00 0 0
Example
0510 AM 33
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
22222
11111
2221
1211
22222
11111
kSkSkSkSkS
kSkSkSkSkS
hh
hh
kXkXkXkXkX
kXkXkXkXkX
21
111 h
hh
22
122 h
hh
0 00 0 00
Example
Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
0510 AM 34
Scatter Diagram of the Mixtures when Sources are Sparse
Scatter Diagram of the Mixtures when Sources are Sparse
3h
6h
5h
1h4h
2h
0510 AM
No of sources = 6No of mixtures = 2
35
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
3h
6h
5h
1h4h
2h
0510 AM
No of sources = 6No of mixtures = 2
36
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
3h
6h
5h
1h4h
2h
0510 AM
ObjectiveEstimation of the single source points
No of sources = 6No of mixtures = 2
37
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Multi source point
38
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
Multi source point
39
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
Average of 15 pairs of speech utterances of length 10 s each
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
)( ofDirection )( ofDirection tkXItkXR )( ofDirection )( ofDirection tkXItkXR
SSPMSP
40
SSPt
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)()(
)()(
112112
111111
tkXjItkXR
tkXjItkXR
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXI
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXIMSP
)( 111 tkX
)( 112 tkX
cos
)()(
)()(
tkXItkXR
tkXItkXR T
Proposed Algorithm for the Detection of Single Source Points
Proposed Algorithm for the Detection of Single Source Points
0510 AM 41
Elimination of OutliersElimination of Outliers
SSPs detection
Clus
terin
g
Outlier elimination
0510 AM 42
0510 AM
Experimental ResultsExperimental Results
dB6747NMSE
No of mixtures =2 No of sources =6
43
Detected Single Source PointsThree mixtures
Detected Single Source PointsThree mixtures
No of mixtures =3 No of sources =60510 AM 44
Comparison with Classical Algorithms for Determined Case
Comparison with Classical Algorithms for Determined Case
No of mixtures =2No of sources =2
Average of 500 experimental results
0510 AM 45
-gt
Comparison with Method Proposed in [1] Underdetermined case
Comparison with Method Proposed in [1] Underdetermined case
[1] Y Li S Amari A Cichocki D W C Ho and S Xie ldquoUnderdetermined blind source separation based on sparse representationrdquo IEEE Transactions on Signal Processing vol 54 p 423ndash437 Feb 2006
0510 AM
Nor
mal
ized
mea
n sq
uare
err
or (N
MSE
) in
mix
ing
mat
rix e
stim
ation
(dB)
Order of the mixing matrices (PxQ)
46
P ndash No of mixturesQ ndash No of sources
Advantages of the Proposed algorithmAdvantages of the Proposed algorithm
Step 1 Convert x in the time domain to the TF domain to get XStep 2 Check the condition
Step 3 If the condition is satisfied then X(k t) is a sample atthe SSP and this sample is kept for mixing matrix estimationotherwise discard the point
Step 4 Repeat Steps 2 to 3 for all the points in the TF planeor until sufficient number of SSPs are obtained
cos
)()(
)()(
tkXItkXR
tkXItkXR T
1) Much simpler constrain the algorithm does not require ldquosingle source zonerdquo
3) The algorithm is extremely simple but effective2) Separation performance is better
0510 AM 47-gt
My Contributions ndash III IV and VMy Contributions ndash III IV and V
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
48
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Mask estimation
Mic 1
Mic P
Mixture in TF domain
Separated signals in TF domain
)( tkX P
)(1 tkX
t
t
k
k
)(1 tkY
)(1 tkY
)( tkYQ
)( tkYQ
QP
0510 AM 49
Mathematical RepresentationMathematical Representation
Q
q
L
lqpqp Pplnslhnx
1
1
0
1)()()(
)()()()()()()( 11 tkSktkSktkSktk QQqq HHHX
)(
)(
)()(
)()(
)(
)( 1
1
1111
tkS
tkS
kHkH
kHkH
tkX
tkX
QPQP
Q
P
)(
)(
)(
)(
)(
)(
)(
)(
)( 11
1
1
11
tkS
kH
kH
tkS
kH
kH
tkS
kH
kH
Q
PQ
Q
q
Pq
q
P
Time domain
Frequency domain
0510 AM 50
P ndash No of mixturesQ ndash No of sources
Single source pointsSingle source pointsInstantaneous mixing
00point at 1 Case 11211111 tkStkStk
)()()(
)()()(
111111
111111
tkSIktkI
tkSRktkR
HX
HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()(
)()()(
222222
222222
tkSIktkI
tkSRktkR
HX
HX
Single source point 2
Real scalar
RealReal
Real scalarReal scalar
Real scalar
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
0510 AM 51
Basic Principle of Single Source Points Detection
Basic Principle of Single Source Points Detection
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
j
H
C
e
cos21
21
UU
UUUUU H
and 20coscos HCH
angle pseudo called is
angleHermitian called is
H The Hermitian angle between the complex
vectors u1 and u2 will remain the same even if the vectors are multiplied by any complex scalars whereas the pseudo angle will change
0510 AM 52
-gt
k
Algorithm for Single Source Points Detection
Algorithm for Single Source Points Detection
t
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)(
)(
)(111
121
111 tkSkH
kH
11
11
j
jr
)(
)(
112
111
tkX
tkX
11
11
j
jr
)(
)(
112
111
tkX
tkX
)( 111 tkX
)( 112 tkX
)(
)(
)(112
122
112 tkSkH
kH θH2
θH1
θH2
rX
rX
)(
)(cos
11
111
tk
tk H
Hq
0510 AM 53
θH1
OR
1k
1k
1t
Clean
Estimated
Mask Estimation by k-means (KM)Mask Estimation by k-means (KM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 54
Clean
Estimated
Mask Estimation by Fuzzy c-means (FCM)Mask Estimation by Fuzzy c-means (FCM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 55
Automatic Detection of Number of SourcesAutomatic Detection of Number of Sources
0510 AM 56
Cluster validation technique
For c = 2 to cmax
Cluster the data into c clustersCalculate the cluster validation index
EndTake c corresponding to the best cluster as the number of sources
-gt
Elimination of Low Energy PointsElimination of Low Energy Points
0510 AM 57
- Blind Separation of Speech Mixtures
- Introduction
- Slide 3
- Slide 4
- Slide 5
- Approaches for BSS of Speech Signals
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Permutation Problem in Frequency Domain BSS
- Motivation
- My Contribution - I
- Algorithm for Solving the Permutation Problem
- Existing Method for Solving the Permutation Problem
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Proposed algorithm Partial separation method (Parallel configuration) Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
- Partial separation method (Parallel configuration)
- Partial separation method (Cascade configuration)
- Advantages of Partial Separation method
- Comparison with Adjacent Bands Correlation Method
- Comparison with DOA method
- My Contribution -II
- Underdetermined Blind Source Separation of Instantaneous Mixtures
- Mathematical Representation of Instantaneous Mixing Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
- Single Source Points in Time-Frequency domain
- Slide 31
- Slide 32
- Scatter Diagram of the Mixtures When Source are Perfectly Sparse
- Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
- Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
- Principle of the Proposed Algorithm for the Detection of Single Source Points
- Slide 39
- Slide 40
- Proposed Algorithm for the Detection of Single Source Points
- Elimination of Outliers
- Slide 43
- Detected Single Source Points Three mixtures
- Comparison with Classical Algorithms for Determined Case
- Comparison with Method Proposed in [1] Underdetermined case
- Advantages of the Proposed algorithm
- My Contributions ndash III IV and V
- Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
- Mathematical Representation
- Single source points
- Basic Principle of Single Source Points Detection
- Algorithm for Single Source Points Detection
- Mask Estimation by k-means (KM)
- Mask Estimation by Fuzzy c-means (FCM)
- Automatic Detection of Number of Sources
- Elimination of Low Energy Points
-
Proposed algorithm Partial separation method(Parallel configuration)
Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
Proposed algorithm Partial separation method(Parallel configuration)
Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
2y
1y
1x
2x
1s
2s
0510 AM 21
Time domain stage
Frequency domain stage
Partial separation method(Parallel configuration)
Partial separation method(Parallel configuration)
0510 AM 22
Time domain stage
Frequency domain stage
Parallel configuration
Partial separation method(Cascade configuration)
Partial separation method(Cascade configuration)
0510 AM 23
Time domain stage
Frequency domain stage
Advantages of Partial Separation methodAdvantages of Partial Separation method
bull Robustness
0510 AM 24
Comparison with Adjacent Bands Correlation Method
Comparison with Adjacent Bands Correlation Method
0510 AM 25
PS - Partial Separation method with confidence check C1 - Correlation between the adjacent bins without confidence check C2 - Correlation between adjacent bins with confidence check Ha - Correlation between the harmonic components with confidence check PS1 - Partial separation method alone without confidence check
0510 AM 26
Comparison with DOA methodComparison with DOA method
My Contribution -IIMy Contribution -II
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
27
Underdetermined Blind Source Separation of Instantaneous Mixtures
Underdetermined Blind Source Separation of Instantaneous Mixtures
t
k
0)(0)( 222221 tkStkS
0)(0)( 222221 tkStkS
0)(0)( 112111 tkStkS
0)(0)( 112111 tkStkS
tkX 1
tkX 22x
1x
0510 AM 28
Mathematical Representation of Instantaneous Mixing
Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
Mathematical Representation of Instantaneous Mixing
Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
)(
)(
)(
)( 1
1
1111
tkS
tkS
hh
hh
tkX
tkX
QPQP
Q
P
)(
)(
)(
)( 1
1
1111
ts
ts
hh
hh
tx
tx
QPQP
Q
P
)()()(11
1
1
11
tkS
h
h
tkS
h
h
tkS
h
h
Q
PQ
Q
q
Pq
q
P
)()()()( 21 tkStkStkStk QhhhX
Time domain
Time-Frequency domain
0510 AM 29
P ndash No of mixturesQ ndash No of sources
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
00point at 1 Case 11211111 tkStkStk
)()()( 1122111111 tkStkStk hhX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 2222221122 tkStkStk hhX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
0510 AM
0 0
30
Q
qqq tkStk
1
hX
2Let Q
00point at 1 Case 11211111 tkStkStk
)()( 111111 tkStk hX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()( 222222 tkStk hX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
0510 AM 31
00point at 1 Case 11211111 tkStkStk
)()( 111111 tkStk hX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()( 222222 tkStk hX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
Scalar
ScalarScalar
Scalar
At single source point 1 At single source point 2
111
111
ofDirection )( ofDirection
ofDirection )( ofDirection
hX
hX
tkI
tkR 222
222
ofDirection )( ofDirection
ofDirection )( ofDirection
hX
hX
tkI
tkR
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
0510 AM
1111 ( of Direction ( of Direction tkItkR XX 2222 ( of Direction ( of Direction tkItkR XX 32
Scatter Diagram of the Mixtures When Source are Perfectly Sparse
Scatter Diagram of the Mixtures When Source are Perfectly Sparse
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
22222
11111
2221
1211
22222
11111
kSkSkSkSkS
kSkSkSkSkS
hh
hh
kXkXkXkXkX
kXkXkXkXkX
21
111 h
hh
22
122 h
hh
0 00 0 0
Example
0510 AM 33
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
22222
11111
2221
1211
22222
11111
kSkSkSkSkS
kSkSkSkSkS
hh
hh
kXkXkXkXkX
kXkXkXkXkX
21
111 h
hh
22
122 h
hh
0 00 0 00
Example
Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
0510 AM 34
Scatter Diagram of the Mixtures when Sources are Sparse
Scatter Diagram of the Mixtures when Sources are Sparse
3h
6h
5h
1h4h
2h
0510 AM
No of sources = 6No of mixtures = 2
35
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
3h
6h
5h
1h4h
2h
0510 AM
No of sources = 6No of mixtures = 2
36
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
3h
6h
5h
1h4h
2h
0510 AM
ObjectiveEstimation of the single source points
No of sources = 6No of mixtures = 2
37
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Multi source point
38
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
Multi source point
39
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
Average of 15 pairs of speech utterances of length 10 s each
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
)( ofDirection )( ofDirection tkXItkXR )( ofDirection )( ofDirection tkXItkXR
SSPMSP
40
SSPt
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)()(
)()(
112112
111111
tkXjItkXR
tkXjItkXR
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXI
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXIMSP
)( 111 tkX
)( 112 tkX
cos
)()(
)()(
tkXItkXR
tkXItkXR T
Proposed Algorithm for the Detection of Single Source Points
Proposed Algorithm for the Detection of Single Source Points
0510 AM 41
Elimination of OutliersElimination of Outliers
SSPs detection
Clus
terin
g
Outlier elimination
0510 AM 42
0510 AM
Experimental ResultsExperimental Results
dB6747NMSE
No of mixtures =2 No of sources =6
43
Detected Single Source PointsThree mixtures
Detected Single Source PointsThree mixtures
No of mixtures =3 No of sources =60510 AM 44
Comparison with Classical Algorithms for Determined Case
Comparison with Classical Algorithms for Determined Case
No of mixtures =2No of sources =2
Average of 500 experimental results
0510 AM 45
-gt
Comparison with Method Proposed in [1] Underdetermined case
Comparison with Method Proposed in [1] Underdetermined case
[1] Y Li S Amari A Cichocki D W C Ho and S Xie ldquoUnderdetermined blind source separation based on sparse representationrdquo IEEE Transactions on Signal Processing vol 54 p 423ndash437 Feb 2006
0510 AM
Nor
mal
ized
mea
n sq
uare
err
or (N
MSE
) in
mix
ing
mat
rix e
stim
ation
(dB)
Order of the mixing matrices (PxQ)
46
P ndash No of mixturesQ ndash No of sources
Advantages of the Proposed algorithmAdvantages of the Proposed algorithm
Step 1 Convert x in the time domain to the TF domain to get XStep 2 Check the condition
Step 3 If the condition is satisfied then X(k t) is a sample atthe SSP and this sample is kept for mixing matrix estimationotherwise discard the point
Step 4 Repeat Steps 2 to 3 for all the points in the TF planeor until sufficient number of SSPs are obtained
cos
)()(
)()(
tkXItkXR
tkXItkXR T
1) Much simpler constrain the algorithm does not require ldquosingle source zonerdquo
3) The algorithm is extremely simple but effective2) Separation performance is better
0510 AM 47-gt
My Contributions ndash III IV and VMy Contributions ndash III IV and V
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
48
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Mask estimation
Mic 1
Mic P
Mixture in TF domain
Separated signals in TF domain
)( tkX P
)(1 tkX
t
t
k
k
)(1 tkY
)(1 tkY
)( tkYQ
)( tkYQ
QP
0510 AM 49
Mathematical RepresentationMathematical Representation
Q
q
L
lqpqp Pplnslhnx
1
1
0
1)()()(
)()()()()()()( 11 tkSktkSktkSktk QQqq HHHX
)(
)(
)()(
)()(
)(
)( 1
1
1111
tkS
tkS
kHkH
kHkH
tkX
tkX
QPQP
Q
P
)(
)(
)(
)(
)(
)(
)(
)(
)( 11
1
1
11
tkS
kH
kH
tkS
kH
kH
tkS
kH
kH
Q
PQ
Q
q
Pq
q
P
Time domain
Frequency domain
0510 AM 50
P ndash No of mixturesQ ndash No of sources
Single source pointsSingle source pointsInstantaneous mixing
00point at 1 Case 11211111 tkStkStk
)()()(
)()()(
111111
111111
tkSIktkI
tkSRktkR
HX
HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()(
)()()(
222222
222222
tkSIktkI
tkSRktkR
HX
HX
Single source point 2
Real scalar
RealReal
Real scalarReal scalar
Real scalar
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
0510 AM 51
Basic Principle of Single Source Points Detection
Basic Principle of Single Source Points Detection
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
j
H
C
e
cos21
21
UU
UUUUU H
and 20coscos HCH
angle pseudo called is
angleHermitian called is
H The Hermitian angle between the complex
vectors u1 and u2 will remain the same even if the vectors are multiplied by any complex scalars whereas the pseudo angle will change
0510 AM 52
-gt
k
Algorithm for Single Source Points Detection
Algorithm for Single Source Points Detection
t
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)(
)(
)(111
121
111 tkSkH
kH
11
11
j
jr
)(
)(
112
111
tkX
tkX
11
11
j
jr
)(
)(
112
111
tkX
tkX
)( 111 tkX
)( 112 tkX
)(
)(
)(112
122
112 tkSkH
kH θH2
θH1
θH2
rX
rX
)(
)(cos
11
111
tk
tk H
Hq
0510 AM 53
θH1
OR
1k
1k
1t
Clean
Estimated
Mask Estimation by k-means (KM)Mask Estimation by k-means (KM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 54
Clean
Estimated
Mask Estimation by Fuzzy c-means (FCM)Mask Estimation by Fuzzy c-means (FCM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 55
Automatic Detection of Number of SourcesAutomatic Detection of Number of Sources
0510 AM 56
Cluster validation technique
For c = 2 to cmax
Cluster the data into c clustersCalculate the cluster validation index
EndTake c corresponding to the best cluster as the number of sources
-gt
Elimination of Low Energy PointsElimination of Low Energy Points
0510 AM 57
- Blind Separation of Speech Mixtures
- Introduction
- Slide 3
- Slide 4
- Slide 5
- Approaches for BSS of Speech Signals
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Permutation Problem in Frequency Domain BSS
- Motivation
- My Contribution - I
- Algorithm for Solving the Permutation Problem
- Existing Method for Solving the Permutation Problem
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Proposed algorithm Partial separation method (Parallel configuration) Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
- Partial separation method (Parallel configuration)
- Partial separation method (Cascade configuration)
- Advantages of Partial Separation method
- Comparison with Adjacent Bands Correlation Method
- Comparison with DOA method
- My Contribution -II
- Underdetermined Blind Source Separation of Instantaneous Mixtures
- Mathematical Representation of Instantaneous Mixing Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
- Single Source Points in Time-Frequency domain
- Slide 31
- Slide 32
- Scatter Diagram of the Mixtures When Source are Perfectly Sparse
- Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
- Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
- Principle of the Proposed Algorithm for the Detection of Single Source Points
- Slide 39
- Slide 40
- Proposed Algorithm for the Detection of Single Source Points
- Elimination of Outliers
- Slide 43
- Detected Single Source Points Three mixtures
- Comparison with Classical Algorithms for Determined Case
- Comparison with Method Proposed in [1] Underdetermined case
- Advantages of the Proposed algorithm
- My Contributions ndash III IV and V
- Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
- Mathematical Representation
- Single source points
- Basic Principle of Single Source Points Detection
- Algorithm for Single Source Points Detection
- Mask Estimation by k-means (KM)
- Mask Estimation by Fuzzy c-means (FCM)
- Automatic Detection of Number of Sources
- Elimination of Low Energy Points
-
Partial separation method(Parallel configuration)
Partial separation method(Parallel configuration)
0510 AM 22
Time domain stage
Frequency domain stage
Parallel configuration
Partial separation method(Cascade configuration)
Partial separation method(Cascade configuration)
0510 AM 23
Time domain stage
Frequency domain stage
Advantages of Partial Separation methodAdvantages of Partial Separation method
bull Robustness
0510 AM 24
Comparison with Adjacent Bands Correlation Method
Comparison with Adjacent Bands Correlation Method
0510 AM 25
PS - Partial Separation method with confidence check C1 - Correlation between the adjacent bins without confidence check C2 - Correlation between adjacent bins with confidence check Ha - Correlation between the harmonic components with confidence check PS1 - Partial separation method alone without confidence check
0510 AM 26
Comparison with DOA methodComparison with DOA method
My Contribution -IIMy Contribution -II
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
27
Underdetermined Blind Source Separation of Instantaneous Mixtures
Underdetermined Blind Source Separation of Instantaneous Mixtures
t
k
0)(0)( 222221 tkStkS
0)(0)( 222221 tkStkS
0)(0)( 112111 tkStkS
0)(0)( 112111 tkStkS
tkX 1
tkX 22x
1x
0510 AM 28
Mathematical Representation of Instantaneous Mixing
Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
Mathematical Representation of Instantaneous Mixing
Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
)(
)(
)(
)( 1
1
1111
tkS
tkS
hh
hh
tkX
tkX
QPQP
Q
P
)(
)(
)(
)( 1
1
1111
ts
ts
hh
hh
tx
tx
QPQP
Q
P
)()()(11
1
1
11
tkS
h
h
tkS
h
h
tkS
h
h
Q
PQ
Q
q
Pq
q
P
)()()()( 21 tkStkStkStk QhhhX
Time domain
Time-Frequency domain
0510 AM 29
P ndash No of mixturesQ ndash No of sources
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
00point at 1 Case 11211111 tkStkStk
)()()( 1122111111 tkStkStk hhX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 2222221122 tkStkStk hhX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
0510 AM
0 0
30
Q
qqq tkStk
1
hX
2Let Q
00point at 1 Case 11211111 tkStkStk
)()( 111111 tkStk hX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()( 222222 tkStk hX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
0510 AM 31
00point at 1 Case 11211111 tkStkStk
)()( 111111 tkStk hX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()( 222222 tkStk hX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
Scalar
ScalarScalar
Scalar
At single source point 1 At single source point 2
111
111
ofDirection )( ofDirection
ofDirection )( ofDirection
hX
hX
tkI
tkR 222
222
ofDirection )( ofDirection
ofDirection )( ofDirection
hX
hX
tkI
tkR
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
0510 AM
1111 ( of Direction ( of Direction tkItkR XX 2222 ( of Direction ( of Direction tkItkR XX 32
Scatter Diagram of the Mixtures When Source are Perfectly Sparse
Scatter Diagram of the Mixtures When Source are Perfectly Sparse
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
22222
11111
2221
1211
22222
11111
kSkSkSkSkS
kSkSkSkSkS
hh
hh
kXkXkXkXkX
kXkXkXkXkX
21
111 h
hh
22
122 h
hh
0 00 0 0
Example
0510 AM 33
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
22222
11111
2221
1211
22222
11111
kSkSkSkSkS
kSkSkSkSkS
hh
hh
kXkXkXkXkX
kXkXkXkXkX
21
111 h
hh
22
122 h
hh
0 00 0 00
Example
Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
0510 AM 34
Scatter Diagram of the Mixtures when Sources are Sparse
Scatter Diagram of the Mixtures when Sources are Sparse
3h
6h
5h
1h4h
2h
0510 AM
No of sources = 6No of mixtures = 2
35
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
3h
6h
5h
1h4h
2h
0510 AM
No of sources = 6No of mixtures = 2
36
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
3h
6h
5h
1h4h
2h
0510 AM
ObjectiveEstimation of the single source points
No of sources = 6No of mixtures = 2
37
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Multi source point
38
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
Multi source point
39
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
Average of 15 pairs of speech utterances of length 10 s each
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
)( ofDirection )( ofDirection tkXItkXR )( ofDirection )( ofDirection tkXItkXR
SSPMSP
40
SSPt
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)()(
)()(
112112
111111
tkXjItkXR
tkXjItkXR
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXI
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXIMSP
)( 111 tkX
)( 112 tkX
cos
)()(
)()(
tkXItkXR
tkXItkXR T
Proposed Algorithm for the Detection of Single Source Points
Proposed Algorithm for the Detection of Single Source Points
0510 AM 41
Elimination of OutliersElimination of Outliers
SSPs detection
Clus
terin
g
Outlier elimination
0510 AM 42
0510 AM
Experimental ResultsExperimental Results
dB6747NMSE
No of mixtures =2 No of sources =6
43
Detected Single Source PointsThree mixtures
Detected Single Source PointsThree mixtures
No of mixtures =3 No of sources =60510 AM 44
Comparison with Classical Algorithms for Determined Case
Comparison with Classical Algorithms for Determined Case
No of mixtures =2No of sources =2
Average of 500 experimental results
0510 AM 45
-gt
Comparison with Method Proposed in [1] Underdetermined case
Comparison with Method Proposed in [1] Underdetermined case
[1] Y Li S Amari A Cichocki D W C Ho and S Xie ldquoUnderdetermined blind source separation based on sparse representationrdquo IEEE Transactions on Signal Processing vol 54 p 423ndash437 Feb 2006
0510 AM
Nor
mal
ized
mea
n sq
uare
err
or (N
MSE
) in
mix
ing
mat
rix e
stim
ation
(dB)
Order of the mixing matrices (PxQ)
46
P ndash No of mixturesQ ndash No of sources
Advantages of the Proposed algorithmAdvantages of the Proposed algorithm
Step 1 Convert x in the time domain to the TF domain to get XStep 2 Check the condition
Step 3 If the condition is satisfied then X(k t) is a sample atthe SSP and this sample is kept for mixing matrix estimationotherwise discard the point
Step 4 Repeat Steps 2 to 3 for all the points in the TF planeor until sufficient number of SSPs are obtained
cos
)()(
)()(
tkXItkXR
tkXItkXR T
1) Much simpler constrain the algorithm does not require ldquosingle source zonerdquo
3) The algorithm is extremely simple but effective2) Separation performance is better
0510 AM 47-gt
My Contributions ndash III IV and VMy Contributions ndash III IV and V
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
48
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Mask estimation
Mic 1
Mic P
Mixture in TF domain
Separated signals in TF domain
)( tkX P
)(1 tkX
t
t
k
k
)(1 tkY
)(1 tkY
)( tkYQ
)( tkYQ
QP
0510 AM 49
Mathematical RepresentationMathematical Representation
Q
q
L
lqpqp Pplnslhnx
1
1
0
1)()()(
)()()()()()()( 11 tkSktkSktkSktk QQqq HHHX
)(
)(
)()(
)()(
)(
)( 1
1
1111
tkS
tkS
kHkH
kHkH
tkX
tkX
QPQP
Q
P
)(
)(
)(
)(
)(
)(
)(
)(
)( 11
1
1
11
tkS
kH
kH
tkS
kH
kH
tkS
kH
kH
Q
PQ
Q
q
Pq
q
P
Time domain
Frequency domain
0510 AM 50
P ndash No of mixturesQ ndash No of sources
Single source pointsSingle source pointsInstantaneous mixing
00point at 1 Case 11211111 tkStkStk
)()()(
)()()(
111111
111111
tkSIktkI
tkSRktkR
HX
HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()(
)()()(
222222
222222
tkSIktkI
tkSRktkR
HX
HX
Single source point 2
Real scalar
RealReal
Real scalarReal scalar
Real scalar
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
0510 AM 51
Basic Principle of Single Source Points Detection
Basic Principle of Single Source Points Detection
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
j
H
C
e
cos21
21
UU
UUUUU H
and 20coscos HCH
angle pseudo called is
angleHermitian called is
H The Hermitian angle between the complex
vectors u1 and u2 will remain the same even if the vectors are multiplied by any complex scalars whereas the pseudo angle will change
0510 AM 52
-gt
k
Algorithm for Single Source Points Detection
Algorithm for Single Source Points Detection
t
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)(
)(
)(111
121
111 tkSkH
kH
11
11
j
jr
)(
)(
112
111
tkX
tkX
11
11
j
jr
)(
)(
112
111
tkX
tkX
)( 111 tkX
)( 112 tkX
)(
)(
)(112
122
112 tkSkH
kH θH2
θH1
θH2
rX
rX
)(
)(cos
11
111
tk
tk H
Hq
0510 AM 53
θH1
OR
1k
1k
1t
Clean
Estimated
Mask Estimation by k-means (KM)Mask Estimation by k-means (KM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 54
Clean
Estimated
Mask Estimation by Fuzzy c-means (FCM)Mask Estimation by Fuzzy c-means (FCM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 55
Automatic Detection of Number of SourcesAutomatic Detection of Number of Sources
0510 AM 56
Cluster validation technique
For c = 2 to cmax
Cluster the data into c clustersCalculate the cluster validation index
EndTake c corresponding to the best cluster as the number of sources
-gt
Elimination of Low Energy PointsElimination of Low Energy Points
0510 AM 57
- Blind Separation of Speech Mixtures
- Introduction
- Slide 3
- Slide 4
- Slide 5
- Approaches for BSS of Speech Signals
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Permutation Problem in Frequency Domain BSS
- Motivation
- My Contribution - I
- Algorithm for Solving the Permutation Problem
- Existing Method for Solving the Permutation Problem
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Proposed algorithm Partial separation method (Parallel configuration) Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
- Partial separation method (Parallel configuration)
- Partial separation method (Cascade configuration)
- Advantages of Partial Separation method
- Comparison with Adjacent Bands Correlation Method
- Comparison with DOA method
- My Contribution -II
- Underdetermined Blind Source Separation of Instantaneous Mixtures
- Mathematical Representation of Instantaneous Mixing Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
- Single Source Points in Time-Frequency domain
- Slide 31
- Slide 32
- Scatter Diagram of the Mixtures When Source are Perfectly Sparse
- Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
- Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
- Principle of the Proposed Algorithm for the Detection of Single Source Points
- Slide 39
- Slide 40
- Proposed Algorithm for the Detection of Single Source Points
- Elimination of Outliers
- Slide 43
- Detected Single Source Points Three mixtures
- Comparison with Classical Algorithms for Determined Case
- Comparison with Method Proposed in [1] Underdetermined case
- Advantages of the Proposed algorithm
- My Contributions ndash III IV and V
- Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
- Mathematical Representation
- Single source points
- Basic Principle of Single Source Points Detection
- Algorithm for Single Source Points Detection
- Mask Estimation by k-means (KM)
- Mask Estimation by Fuzzy c-means (FCM)
- Automatic Detection of Number of Sources
- Elimination of Low Energy Points
-
Parallel configuration
Partial separation method(Cascade configuration)
Partial separation method(Cascade configuration)
0510 AM 23
Time domain stage
Frequency domain stage
Advantages of Partial Separation methodAdvantages of Partial Separation method
bull Robustness
0510 AM 24
Comparison with Adjacent Bands Correlation Method
Comparison with Adjacent Bands Correlation Method
0510 AM 25
PS - Partial Separation method with confidence check C1 - Correlation between the adjacent bins without confidence check C2 - Correlation between adjacent bins with confidence check Ha - Correlation between the harmonic components with confidence check PS1 - Partial separation method alone without confidence check
0510 AM 26
Comparison with DOA methodComparison with DOA method
My Contribution -IIMy Contribution -II
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
27
Underdetermined Blind Source Separation of Instantaneous Mixtures
Underdetermined Blind Source Separation of Instantaneous Mixtures
t
k
0)(0)( 222221 tkStkS
0)(0)( 222221 tkStkS
0)(0)( 112111 tkStkS
0)(0)( 112111 tkStkS
tkX 1
tkX 22x
1x
0510 AM 28
Mathematical Representation of Instantaneous Mixing
Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
Mathematical Representation of Instantaneous Mixing
Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
)(
)(
)(
)( 1
1
1111
tkS
tkS
hh
hh
tkX
tkX
QPQP
Q
P
)(
)(
)(
)( 1
1
1111
ts
ts
hh
hh
tx
tx
QPQP
Q
P
)()()(11
1
1
11
tkS
h
h
tkS
h
h
tkS
h
h
Q
PQ
Q
q
Pq
q
P
)()()()( 21 tkStkStkStk QhhhX
Time domain
Time-Frequency domain
0510 AM 29
P ndash No of mixturesQ ndash No of sources
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
00point at 1 Case 11211111 tkStkStk
)()()( 1122111111 tkStkStk hhX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 2222221122 tkStkStk hhX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
0510 AM
0 0
30
Q
qqq tkStk
1
hX
2Let Q
00point at 1 Case 11211111 tkStkStk
)()( 111111 tkStk hX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()( 222222 tkStk hX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
0510 AM 31
00point at 1 Case 11211111 tkStkStk
)()( 111111 tkStk hX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()( 222222 tkStk hX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
Scalar
ScalarScalar
Scalar
At single source point 1 At single source point 2
111
111
ofDirection )( ofDirection
ofDirection )( ofDirection
hX
hX
tkI
tkR 222
222
ofDirection )( ofDirection
ofDirection )( ofDirection
hX
hX
tkI
tkR
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
0510 AM
1111 ( of Direction ( of Direction tkItkR XX 2222 ( of Direction ( of Direction tkItkR XX 32
Scatter Diagram of the Mixtures When Source are Perfectly Sparse
Scatter Diagram of the Mixtures When Source are Perfectly Sparse
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
22222
11111
2221
1211
22222
11111
kSkSkSkSkS
kSkSkSkSkS
hh
hh
kXkXkXkXkX
kXkXkXkXkX
21
111 h
hh
22
122 h
hh
0 00 0 0
Example
0510 AM 33
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
22222
11111
2221
1211
22222
11111
kSkSkSkSkS
kSkSkSkSkS
hh
hh
kXkXkXkXkX
kXkXkXkXkX
21
111 h
hh
22
122 h
hh
0 00 0 00
Example
Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
0510 AM 34
Scatter Diagram of the Mixtures when Sources are Sparse
Scatter Diagram of the Mixtures when Sources are Sparse
3h
6h
5h
1h4h
2h
0510 AM
No of sources = 6No of mixtures = 2
35
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
3h
6h
5h
1h4h
2h
0510 AM
No of sources = 6No of mixtures = 2
36
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
3h
6h
5h
1h4h
2h
0510 AM
ObjectiveEstimation of the single source points
No of sources = 6No of mixtures = 2
37
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Multi source point
38
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
Multi source point
39
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
Average of 15 pairs of speech utterances of length 10 s each
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
)( ofDirection )( ofDirection tkXItkXR )( ofDirection )( ofDirection tkXItkXR
SSPMSP
40
SSPt
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)()(
)()(
112112
111111
tkXjItkXR
tkXjItkXR
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXI
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXIMSP
)( 111 tkX
)( 112 tkX
cos
)()(
)()(
tkXItkXR
tkXItkXR T
Proposed Algorithm for the Detection of Single Source Points
Proposed Algorithm for the Detection of Single Source Points
0510 AM 41
Elimination of OutliersElimination of Outliers
SSPs detection
Clus
terin
g
Outlier elimination
0510 AM 42
0510 AM
Experimental ResultsExperimental Results
dB6747NMSE
No of mixtures =2 No of sources =6
43
Detected Single Source PointsThree mixtures
Detected Single Source PointsThree mixtures
No of mixtures =3 No of sources =60510 AM 44
Comparison with Classical Algorithms for Determined Case
Comparison with Classical Algorithms for Determined Case
No of mixtures =2No of sources =2
Average of 500 experimental results
0510 AM 45
-gt
Comparison with Method Proposed in [1] Underdetermined case
Comparison with Method Proposed in [1] Underdetermined case
[1] Y Li S Amari A Cichocki D W C Ho and S Xie ldquoUnderdetermined blind source separation based on sparse representationrdquo IEEE Transactions on Signal Processing vol 54 p 423ndash437 Feb 2006
0510 AM
Nor
mal
ized
mea
n sq
uare
err
or (N
MSE
) in
mix
ing
mat
rix e
stim
ation
(dB)
Order of the mixing matrices (PxQ)
46
P ndash No of mixturesQ ndash No of sources
Advantages of the Proposed algorithmAdvantages of the Proposed algorithm
Step 1 Convert x in the time domain to the TF domain to get XStep 2 Check the condition
Step 3 If the condition is satisfied then X(k t) is a sample atthe SSP and this sample is kept for mixing matrix estimationotherwise discard the point
Step 4 Repeat Steps 2 to 3 for all the points in the TF planeor until sufficient number of SSPs are obtained
cos
)()(
)()(
tkXItkXR
tkXItkXR T
1) Much simpler constrain the algorithm does not require ldquosingle source zonerdquo
3) The algorithm is extremely simple but effective2) Separation performance is better
0510 AM 47-gt
My Contributions ndash III IV and VMy Contributions ndash III IV and V
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
48
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Mask estimation
Mic 1
Mic P
Mixture in TF domain
Separated signals in TF domain
)( tkX P
)(1 tkX
t
t
k
k
)(1 tkY
)(1 tkY
)( tkYQ
)( tkYQ
QP
0510 AM 49
Mathematical RepresentationMathematical Representation
Q
q
L
lqpqp Pplnslhnx
1
1
0
1)()()(
)()()()()()()( 11 tkSktkSktkSktk QQqq HHHX
)(
)(
)()(
)()(
)(
)( 1
1
1111
tkS
tkS
kHkH
kHkH
tkX
tkX
QPQP
Q
P
)(
)(
)(
)(
)(
)(
)(
)(
)( 11
1
1
11
tkS
kH
kH
tkS
kH
kH
tkS
kH
kH
Q
PQ
Q
q
Pq
q
P
Time domain
Frequency domain
0510 AM 50
P ndash No of mixturesQ ndash No of sources
Single source pointsSingle source pointsInstantaneous mixing
00point at 1 Case 11211111 tkStkStk
)()()(
)()()(
111111
111111
tkSIktkI
tkSRktkR
HX
HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()(
)()()(
222222
222222
tkSIktkI
tkSRktkR
HX
HX
Single source point 2
Real scalar
RealReal
Real scalarReal scalar
Real scalar
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
0510 AM 51
Basic Principle of Single Source Points Detection
Basic Principle of Single Source Points Detection
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
j
H
C
e
cos21
21
UU
UUUUU H
and 20coscos HCH
angle pseudo called is
angleHermitian called is
H The Hermitian angle between the complex
vectors u1 and u2 will remain the same even if the vectors are multiplied by any complex scalars whereas the pseudo angle will change
0510 AM 52
-gt
k
Algorithm for Single Source Points Detection
Algorithm for Single Source Points Detection
t
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)(
)(
)(111
121
111 tkSkH
kH
11
11
j
jr
)(
)(
112
111
tkX
tkX
11
11
j
jr
)(
)(
112
111
tkX
tkX
)( 111 tkX
)( 112 tkX
)(
)(
)(112
122
112 tkSkH
kH θH2
θH1
θH2
rX
rX
)(
)(cos
11
111
tk
tk H
Hq
0510 AM 53
θH1
OR
1k
1k
1t
Clean
Estimated
Mask Estimation by k-means (KM)Mask Estimation by k-means (KM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 54
Clean
Estimated
Mask Estimation by Fuzzy c-means (FCM)Mask Estimation by Fuzzy c-means (FCM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 55
Automatic Detection of Number of SourcesAutomatic Detection of Number of Sources
0510 AM 56
Cluster validation technique
For c = 2 to cmax
Cluster the data into c clustersCalculate the cluster validation index
EndTake c corresponding to the best cluster as the number of sources
-gt
Elimination of Low Energy PointsElimination of Low Energy Points
0510 AM 57
- Blind Separation of Speech Mixtures
- Introduction
- Slide 3
- Slide 4
- Slide 5
- Approaches for BSS of Speech Signals
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Permutation Problem in Frequency Domain BSS
- Motivation
- My Contribution - I
- Algorithm for Solving the Permutation Problem
- Existing Method for Solving the Permutation Problem
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Proposed algorithm Partial separation method (Parallel configuration) Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
- Partial separation method (Parallel configuration)
- Partial separation method (Cascade configuration)
- Advantages of Partial Separation method
- Comparison with Adjacent Bands Correlation Method
- Comparison with DOA method
- My Contribution -II
- Underdetermined Blind Source Separation of Instantaneous Mixtures
- Mathematical Representation of Instantaneous Mixing Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
- Single Source Points in Time-Frequency domain
- Slide 31
- Slide 32
- Scatter Diagram of the Mixtures When Source are Perfectly Sparse
- Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
- Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
- Principle of the Proposed Algorithm for the Detection of Single Source Points
- Slide 39
- Slide 40
- Proposed Algorithm for the Detection of Single Source Points
- Elimination of Outliers
- Slide 43
- Detected Single Source Points Three mixtures
- Comparison with Classical Algorithms for Determined Case
- Comparison with Method Proposed in [1] Underdetermined case
- Advantages of the Proposed algorithm
- My Contributions ndash III IV and V
- Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
- Mathematical Representation
- Single source points
- Basic Principle of Single Source Points Detection
- Algorithm for Single Source Points Detection
- Mask Estimation by k-means (KM)
- Mask Estimation by Fuzzy c-means (FCM)
- Automatic Detection of Number of Sources
- Elimination of Low Energy Points
-
Advantages of Partial Separation methodAdvantages of Partial Separation method
bull Robustness
0510 AM 24
Comparison with Adjacent Bands Correlation Method
Comparison with Adjacent Bands Correlation Method
0510 AM 25
PS - Partial Separation method with confidence check C1 - Correlation between the adjacent bins without confidence check C2 - Correlation between adjacent bins with confidence check Ha - Correlation between the harmonic components with confidence check PS1 - Partial separation method alone without confidence check
0510 AM 26
Comparison with DOA methodComparison with DOA method
My Contribution -IIMy Contribution -II
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
27
Underdetermined Blind Source Separation of Instantaneous Mixtures
Underdetermined Blind Source Separation of Instantaneous Mixtures
t
k
0)(0)( 222221 tkStkS
0)(0)( 222221 tkStkS
0)(0)( 112111 tkStkS
0)(0)( 112111 tkStkS
tkX 1
tkX 22x
1x
0510 AM 28
Mathematical Representation of Instantaneous Mixing
Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
Mathematical Representation of Instantaneous Mixing
Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
)(
)(
)(
)( 1
1
1111
tkS
tkS
hh
hh
tkX
tkX
QPQP
Q
P
)(
)(
)(
)( 1
1
1111
ts
ts
hh
hh
tx
tx
QPQP
Q
P
)()()(11
1
1
11
tkS
h
h
tkS
h
h
tkS
h
h
Q
PQ
Q
q
Pq
q
P
)()()()( 21 tkStkStkStk QhhhX
Time domain
Time-Frequency domain
0510 AM 29
P ndash No of mixturesQ ndash No of sources
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
00point at 1 Case 11211111 tkStkStk
)()()( 1122111111 tkStkStk hhX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 2222221122 tkStkStk hhX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
0510 AM
0 0
30
Q
qqq tkStk
1
hX
2Let Q
00point at 1 Case 11211111 tkStkStk
)()( 111111 tkStk hX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()( 222222 tkStk hX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
0510 AM 31
00point at 1 Case 11211111 tkStkStk
)()( 111111 tkStk hX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()( 222222 tkStk hX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
Scalar
ScalarScalar
Scalar
At single source point 1 At single source point 2
111
111
ofDirection )( ofDirection
ofDirection )( ofDirection
hX
hX
tkI
tkR 222
222
ofDirection )( ofDirection
ofDirection )( ofDirection
hX
hX
tkI
tkR
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
0510 AM
1111 ( of Direction ( of Direction tkItkR XX 2222 ( of Direction ( of Direction tkItkR XX 32
Scatter Diagram of the Mixtures When Source are Perfectly Sparse
Scatter Diagram of the Mixtures When Source are Perfectly Sparse
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
22222
11111
2221
1211
22222
11111
kSkSkSkSkS
kSkSkSkSkS
hh
hh
kXkXkXkXkX
kXkXkXkXkX
21
111 h
hh
22
122 h
hh
0 00 0 0
Example
0510 AM 33
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
22222
11111
2221
1211
22222
11111
kSkSkSkSkS
kSkSkSkSkS
hh
hh
kXkXkXkXkX
kXkXkXkXkX
21
111 h
hh
22
122 h
hh
0 00 0 00
Example
Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
0510 AM 34
Scatter Diagram of the Mixtures when Sources are Sparse
Scatter Diagram of the Mixtures when Sources are Sparse
3h
6h
5h
1h4h
2h
0510 AM
No of sources = 6No of mixtures = 2
35
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
3h
6h
5h
1h4h
2h
0510 AM
No of sources = 6No of mixtures = 2
36
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
3h
6h
5h
1h4h
2h
0510 AM
ObjectiveEstimation of the single source points
No of sources = 6No of mixtures = 2
37
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Multi source point
38
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
Multi source point
39
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
Average of 15 pairs of speech utterances of length 10 s each
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
)( ofDirection )( ofDirection tkXItkXR )( ofDirection )( ofDirection tkXItkXR
SSPMSP
40
SSPt
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)()(
)()(
112112
111111
tkXjItkXR
tkXjItkXR
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXI
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXIMSP
)( 111 tkX
)( 112 tkX
cos
)()(
)()(
tkXItkXR
tkXItkXR T
Proposed Algorithm for the Detection of Single Source Points
Proposed Algorithm for the Detection of Single Source Points
0510 AM 41
Elimination of OutliersElimination of Outliers
SSPs detection
Clus
terin
g
Outlier elimination
0510 AM 42
0510 AM
Experimental ResultsExperimental Results
dB6747NMSE
No of mixtures =2 No of sources =6
43
Detected Single Source PointsThree mixtures
Detected Single Source PointsThree mixtures
No of mixtures =3 No of sources =60510 AM 44
Comparison with Classical Algorithms for Determined Case
Comparison with Classical Algorithms for Determined Case
No of mixtures =2No of sources =2
Average of 500 experimental results
0510 AM 45
-gt
Comparison with Method Proposed in [1] Underdetermined case
Comparison with Method Proposed in [1] Underdetermined case
[1] Y Li S Amari A Cichocki D W C Ho and S Xie ldquoUnderdetermined blind source separation based on sparse representationrdquo IEEE Transactions on Signal Processing vol 54 p 423ndash437 Feb 2006
0510 AM
Nor
mal
ized
mea
n sq
uare
err
or (N
MSE
) in
mix
ing
mat
rix e
stim
ation
(dB)
Order of the mixing matrices (PxQ)
46
P ndash No of mixturesQ ndash No of sources
Advantages of the Proposed algorithmAdvantages of the Proposed algorithm
Step 1 Convert x in the time domain to the TF domain to get XStep 2 Check the condition
Step 3 If the condition is satisfied then X(k t) is a sample atthe SSP and this sample is kept for mixing matrix estimationotherwise discard the point
Step 4 Repeat Steps 2 to 3 for all the points in the TF planeor until sufficient number of SSPs are obtained
cos
)()(
)()(
tkXItkXR
tkXItkXR T
1) Much simpler constrain the algorithm does not require ldquosingle source zonerdquo
3) The algorithm is extremely simple but effective2) Separation performance is better
0510 AM 47-gt
My Contributions ndash III IV and VMy Contributions ndash III IV and V
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
48
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Mask estimation
Mic 1
Mic P
Mixture in TF domain
Separated signals in TF domain
)( tkX P
)(1 tkX
t
t
k
k
)(1 tkY
)(1 tkY
)( tkYQ
)( tkYQ
QP
0510 AM 49
Mathematical RepresentationMathematical Representation
Q
q
L
lqpqp Pplnslhnx
1
1
0
1)()()(
)()()()()()()( 11 tkSktkSktkSktk QQqq HHHX
)(
)(
)()(
)()(
)(
)( 1
1
1111
tkS
tkS
kHkH
kHkH
tkX
tkX
QPQP
Q
P
)(
)(
)(
)(
)(
)(
)(
)(
)( 11
1
1
11
tkS
kH
kH
tkS
kH
kH
tkS
kH
kH
Q
PQ
Q
q
Pq
q
P
Time domain
Frequency domain
0510 AM 50
P ndash No of mixturesQ ndash No of sources
Single source pointsSingle source pointsInstantaneous mixing
00point at 1 Case 11211111 tkStkStk
)()()(
)()()(
111111
111111
tkSIktkI
tkSRktkR
HX
HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()(
)()()(
222222
222222
tkSIktkI
tkSRktkR
HX
HX
Single source point 2
Real scalar
RealReal
Real scalarReal scalar
Real scalar
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
0510 AM 51
Basic Principle of Single Source Points Detection
Basic Principle of Single Source Points Detection
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
j
H
C
e
cos21
21
UU
UUUUU H
and 20coscos HCH
angle pseudo called is
angleHermitian called is
H The Hermitian angle between the complex
vectors u1 and u2 will remain the same even if the vectors are multiplied by any complex scalars whereas the pseudo angle will change
0510 AM 52
-gt
k
Algorithm for Single Source Points Detection
Algorithm for Single Source Points Detection
t
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)(
)(
)(111
121
111 tkSkH
kH
11
11
j
jr
)(
)(
112
111
tkX
tkX
11
11
j
jr
)(
)(
112
111
tkX
tkX
)( 111 tkX
)( 112 tkX
)(
)(
)(112
122
112 tkSkH
kH θH2
θH1
θH2
rX
rX
)(
)(cos
11
111
tk
tk H
Hq
0510 AM 53
θH1
OR
1k
1k
1t
Clean
Estimated
Mask Estimation by k-means (KM)Mask Estimation by k-means (KM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 54
Clean
Estimated
Mask Estimation by Fuzzy c-means (FCM)Mask Estimation by Fuzzy c-means (FCM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 55
Automatic Detection of Number of SourcesAutomatic Detection of Number of Sources
0510 AM 56
Cluster validation technique
For c = 2 to cmax
Cluster the data into c clustersCalculate the cluster validation index
EndTake c corresponding to the best cluster as the number of sources
-gt
Elimination of Low Energy PointsElimination of Low Energy Points
0510 AM 57
- Blind Separation of Speech Mixtures
- Introduction
- Slide 3
- Slide 4
- Slide 5
- Approaches for BSS of Speech Signals
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Permutation Problem in Frequency Domain BSS
- Motivation
- My Contribution - I
- Algorithm for Solving the Permutation Problem
- Existing Method for Solving the Permutation Problem
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Proposed algorithm Partial separation method (Parallel configuration) Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
- Partial separation method (Parallel configuration)
- Partial separation method (Cascade configuration)
- Advantages of Partial Separation method
- Comparison with Adjacent Bands Correlation Method
- Comparison with DOA method
- My Contribution -II
- Underdetermined Blind Source Separation of Instantaneous Mixtures
- Mathematical Representation of Instantaneous Mixing Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
- Single Source Points in Time-Frequency domain
- Slide 31
- Slide 32
- Scatter Diagram of the Mixtures When Source are Perfectly Sparse
- Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
- Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
- Principle of the Proposed Algorithm for the Detection of Single Source Points
- Slide 39
- Slide 40
- Proposed Algorithm for the Detection of Single Source Points
- Elimination of Outliers
- Slide 43
- Detected Single Source Points Three mixtures
- Comparison with Classical Algorithms for Determined Case
- Comparison with Method Proposed in [1] Underdetermined case
- Advantages of the Proposed algorithm
- My Contributions ndash III IV and V
- Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
- Mathematical Representation
- Single source points
- Basic Principle of Single Source Points Detection
- Algorithm for Single Source Points Detection
- Mask Estimation by k-means (KM)
- Mask Estimation by Fuzzy c-means (FCM)
- Automatic Detection of Number of Sources
- Elimination of Low Energy Points
-
Comparison with Adjacent Bands Correlation Method
Comparison with Adjacent Bands Correlation Method
0510 AM 25
PS - Partial Separation method with confidence check C1 - Correlation between the adjacent bins without confidence check C2 - Correlation between adjacent bins with confidence check Ha - Correlation between the harmonic components with confidence check PS1 - Partial separation method alone without confidence check
0510 AM 26
Comparison with DOA methodComparison with DOA method
My Contribution -IIMy Contribution -II
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
27
Underdetermined Blind Source Separation of Instantaneous Mixtures
Underdetermined Blind Source Separation of Instantaneous Mixtures
t
k
0)(0)( 222221 tkStkS
0)(0)( 222221 tkStkS
0)(0)( 112111 tkStkS
0)(0)( 112111 tkStkS
tkX 1
tkX 22x
1x
0510 AM 28
Mathematical Representation of Instantaneous Mixing
Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
Mathematical Representation of Instantaneous Mixing
Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
)(
)(
)(
)( 1
1
1111
tkS
tkS
hh
hh
tkX
tkX
QPQP
Q
P
)(
)(
)(
)( 1
1
1111
ts
ts
hh
hh
tx
tx
QPQP
Q
P
)()()(11
1
1
11
tkS
h
h
tkS
h
h
tkS
h
h
Q
PQ
Q
q
Pq
q
P
)()()()( 21 tkStkStkStk QhhhX
Time domain
Time-Frequency domain
0510 AM 29
P ndash No of mixturesQ ndash No of sources
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
00point at 1 Case 11211111 tkStkStk
)()()( 1122111111 tkStkStk hhX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 2222221122 tkStkStk hhX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
0510 AM
0 0
30
Q
qqq tkStk
1
hX
2Let Q
00point at 1 Case 11211111 tkStkStk
)()( 111111 tkStk hX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()( 222222 tkStk hX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
0510 AM 31
00point at 1 Case 11211111 tkStkStk
)()( 111111 tkStk hX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()( 222222 tkStk hX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
Scalar
ScalarScalar
Scalar
At single source point 1 At single source point 2
111
111
ofDirection )( ofDirection
ofDirection )( ofDirection
hX
hX
tkI
tkR 222
222
ofDirection )( ofDirection
ofDirection )( ofDirection
hX
hX
tkI
tkR
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
0510 AM
1111 ( of Direction ( of Direction tkItkR XX 2222 ( of Direction ( of Direction tkItkR XX 32
Scatter Diagram of the Mixtures When Source are Perfectly Sparse
Scatter Diagram of the Mixtures When Source are Perfectly Sparse
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
22222
11111
2221
1211
22222
11111
kSkSkSkSkS
kSkSkSkSkS
hh
hh
kXkXkXkXkX
kXkXkXkXkX
21
111 h
hh
22
122 h
hh
0 00 0 0
Example
0510 AM 33
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
22222
11111
2221
1211
22222
11111
kSkSkSkSkS
kSkSkSkSkS
hh
hh
kXkXkXkXkX
kXkXkXkXkX
21
111 h
hh
22
122 h
hh
0 00 0 00
Example
Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
0510 AM 34
Scatter Diagram of the Mixtures when Sources are Sparse
Scatter Diagram of the Mixtures when Sources are Sparse
3h
6h
5h
1h4h
2h
0510 AM
No of sources = 6No of mixtures = 2
35
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
3h
6h
5h
1h4h
2h
0510 AM
No of sources = 6No of mixtures = 2
36
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
3h
6h
5h
1h4h
2h
0510 AM
ObjectiveEstimation of the single source points
No of sources = 6No of mixtures = 2
37
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Multi source point
38
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
Multi source point
39
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
Average of 15 pairs of speech utterances of length 10 s each
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
)( ofDirection )( ofDirection tkXItkXR )( ofDirection )( ofDirection tkXItkXR
SSPMSP
40
SSPt
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)()(
)()(
112112
111111
tkXjItkXR
tkXjItkXR
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXI
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXIMSP
)( 111 tkX
)( 112 tkX
cos
)()(
)()(
tkXItkXR
tkXItkXR T
Proposed Algorithm for the Detection of Single Source Points
Proposed Algorithm for the Detection of Single Source Points
0510 AM 41
Elimination of OutliersElimination of Outliers
SSPs detection
Clus
terin
g
Outlier elimination
0510 AM 42
0510 AM
Experimental ResultsExperimental Results
dB6747NMSE
No of mixtures =2 No of sources =6
43
Detected Single Source PointsThree mixtures
Detected Single Source PointsThree mixtures
No of mixtures =3 No of sources =60510 AM 44
Comparison with Classical Algorithms for Determined Case
Comparison with Classical Algorithms for Determined Case
No of mixtures =2No of sources =2
Average of 500 experimental results
0510 AM 45
-gt
Comparison with Method Proposed in [1] Underdetermined case
Comparison with Method Proposed in [1] Underdetermined case
[1] Y Li S Amari A Cichocki D W C Ho and S Xie ldquoUnderdetermined blind source separation based on sparse representationrdquo IEEE Transactions on Signal Processing vol 54 p 423ndash437 Feb 2006
0510 AM
Nor
mal
ized
mea
n sq
uare
err
or (N
MSE
) in
mix
ing
mat
rix e
stim
ation
(dB)
Order of the mixing matrices (PxQ)
46
P ndash No of mixturesQ ndash No of sources
Advantages of the Proposed algorithmAdvantages of the Proposed algorithm
Step 1 Convert x in the time domain to the TF domain to get XStep 2 Check the condition
Step 3 If the condition is satisfied then X(k t) is a sample atthe SSP and this sample is kept for mixing matrix estimationotherwise discard the point
Step 4 Repeat Steps 2 to 3 for all the points in the TF planeor until sufficient number of SSPs are obtained
cos
)()(
)()(
tkXItkXR
tkXItkXR T
1) Much simpler constrain the algorithm does not require ldquosingle source zonerdquo
3) The algorithm is extremely simple but effective2) Separation performance is better
0510 AM 47-gt
My Contributions ndash III IV and VMy Contributions ndash III IV and V
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
48
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Mask estimation
Mic 1
Mic P
Mixture in TF domain
Separated signals in TF domain
)( tkX P
)(1 tkX
t
t
k
k
)(1 tkY
)(1 tkY
)( tkYQ
)( tkYQ
QP
0510 AM 49
Mathematical RepresentationMathematical Representation
Q
q
L
lqpqp Pplnslhnx
1
1
0
1)()()(
)()()()()()()( 11 tkSktkSktkSktk QQqq HHHX
)(
)(
)()(
)()(
)(
)( 1
1
1111
tkS
tkS
kHkH
kHkH
tkX
tkX
QPQP
Q
P
)(
)(
)(
)(
)(
)(
)(
)(
)( 11
1
1
11
tkS
kH
kH
tkS
kH
kH
tkS
kH
kH
Q
PQ
Q
q
Pq
q
P
Time domain
Frequency domain
0510 AM 50
P ndash No of mixturesQ ndash No of sources
Single source pointsSingle source pointsInstantaneous mixing
00point at 1 Case 11211111 tkStkStk
)()()(
)()()(
111111
111111
tkSIktkI
tkSRktkR
HX
HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()(
)()()(
222222
222222
tkSIktkI
tkSRktkR
HX
HX
Single source point 2
Real scalar
RealReal
Real scalarReal scalar
Real scalar
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
0510 AM 51
Basic Principle of Single Source Points Detection
Basic Principle of Single Source Points Detection
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
j
H
C
e
cos21
21
UU
UUUUU H
and 20coscos HCH
angle pseudo called is
angleHermitian called is
H The Hermitian angle between the complex
vectors u1 and u2 will remain the same even if the vectors are multiplied by any complex scalars whereas the pseudo angle will change
0510 AM 52
-gt
k
Algorithm for Single Source Points Detection
Algorithm for Single Source Points Detection
t
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)(
)(
)(111
121
111 tkSkH
kH
11
11
j
jr
)(
)(
112
111
tkX
tkX
11
11
j
jr
)(
)(
112
111
tkX
tkX
)( 111 tkX
)( 112 tkX
)(
)(
)(112
122
112 tkSkH
kH θH2
θH1
θH2
rX
rX
)(
)(cos
11
111
tk
tk H
Hq
0510 AM 53
θH1
OR
1k
1k
1t
Clean
Estimated
Mask Estimation by k-means (KM)Mask Estimation by k-means (KM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 54
Clean
Estimated
Mask Estimation by Fuzzy c-means (FCM)Mask Estimation by Fuzzy c-means (FCM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 55
Automatic Detection of Number of SourcesAutomatic Detection of Number of Sources
0510 AM 56
Cluster validation technique
For c = 2 to cmax
Cluster the data into c clustersCalculate the cluster validation index
EndTake c corresponding to the best cluster as the number of sources
-gt
Elimination of Low Energy PointsElimination of Low Energy Points
0510 AM 57
- Blind Separation of Speech Mixtures
- Introduction
- Slide 3
- Slide 4
- Slide 5
- Approaches for BSS of Speech Signals
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Permutation Problem in Frequency Domain BSS
- Motivation
- My Contribution - I
- Algorithm for Solving the Permutation Problem
- Existing Method for Solving the Permutation Problem
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Proposed algorithm Partial separation method (Parallel configuration) Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
- Partial separation method (Parallel configuration)
- Partial separation method (Cascade configuration)
- Advantages of Partial Separation method
- Comparison with Adjacent Bands Correlation Method
- Comparison with DOA method
- My Contribution -II
- Underdetermined Blind Source Separation of Instantaneous Mixtures
- Mathematical Representation of Instantaneous Mixing Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
- Single Source Points in Time-Frequency domain
- Slide 31
- Slide 32
- Scatter Diagram of the Mixtures When Source are Perfectly Sparse
- Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
- Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
- Principle of the Proposed Algorithm for the Detection of Single Source Points
- Slide 39
- Slide 40
- Proposed Algorithm for the Detection of Single Source Points
- Elimination of Outliers
- Slide 43
- Detected Single Source Points Three mixtures
- Comparison with Classical Algorithms for Determined Case
- Comparison with Method Proposed in [1] Underdetermined case
- Advantages of the Proposed algorithm
- My Contributions ndash III IV and V
- Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
- Mathematical Representation
- Single source points
- Basic Principle of Single Source Points Detection
- Algorithm for Single Source Points Detection
- Mask Estimation by k-means (KM)
- Mask Estimation by Fuzzy c-means (FCM)
- Automatic Detection of Number of Sources
- Elimination of Low Energy Points
-
PS - Partial Separation method with confidence check C1 - Correlation between the adjacent bins without confidence check C2 - Correlation between adjacent bins with confidence check Ha - Correlation between the harmonic components with confidence check PS1 - Partial separation method alone without confidence check
0510 AM 26
Comparison with DOA methodComparison with DOA method
My Contribution -IIMy Contribution -II
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
27
Underdetermined Blind Source Separation of Instantaneous Mixtures
Underdetermined Blind Source Separation of Instantaneous Mixtures
t
k
0)(0)( 222221 tkStkS
0)(0)( 222221 tkStkS
0)(0)( 112111 tkStkS
0)(0)( 112111 tkStkS
tkX 1
tkX 22x
1x
0510 AM 28
Mathematical Representation of Instantaneous Mixing
Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
Mathematical Representation of Instantaneous Mixing
Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
)(
)(
)(
)( 1
1
1111
tkS
tkS
hh
hh
tkX
tkX
QPQP
Q
P
)(
)(
)(
)( 1
1
1111
ts
ts
hh
hh
tx
tx
QPQP
Q
P
)()()(11
1
1
11
tkS
h
h
tkS
h
h
tkS
h
h
Q
PQ
Q
q
Pq
q
P
)()()()( 21 tkStkStkStk QhhhX
Time domain
Time-Frequency domain
0510 AM 29
P ndash No of mixturesQ ndash No of sources
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
00point at 1 Case 11211111 tkStkStk
)()()( 1122111111 tkStkStk hhX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 2222221122 tkStkStk hhX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
0510 AM
0 0
30
Q
qqq tkStk
1
hX
2Let Q
00point at 1 Case 11211111 tkStkStk
)()( 111111 tkStk hX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()( 222222 tkStk hX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
0510 AM 31
00point at 1 Case 11211111 tkStkStk
)()( 111111 tkStk hX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()( 222222 tkStk hX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
Scalar
ScalarScalar
Scalar
At single source point 1 At single source point 2
111
111
ofDirection )( ofDirection
ofDirection )( ofDirection
hX
hX
tkI
tkR 222
222
ofDirection )( ofDirection
ofDirection )( ofDirection
hX
hX
tkI
tkR
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
0510 AM
1111 ( of Direction ( of Direction tkItkR XX 2222 ( of Direction ( of Direction tkItkR XX 32
Scatter Diagram of the Mixtures When Source are Perfectly Sparse
Scatter Diagram of the Mixtures When Source are Perfectly Sparse
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
22222
11111
2221
1211
22222
11111
kSkSkSkSkS
kSkSkSkSkS
hh
hh
kXkXkXkXkX
kXkXkXkXkX
21
111 h
hh
22
122 h
hh
0 00 0 0
Example
0510 AM 33
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
22222
11111
2221
1211
22222
11111
kSkSkSkSkS
kSkSkSkSkS
hh
hh
kXkXkXkXkX
kXkXkXkXkX
21
111 h
hh
22
122 h
hh
0 00 0 00
Example
Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
0510 AM 34
Scatter Diagram of the Mixtures when Sources are Sparse
Scatter Diagram of the Mixtures when Sources are Sparse
3h
6h
5h
1h4h
2h
0510 AM
No of sources = 6No of mixtures = 2
35
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
3h
6h
5h
1h4h
2h
0510 AM
No of sources = 6No of mixtures = 2
36
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
3h
6h
5h
1h4h
2h
0510 AM
ObjectiveEstimation of the single source points
No of sources = 6No of mixtures = 2
37
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Multi source point
38
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
Multi source point
39
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
Average of 15 pairs of speech utterances of length 10 s each
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
)( ofDirection )( ofDirection tkXItkXR )( ofDirection )( ofDirection tkXItkXR
SSPMSP
40
SSPt
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)()(
)()(
112112
111111
tkXjItkXR
tkXjItkXR
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXI
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXIMSP
)( 111 tkX
)( 112 tkX
cos
)()(
)()(
tkXItkXR
tkXItkXR T
Proposed Algorithm for the Detection of Single Source Points
Proposed Algorithm for the Detection of Single Source Points
0510 AM 41
Elimination of OutliersElimination of Outliers
SSPs detection
Clus
terin
g
Outlier elimination
0510 AM 42
0510 AM
Experimental ResultsExperimental Results
dB6747NMSE
No of mixtures =2 No of sources =6
43
Detected Single Source PointsThree mixtures
Detected Single Source PointsThree mixtures
No of mixtures =3 No of sources =60510 AM 44
Comparison with Classical Algorithms for Determined Case
Comparison with Classical Algorithms for Determined Case
No of mixtures =2No of sources =2
Average of 500 experimental results
0510 AM 45
-gt
Comparison with Method Proposed in [1] Underdetermined case
Comparison with Method Proposed in [1] Underdetermined case
[1] Y Li S Amari A Cichocki D W C Ho and S Xie ldquoUnderdetermined blind source separation based on sparse representationrdquo IEEE Transactions on Signal Processing vol 54 p 423ndash437 Feb 2006
0510 AM
Nor
mal
ized
mea
n sq
uare
err
or (N
MSE
) in
mix
ing
mat
rix e
stim
ation
(dB)
Order of the mixing matrices (PxQ)
46
P ndash No of mixturesQ ndash No of sources
Advantages of the Proposed algorithmAdvantages of the Proposed algorithm
Step 1 Convert x in the time domain to the TF domain to get XStep 2 Check the condition
Step 3 If the condition is satisfied then X(k t) is a sample atthe SSP and this sample is kept for mixing matrix estimationotherwise discard the point
Step 4 Repeat Steps 2 to 3 for all the points in the TF planeor until sufficient number of SSPs are obtained
cos
)()(
)()(
tkXItkXR
tkXItkXR T
1) Much simpler constrain the algorithm does not require ldquosingle source zonerdquo
3) The algorithm is extremely simple but effective2) Separation performance is better
0510 AM 47-gt
My Contributions ndash III IV and VMy Contributions ndash III IV and V
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
48
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Mask estimation
Mic 1
Mic P
Mixture in TF domain
Separated signals in TF domain
)( tkX P
)(1 tkX
t
t
k
k
)(1 tkY
)(1 tkY
)( tkYQ
)( tkYQ
QP
0510 AM 49
Mathematical RepresentationMathematical Representation
Q
q
L
lqpqp Pplnslhnx
1
1
0
1)()()(
)()()()()()()( 11 tkSktkSktkSktk QQqq HHHX
)(
)(
)()(
)()(
)(
)( 1
1
1111
tkS
tkS
kHkH
kHkH
tkX
tkX
QPQP
Q
P
)(
)(
)(
)(
)(
)(
)(
)(
)( 11
1
1
11
tkS
kH
kH
tkS
kH
kH
tkS
kH
kH
Q
PQ
Q
q
Pq
q
P
Time domain
Frequency domain
0510 AM 50
P ndash No of mixturesQ ndash No of sources
Single source pointsSingle source pointsInstantaneous mixing
00point at 1 Case 11211111 tkStkStk
)()()(
)()()(
111111
111111
tkSIktkI
tkSRktkR
HX
HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()(
)()()(
222222
222222
tkSIktkI
tkSRktkR
HX
HX
Single source point 2
Real scalar
RealReal
Real scalarReal scalar
Real scalar
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
0510 AM 51
Basic Principle of Single Source Points Detection
Basic Principle of Single Source Points Detection
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
j
H
C
e
cos21
21
UU
UUUUU H
and 20coscos HCH
angle pseudo called is
angleHermitian called is
H The Hermitian angle between the complex
vectors u1 and u2 will remain the same even if the vectors are multiplied by any complex scalars whereas the pseudo angle will change
0510 AM 52
-gt
k
Algorithm for Single Source Points Detection
Algorithm for Single Source Points Detection
t
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)(
)(
)(111
121
111 tkSkH
kH
11
11
j
jr
)(
)(
112
111
tkX
tkX
11
11
j
jr
)(
)(
112
111
tkX
tkX
)( 111 tkX
)( 112 tkX
)(
)(
)(112
122
112 tkSkH
kH θH2
θH1
θH2
rX
rX
)(
)(cos
11
111
tk
tk H
Hq
0510 AM 53
θH1
OR
1k
1k
1t
Clean
Estimated
Mask Estimation by k-means (KM)Mask Estimation by k-means (KM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 54
Clean
Estimated
Mask Estimation by Fuzzy c-means (FCM)Mask Estimation by Fuzzy c-means (FCM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 55
Automatic Detection of Number of SourcesAutomatic Detection of Number of Sources
0510 AM 56
Cluster validation technique
For c = 2 to cmax
Cluster the data into c clustersCalculate the cluster validation index
EndTake c corresponding to the best cluster as the number of sources
-gt
Elimination of Low Energy PointsElimination of Low Energy Points
0510 AM 57
- Blind Separation of Speech Mixtures
- Introduction
- Slide 3
- Slide 4
- Slide 5
- Approaches for BSS of Speech Signals
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Permutation Problem in Frequency Domain BSS
- Motivation
- My Contribution - I
- Algorithm for Solving the Permutation Problem
- Existing Method for Solving the Permutation Problem
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Proposed algorithm Partial separation method (Parallel configuration) Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
- Partial separation method (Parallel configuration)
- Partial separation method (Cascade configuration)
- Advantages of Partial Separation method
- Comparison with Adjacent Bands Correlation Method
- Comparison with DOA method
- My Contribution -II
- Underdetermined Blind Source Separation of Instantaneous Mixtures
- Mathematical Representation of Instantaneous Mixing Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
- Single Source Points in Time-Frequency domain
- Slide 31
- Slide 32
- Scatter Diagram of the Mixtures When Source are Perfectly Sparse
- Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
- Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
- Principle of the Proposed Algorithm for the Detection of Single Source Points
- Slide 39
- Slide 40
- Proposed Algorithm for the Detection of Single Source Points
- Elimination of Outliers
- Slide 43
- Detected Single Source Points Three mixtures
- Comparison with Classical Algorithms for Determined Case
- Comparison with Method Proposed in [1] Underdetermined case
- Advantages of the Proposed algorithm
- My Contributions ndash III IV and V
- Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
- Mathematical Representation
- Single source points
- Basic Principle of Single Source Points Detection
- Algorithm for Single Source Points Detection
- Mask Estimation by k-means (KM)
- Mask Estimation by Fuzzy c-means (FCM)
- Automatic Detection of Number of Sources
- Elimination of Low Energy Points
-
My Contribution -IIMy Contribution -II
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
27
Underdetermined Blind Source Separation of Instantaneous Mixtures
Underdetermined Blind Source Separation of Instantaneous Mixtures
t
k
0)(0)( 222221 tkStkS
0)(0)( 222221 tkStkS
0)(0)( 112111 tkStkS
0)(0)( 112111 tkStkS
tkX 1
tkX 22x
1x
0510 AM 28
Mathematical Representation of Instantaneous Mixing
Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
Mathematical Representation of Instantaneous Mixing
Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
)(
)(
)(
)( 1
1
1111
tkS
tkS
hh
hh
tkX
tkX
QPQP
Q
P
)(
)(
)(
)( 1
1
1111
ts
ts
hh
hh
tx
tx
QPQP
Q
P
)()()(11
1
1
11
tkS
h
h
tkS
h
h
tkS
h
h
Q
PQ
Q
q
Pq
q
P
)()()()( 21 tkStkStkStk QhhhX
Time domain
Time-Frequency domain
0510 AM 29
P ndash No of mixturesQ ndash No of sources
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
00point at 1 Case 11211111 tkStkStk
)()()( 1122111111 tkStkStk hhX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 2222221122 tkStkStk hhX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
0510 AM
0 0
30
Q
qqq tkStk
1
hX
2Let Q
00point at 1 Case 11211111 tkStkStk
)()( 111111 tkStk hX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()( 222222 tkStk hX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
0510 AM 31
00point at 1 Case 11211111 tkStkStk
)()( 111111 tkStk hX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()( 222222 tkStk hX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
Scalar
ScalarScalar
Scalar
At single source point 1 At single source point 2
111
111
ofDirection )( ofDirection
ofDirection )( ofDirection
hX
hX
tkI
tkR 222
222
ofDirection )( ofDirection
ofDirection )( ofDirection
hX
hX
tkI
tkR
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
0510 AM
1111 ( of Direction ( of Direction tkItkR XX 2222 ( of Direction ( of Direction tkItkR XX 32
Scatter Diagram of the Mixtures When Source are Perfectly Sparse
Scatter Diagram of the Mixtures When Source are Perfectly Sparse
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
22222
11111
2221
1211
22222
11111
kSkSkSkSkS
kSkSkSkSkS
hh
hh
kXkXkXkXkX
kXkXkXkXkX
21
111 h
hh
22
122 h
hh
0 00 0 0
Example
0510 AM 33
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
22222
11111
2221
1211
22222
11111
kSkSkSkSkS
kSkSkSkSkS
hh
hh
kXkXkXkXkX
kXkXkXkXkX
21
111 h
hh
22
122 h
hh
0 00 0 00
Example
Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
0510 AM 34
Scatter Diagram of the Mixtures when Sources are Sparse
Scatter Diagram of the Mixtures when Sources are Sparse
3h
6h
5h
1h4h
2h
0510 AM
No of sources = 6No of mixtures = 2
35
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
3h
6h
5h
1h4h
2h
0510 AM
No of sources = 6No of mixtures = 2
36
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
3h
6h
5h
1h4h
2h
0510 AM
ObjectiveEstimation of the single source points
No of sources = 6No of mixtures = 2
37
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Multi source point
38
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
Multi source point
39
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
Average of 15 pairs of speech utterances of length 10 s each
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
)( ofDirection )( ofDirection tkXItkXR )( ofDirection )( ofDirection tkXItkXR
SSPMSP
40
SSPt
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)()(
)()(
112112
111111
tkXjItkXR
tkXjItkXR
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXI
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXIMSP
)( 111 tkX
)( 112 tkX
cos
)()(
)()(
tkXItkXR
tkXItkXR T
Proposed Algorithm for the Detection of Single Source Points
Proposed Algorithm for the Detection of Single Source Points
0510 AM 41
Elimination of OutliersElimination of Outliers
SSPs detection
Clus
terin
g
Outlier elimination
0510 AM 42
0510 AM
Experimental ResultsExperimental Results
dB6747NMSE
No of mixtures =2 No of sources =6
43
Detected Single Source PointsThree mixtures
Detected Single Source PointsThree mixtures
No of mixtures =3 No of sources =60510 AM 44
Comparison with Classical Algorithms for Determined Case
Comparison with Classical Algorithms for Determined Case
No of mixtures =2No of sources =2
Average of 500 experimental results
0510 AM 45
-gt
Comparison with Method Proposed in [1] Underdetermined case
Comparison with Method Proposed in [1] Underdetermined case
[1] Y Li S Amari A Cichocki D W C Ho and S Xie ldquoUnderdetermined blind source separation based on sparse representationrdquo IEEE Transactions on Signal Processing vol 54 p 423ndash437 Feb 2006
0510 AM
Nor
mal
ized
mea
n sq
uare
err
or (N
MSE
) in
mix
ing
mat
rix e
stim
ation
(dB)
Order of the mixing matrices (PxQ)
46
P ndash No of mixturesQ ndash No of sources
Advantages of the Proposed algorithmAdvantages of the Proposed algorithm
Step 1 Convert x in the time domain to the TF domain to get XStep 2 Check the condition
Step 3 If the condition is satisfied then X(k t) is a sample atthe SSP and this sample is kept for mixing matrix estimationotherwise discard the point
Step 4 Repeat Steps 2 to 3 for all the points in the TF planeor until sufficient number of SSPs are obtained
cos
)()(
)()(
tkXItkXR
tkXItkXR T
1) Much simpler constrain the algorithm does not require ldquosingle source zonerdquo
3) The algorithm is extremely simple but effective2) Separation performance is better
0510 AM 47-gt
My Contributions ndash III IV and VMy Contributions ndash III IV and V
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
48
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Mask estimation
Mic 1
Mic P
Mixture in TF domain
Separated signals in TF domain
)( tkX P
)(1 tkX
t
t
k
k
)(1 tkY
)(1 tkY
)( tkYQ
)( tkYQ
QP
0510 AM 49
Mathematical RepresentationMathematical Representation
Q
q
L
lqpqp Pplnslhnx
1
1
0
1)()()(
)()()()()()()( 11 tkSktkSktkSktk QQqq HHHX
)(
)(
)()(
)()(
)(
)( 1
1
1111
tkS
tkS
kHkH
kHkH
tkX
tkX
QPQP
Q
P
)(
)(
)(
)(
)(
)(
)(
)(
)( 11
1
1
11
tkS
kH
kH
tkS
kH
kH
tkS
kH
kH
Q
PQ
Q
q
Pq
q
P
Time domain
Frequency domain
0510 AM 50
P ndash No of mixturesQ ndash No of sources
Single source pointsSingle source pointsInstantaneous mixing
00point at 1 Case 11211111 tkStkStk
)()()(
)()()(
111111
111111
tkSIktkI
tkSRktkR
HX
HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()(
)()()(
222222
222222
tkSIktkI
tkSRktkR
HX
HX
Single source point 2
Real scalar
RealReal
Real scalarReal scalar
Real scalar
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
0510 AM 51
Basic Principle of Single Source Points Detection
Basic Principle of Single Source Points Detection
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
j
H
C
e
cos21
21
UU
UUUUU H
and 20coscos HCH
angle pseudo called is
angleHermitian called is
H The Hermitian angle between the complex
vectors u1 and u2 will remain the same even if the vectors are multiplied by any complex scalars whereas the pseudo angle will change
0510 AM 52
-gt
k
Algorithm for Single Source Points Detection
Algorithm for Single Source Points Detection
t
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)(
)(
)(111
121
111 tkSkH
kH
11
11
j
jr
)(
)(
112
111
tkX
tkX
11
11
j
jr
)(
)(
112
111
tkX
tkX
)( 111 tkX
)( 112 tkX
)(
)(
)(112
122
112 tkSkH
kH θH2
θH1
θH2
rX
rX
)(
)(cos
11
111
tk
tk H
Hq
0510 AM 53
θH1
OR
1k
1k
1t
Clean
Estimated
Mask Estimation by k-means (KM)Mask Estimation by k-means (KM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 54
Clean
Estimated
Mask Estimation by Fuzzy c-means (FCM)Mask Estimation by Fuzzy c-means (FCM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 55
Automatic Detection of Number of SourcesAutomatic Detection of Number of Sources
0510 AM 56
Cluster validation technique
For c = 2 to cmax
Cluster the data into c clustersCalculate the cluster validation index
EndTake c corresponding to the best cluster as the number of sources
-gt
Elimination of Low Energy PointsElimination of Low Energy Points
0510 AM 57
- Blind Separation of Speech Mixtures
- Introduction
- Slide 3
- Slide 4
- Slide 5
- Approaches for BSS of Speech Signals
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Permutation Problem in Frequency Domain BSS
- Motivation
- My Contribution - I
- Algorithm for Solving the Permutation Problem
- Existing Method for Solving the Permutation Problem
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Proposed algorithm Partial separation method (Parallel configuration) Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
- Partial separation method (Parallel configuration)
- Partial separation method (Cascade configuration)
- Advantages of Partial Separation method
- Comparison with Adjacent Bands Correlation Method
- Comparison with DOA method
- My Contribution -II
- Underdetermined Blind Source Separation of Instantaneous Mixtures
- Mathematical Representation of Instantaneous Mixing Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
- Single Source Points in Time-Frequency domain
- Slide 31
- Slide 32
- Scatter Diagram of the Mixtures When Source are Perfectly Sparse
- Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
- Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
- Principle of the Proposed Algorithm for the Detection of Single Source Points
- Slide 39
- Slide 40
- Proposed Algorithm for the Detection of Single Source Points
- Elimination of Outliers
- Slide 43
- Detected Single Source Points Three mixtures
- Comparison with Classical Algorithms for Determined Case
- Comparison with Method Proposed in [1] Underdetermined case
- Advantages of the Proposed algorithm
- My Contributions ndash III IV and V
- Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
- Mathematical Representation
- Single source points
- Basic Principle of Single Source Points Detection
- Algorithm for Single Source Points Detection
- Mask Estimation by k-means (KM)
- Mask Estimation by Fuzzy c-means (FCM)
- Automatic Detection of Number of Sources
- Elimination of Low Energy Points
-
Underdetermined Blind Source Separation of Instantaneous Mixtures
Underdetermined Blind Source Separation of Instantaneous Mixtures
t
k
0)(0)( 222221 tkStkS
0)(0)( 222221 tkStkS
0)(0)( 112111 tkStkS
0)(0)( 112111 tkStkS
tkX 1
tkX 22x
1x
0510 AM 28
Mathematical Representation of Instantaneous Mixing
Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
Mathematical Representation of Instantaneous Mixing
Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
)(
)(
)(
)( 1
1
1111
tkS
tkS
hh
hh
tkX
tkX
QPQP
Q
P
)(
)(
)(
)( 1
1
1111
ts
ts
hh
hh
tx
tx
QPQP
Q
P
)()()(11
1
1
11
tkS
h
h
tkS
h
h
tkS
h
h
Q
PQ
Q
q
Pq
q
P
)()()()( 21 tkStkStkStk QhhhX
Time domain
Time-Frequency domain
0510 AM 29
P ndash No of mixturesQ ndash No of sources
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
00point at 1 Case 11211111 tkStkStk
)()()( 1122111111 tkStkStk hhX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 2222221122 tkStkStk hhX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
0510 AM
0 0
30
Q
qqq tkStk
1
hX
2Let Q
00point at 1 Case 11211111 tkStkStk
)()( 111111 tkStk hX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()( 222222 tkStk hX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
0510 AM 31
00point at 1 Case 11211111 tkStkStk
)()( 111111 tkStk hX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()( 222222 tkStk hX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
Scalar
ScalarScalar
Scalar
At single source point 1 At single source point 2
111
111
ofDirection )( ofDirection
ofDirection )( ofDirection
hX
hX
tkI
tkR 222
222
ofDirection )( ofDirection
ofDirection )( ofDirection
hX
hX
tkI
tkR
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
0510 AM
1111 ( of Direction ( of Direction tkItkR XX 2222 ( of Direction ( of Direction tkItkR XX 32
Scatter Diagram of the Mixtures When Source are Perfectly Sparse
Scatter Diagram of the Mixtures When Source are Perfectly Sparse
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
22222
11111
2221
1211
22222
11111
kSkSkSkSkS
kSkSkSkSkS
hh
hh
kXkXkXkXkX
kXkXkXkXkX
21
111 h
hh
22
122 h
hh
0 00 0 0
Example
0510 AM 33
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
22222
11111
2221
1211
22222
11111
kSkSkSkSkS
kSkSkSkSkS
hh
hh
kXkXkXkXkX
kXkXkXkXkX
21
111 h
hh
22
122 h
hh
0 00 0 00
Example
Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
0510 AM 34
Scatter Diagram of the Mixtures when Sources are Sparse
Scatter Diagram of the Mixtures when Sources are Sparse
3h
6h
5h
1h4h
2h
0510 AM
No of sources = 6No of mixtures = 2
35
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
3h
6h
5h
1h4h
2h
0510 AM
No of sources = 6No of mixtures = 2
36
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
3h
6h
5h
1h4h
2h
0510 AM
ObjectiveEstimation of the single source points
No of sources = 6No of mixtures = 2
37
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Multi source point
38
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
Multi source point
39
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
Average of 15 pairs of speech utterances of length 10 s each
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
)( ofDirection )( ofDirection tkXItkXR )( ofDirection )( ofDirection tkXItkXR
SSPMSP
40
SSPt
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)()(
)()(
112112
111111
tkXjItkXR
tkXjItkXR
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXI
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXIMSP
)( 111 tkX
)( 112 tkX
cos
)()(
)()(
tkXItkXR
tkXItkXR T
Proposed Algorithm for the Detection of Single Source Points
Proposed Algorithm for the Detection of Single Source Points
0510 AM 41
Elimination of OutliersElimination of Outliers
SSPs detection
Clus
terin
g
Outlier elimination
0510 AM 42
0510 AM
Experimental ResultsExperimental Results
dB6747NMSE
No of mixtures =2 No of sources =6
43
Detected Single Source PointsThree mixtures
Detected Single Source PointsThree mixtures
No of mixtures =3 No of sources =60510 AM 44
Comparison with Classical Algorithms for Determined Case
Comparison with Classical Algorithms for Determined Case
No of mixtures =2No of sources =2
Average of 500 experimental results
0510 AM 45
-gt
Comparison with Method Proposed in [1] Underdetermined case
Comparison with Method Proposed in [1] Underdetermined case
[1] Y Li S Amari A Cichocki D W C Ho and S Xie ldquoUnderdetermined blind source separation based on sparse representationrdquo IEEE Transactions on Signal Processing vol 54 p 423ndash437 Feb 2006
0510 AM
Nor
mal
ized
mea
n sq
uare
err
or (N
MSE
) in
mix
ing
mat
rix e
stim
ation
(dB)
Order of the mixing matrices (PxQ)
46
P ndash No of mixturesQ ndash No of sources
Advantages of the Proposed algorithmAdvantages of the Proposed algorithm
Step 1 Convert x in the time domain to the TF domain to get XStep 2 Check the condition
Step 3 If the condition is satisfied then X(k t) is a sample atthe SSP and this sample is kept for mixing matrix estimationotherwise discard the point
Step 4 Repeat Steps 2 to 3 for all the points in the TF planeor until sufficient number of SSPs are obtained
cos
)()(
)()(
tkXItkXR
tkXItkXR T
1) Much simpler constrain the algorithm does not require ldquosingle source zonerdquo
3) The algorithm is extremely simple but effective2) Separation performance is better
0510 AM 47-gt
My Contributions ndash III IV and VMy Contributions ndash III IV and V
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
48
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Mask estimation
Mic 1
Mic P
Mixture in TF domain
Separated signals in TF domain
)( tkX P
)(1 tkX
t
t
k
k
)(1 tkY
)(1 tkY
)( tkYQ
)( tkYQ
QP
0510 AM 49
Mathematical RepresentationMathematical Representation
Q
q
L
lqpqp Pplnslhnx
1
1
0
1)()()(
)()()()()()()( 11 tkSktkSktkSktk QQqq HHHX
)(
)(
)()(
)()(
)(
)( 1
1
1111
tkS
tkS
kHkH
kHkH
tkX
tkX
QPQP
Q
P
)(
)(
)(
)(
)(
)(
)(
)(
)( 11
1
1
11
tkS
kH
kH
tkS
kH
kH
tkS
kH
kH
Q
PQ
Q
q
Pq
q
P
Time domain
Frequency domain
0510 AM 50
P ndash No of mixturesQ ndash No of sources
Single source pointsSingle source pointsInstantaneous mixing
00point at 1 Case 11211111 tkStkStk
)()()(
)()()(
111111
111111
tkSIktkI
tkSRktkR
HX
HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()(
)()()(
222222
222222
tkSIktkI
tkSRktkR
HX
HX
Single source point 2
Real scalar
RealReal
Real scalarReal scalar
Real scalar
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
0510 AM 51
Basic Principle of Single Source Points Detection
Basic Principle of Single Source Points Detection
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
j
H
C
e
cos21
21
UU
UUUUU H
and 20coscos HCH
angle pseudo called is
angleHermitian called is
H The Hermitian angle between the complex
vectors u1 and u2 will remain the same even if the vectors are multiplied by any complex scalars whereas the pseudo angle will change
0510 AM 52
-gt
k
Algorithm for Single Source Points Detection
Algorithm for Single Source Points Detection
t
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)(
)(
)(111
121
111 tkSkH
kH
11
11
j
jr
)(
)(
112
111
tkX
tkX
11
11
j
jr
)(
)(
112
111
tkX
tkX
)( 111 tkX
)( 112 tkX
)(
)(
)(112
122
112 tkSkH
kH θH2
θH1
θH2
rX
rX
)(
)(cos
11
111
tk
tk H
Hq
0510 AM 53
θH1
OR
1k
1k
1t
Clean
Estimated
Mask Estimation by k-means (KM)Mask Estimation by k-means (KM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 54
Clean
Estimated
Mask Estimation by Fuzzy c-means (FCM)Mask Estimation by Fuzzy c-means (FCM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 55
Automatic Detection of Number of SourcesAutomatic Detection of Number of Sources
0510 AM 56
Cluster validation technique
For c = 2 to cmax
Cluster the data into c clustersCalculate the cluster validation index
EndTake c corresponding to the best cluster as the number of sources
-gt
Elimination of Low Energy PointsElimination of Low Energy Points
0510 AM 57
- Blind Separation of Speech Mixtures
- Introduction
- Slide 3
- Slide 4
- Slide 5
- Approaches for BSS of Speech Signals
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Permutation Problem in Frequency Domain BSS
- Motivation
- My Contribution - I
- Algorithm for Solving the Permutation Problem
- Existing Method for Solving the Permutation Problem
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Proposed algorithm Partial separation method (Parallel configuration) Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
- Partial separation method (Parallel configuration)
- Partial separation method (Cascade configuration)
- Advantages of Partial Separation method
- Comparison with Adjacent Bands Correlation Method
- Comparison with DOA method
- My Contribution -II
- Underdetermined Blind Source Separation of Instantaneous Mixtures
- Mathematical Representation of Instantaneous Mixing Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
- Single Source Points in Time-Frequency domain
- Slide 31
- Slide 32
- Scatter Diagram of the Mixtures When Source are Perfectly Sparse
- Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
- Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
- Principle of the Proposed Algorithm for the Detection of Single Source Points
- Slide 39
- Slide 40
- Proposed Algorithm for the Detection of Single Source Points
- Elimination of Outliers
- Slide 43
- Detected Single Source Points Three mixtures
- Comparison with Classical Algorithms for Determined Case
- Comparison with Method Proposed in [1] Underdetermined case
- Advantages of the Proposed algorithm
- My Contributions ndash III IV and V
- Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
- Mathematical Representation
- Single source points
- Basic Principle of Single Source Points Detection
- Algorithm for Single Source Points Detection
- Mask Estimation by k-means (KM)
- Mask Estimation by Fuzzy c-means (FCM)
- Automatic Detection of Number of Sources
- Elimination of Low Energy Points
-
Mathematical Representation of Instantaneous Mixing
Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
Mathematical Representation of Instantaneous Mixing
Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
)(
)(
)(
)( 1
1
1111
tkS
tkS
hh
hh
tkX
tkX
QPQP
Q
P
)(
)(
)(
)( 1
1
1111
ts
ts
hh
hh
tx
tx
QPQP
Q
P
)()()(11
1
1
11
tkS
h
h
tkS
h
h
tkS
h
h
Q
PQ
Q
q
Pq
q
P
)()()()( 21 tkStkStkStk QhhhX
Time domain
Time-Frequency domain
0510 AM 29
P ndash No of mixturesQ ndash No of sources
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
00point at 1 Case 11211111 tkStkStk
)()()( 1122111111 tkStkStk hhX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 2222221122 tkStkStk hhX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
0510 AM
0 0
30
Q
qqq tkStk
1
hX
2Let Q
00point at 1 Case 11211111 tkStkStk
)()( 111111 tkStk hX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()( 222222 tkStk hX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
0510 AM 31
00point at 1 Case 11211111 tkStkStk
)()( 111111 tkStk hX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()( 222222 tkStk hX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
Scalar
ScalarScalar
Scalar
At single source point 1 At single source point 2
111
111
ofDirection )( ofDirection
ofDirection )( ofDirection
hX
hX
tkI
tkR 222
222
ofDirection )( ofDirection
ofDirection )( ofDirection
hX
hX
tkI
tkR
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
0510 AM
1111 ( of Direction ( of Direction tkItkR XX 2222 ( of Direction ( of Direction tkItkR XX 32
Scatter Diagram of the Mixtures When Source are Perfectly Sparse
Scatter Diagram of the Mixtures When Source are Perfectly Sparse
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
22222
11111
2221
1211
22222
11111
kSkSkSkSkS
kSkSkSkSkS
hh
hh
kXkXkXkXkX
kXkXkXkXkX
21
111 h
hh
22
122 h
hh
0 00 0 0
Example
0510 AM 33
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
22222
11111
2221
1211
22222
11111
kSkSkSkSkS
kSkSkSkSkS
hh
hh
kXkXkXkXkX
kXkXkXkXkX
21
111 h
hh
22
122 h
hh
0 00 0 00
Example
Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
0510 AM 34
Scatter Diagram of the Mixtures when Sources are Sparse
Scatter Diagram of the Mixtures when Sources are Sparse
3h
6h
5h
1h4h
2h
0510 AM
No of sources = 6No of mixtures = 2
35
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
3h
6h
5h
1h4h
2h
0510 AM
No of sources = 6No of mixtures = 2
36
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
3h
6h
5h
1h4h
2h
0510 AM
ObjectiveEstimation of the single source points
No of sources = 6No of mixtures = 2
37
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Multi source point
38
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
Multi source point
39
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
Average of 15 pairs of speech utterances of length 10 s each
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
)( ofDirection )( ofDirection tkXItkXR )( ofDirection )( ofDirection tkXItkXR
SSPMSP
40
SSPt
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)()(
)()(
112112
111111
tkXjItkXR
tkXjItkXR
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXI
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXIMSP
)( 111 tkX
)( 112 tkX
cos
)()(
)()(
tkXItkXR
tkXItkXR T
Proposed Algorithm for the Detection of Single Source Points
Proposed Algorithm for the Detection of Single Source Points
0510 AM 41
Elimination of OutliersElimination of Outliers
SSPs detection
Clus
terin
g
Outlier elimination
0510 AM 42
0510 AM
Experimental ResultsExperimental Results
dB6747NMSE
No of mixtures =2 No of sources =6
43
Detected Single Source PointsThree mixtures
Detected Single Source PointsThree mixtures
No of mixtures =3 No of sources =60510 AM 44
Comparison with Classical Algorithms for Determined Case
Comparison with Classical Algorithms for Determined Case
No of mixtures =2No of sources =2
Average of 500 experimental results
0510 AM 45
-gt
Comparison with Method Proposed in [1] Underdetermined case
Comparison with Method Proposed in [1] Underdetermined case
[1] Y Li S Amari A Cichocki D W C Ho and S Xie ldquoUnderdetermined blind source separation based on sparse representationrdquo IEEE Transactions on Signal Processing vol 54 p 423ndash437 Feb 2006
0510 AM
Nor
mal
ized
mea
n sq
uare
err
or (N
MSE
) in
mix
ing
mat
rix e
stim
ation
(dB)
Order of the mixing matrices (PxQ)
46
P ndash No of mixturesQ ndash No of sources
Advantages of the Proposed algorithmAdvantages of the Proposed algorithm
Step 1 Convert x in the time domain to the TF domain to get XStep 2 Check the condition
Step 3 If the condition is satisfied then X(k t) is a sample atthe SSP and this sample is kept for mixing matrix estimationotherwise discard the point
Step 4 Repeat Steps 2 to 3 for all the points in the TF planeor until sufficient number of SSPs are obtained
cos
)()(
)()(
tkXItkXR
tkXItkXR T
1) Much simpler constrain the algorithm does not require ldquosingle source zonerdquo
3) The algorithm is extremely simple but effective2) Separation performance is better
0510 AM 47-gt
My Contributions ndash III IV and VMy Contributions ndash III IV and V
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
48
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Mask estimation
Mic 1
Mic P
Mixture in TF domain
Separated signals in TF domain
)( tkX P
)(1 tkX
t
t
k
k
)(1 tkY
)(1 tkY
)( tkYQ
)( tkYQ
QP
0510 AM 49
Mathematical RepresentationMathematical Representation
Q
q
L
lqpqp Pplnslhnx
1
1
0
1)()()(
)()()()()()()( 11 tkSktkSktkSktk QQqq HHHX
)(
)(
)()(
)()(
)(
)( 1
1
1111
tkS
tkS
kHkH
kHkH
tkX
tkX
QPQP
Q
P
)(
)(
)(
)(
)(
)(
)(
)(
)( 11
1
1
11
tkS
kH
kH
tkS
kH
kH
tkS
kH
kH
Q
PQ
Q
q
Pq
q
P
Time domain
Frequency domain
0510 AM 50
P ndash No of mixturesQ ndash No of sources
Single source pointsSingle source pointsInstantaneous mixing
00point at 1 Case 11211111 tkStkStk
)()()(
)()()(
111111
111111
tkSIktkI
tkSRktkR
HX
HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()(
)()()(
222222
222222
tkSIktkI
tkSRktkR
HX
HX
Single source point 2
Real scalar
RealReal
Real scalarReal scalar
Real scalar
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
0510 AM 51
Basic Principle of Single Source Points Detection
Basic Principle of Single Source Points Detection
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
j
H
C
e
cos21
21
UU
UUUUU H
and 20coscos HCH
angle pseudo called is
angleHermitian called is
H The Hermitian angle between the complex
vectors u1 and u2 will remain the same even if the vectors are multiplied by any complex scalars whereas the pseudo angle will change
0510 AM 52
-gt
k
Algorithm for Single Source Points Detection
Algorithm for Single Source Points Detection
t
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)(
)(
)(111
121
111 tkSkH
kH
11
11
j
jr
)(
)(
112
111
tkX
tkX
11
11
j
jr
)(
)(
112
111
tkX
tkX
)( 111 tkX
)( 112 tkX
)(
)(
)(112
122
112 tkSkH
kH θH2
θH1
θH2
rX
rX
)(
)(cos
11
111
tk
tk H
Hq
0510 AM 53
θH1
OR
1k
1k
1t
Clean
Estimated
Mask Estimation by k-means (KM)Mask Estimation by k-means (KM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 54
Clean
Estimated
Mask Estimation by Fuzzy c-means (FCM)Mask Estimation by Fuzzy c-means (FCM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 55
Automatic Detection of Number of SourcesAutomatic Detection of Number of Sources
0510 AM 56
Cluster validation technique
For c = 2 to cmax
Cluster the data into c clustersCalculate the cluster validation index
EndTake c corresponding to the best cluster as the number of sources
-gt
Elimination of Low Energy PointsElimination of Low Energy Points
0510 AM 57
- Blind Separation of Speech Mixtures
- Introduction
- Slide 3
- Slide 4
- Slide 5
- Approaches for BSS of Speech Signals
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Permutation Problem in Frequency Domain BSS
- Motivation
- My Contribution - I
- Algorithm for Solving the Permutation Problem
- Existing Method for Solving the Permutation Problem
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Proposed algorithm Partial separation method (Parallel configuration) Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
- Partial separation method (Parallel configuration)
- Partial separation method (Cascade configuration)
- Advantages of Partial Separation method
- Comparison with Adjacent Bands Correlation Method
- Comparison with DOA method
- My Contribution -II
- Underdetermined Blind Source Separation of Instantaneous Mixtures
- Mathematical Representation of Instantaneous Mixing Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
- Single Source Points in Time-Frequency domain
- Slide 31
- Slide 32
- Scatter Diagram of the Mixtures When Source are Perfectly Sparse
- Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
- Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
- Principle of the Proposed Algorithm for the Detection of Single Source Points
- Slide 39
- Slide 40
- Proposed Algorithm for the Detection of Single Source Points
- Elimination of Outliers
- Slide 43
- Detected Single Source Points Three mixtures
- Comparison with Classical Algorithms for Determined Case
- Comparison with Method Proposed in [1] Underdetermined case
- Advantages of the Proposed algorithm
- My Contributions ndash III IV and V
- Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
- Mathematical Representation
- Single source points
- Basic Principle of Single Source Points Detection
- Algorithm for Single Source Points Detection
- Mask Estimation by k-means (KM)
- Mask Estimation by Fuzzy c-means (FCM)
- Automatic Detection of Number of Sources
- Elimination of Low Energy Points
-
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
00point at 1 Case 11211111 tkStkStk
)()()( 1122111111 tkStkStk hhX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 2222221122 tkStkStk hhX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
0510 AM
0 0
30
Q
qqq tkStk
1
hX
2Let Q
00point at 1 Case 11211111 tkStkStk
)()( 111111 tkStk hX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()( 222222 tkStk hX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
0510 AM 31
00point at 1 Case 11211111 tkStkStk
)()( 111111 tkStk hX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()( 222222 tkStk hX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
Scalar
ScalarScalar
Scalar
At single source point 1 At single source point 2
111
111
ofDirection )( ofDirection
ofDirection )( ofDirection
hX
hX
tkI
tkR 222
222
ofDirection )( ofDirection
ofDirection )( ofDirection
hX
hX
tkI
tkR
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
0510 AM
1111 ( of Direction ( of Direction tkItkR XX 2222 ( of Direction ( of Direction tkItkR XX 32
Scatter Diagram of the Mixtures When Source are Perfectly Sparse
Scatter Diagram of the Mixtures When Source are Perfectly Sparse
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
22222
11111
2221
1211
22222
11111
kSkSkSkSkS
kSkSkSkSkS
hh
hh
kXkXkXkXkX
kXkXkXkXkX
21
111 h
hh
22
122 h
hh
0 00 0 0
Example
0510 AM 33
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
22222
11111
2221
1211
22222
11111
kSkSkSkSkS
kSkSkSkSkS
hh
hh
kXkXkXkXkX
kXkXkXkXkX
21
111 h
hh
22
122 h
hh
0 00 0 00
Example
Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
0510 AM 34
Scatter Diagram of the Mixtures when Sources are Sparse
Scatter Diagram of the Mixtures when Sources are Sparse
3h
6h
5h
1h4h
2h
0510 AM
No of sources = 6No of mixtures = 2
35
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
3h
6h
5h
1h4h
2h
0510 AM
No of sources = 6No of mixtures = 2
36
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
3h
6h
5h
1h4h
2h
0510 AM
ObjectiveEstimation of the single source points
No of sources = 6No of mixtures = 2
37
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Multi source point
38
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
Multi source point
39
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
Average of 15 pairs of speech utterances of length 10 s each
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
)( ofDirection )( ofDirection tkXItkXR )( ofDirection )( ofDirection tkXItkXR
SSPMSP
40
SSPt
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)()(
)()(
112112
111111
tkXjItkXR
tkXjItkXR
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXI
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXIMSP
)( 111 tkX
)( 112 tkX
cos
)()(
)()(
tkXItkXR
tkXItkXR T
Proposed Algorithm for the Detection of Single Source Points
Proposed Algorithm for the Detection of Single Source Points
0510 AM 41
Elimination of OutliersElimination of Outliers
SSPs detection
Clus
terin
g
Outlier elimination
0510 AM 42
0510 AM
Experimental ResultsExperimental Results
dB6747NMSE
No of mixtures =2 No of sources =6
43
Detected Single Source PointsThree mixtures
Detected Single Source PointsThree mixtures
No of mixtures =3 No of sources =60510 AM 44
Comparison with Classical Algorithms for Determined Case
Comparison with Classical Algorithms for Determined Case
No of mixtures =2No of sources =2
Average of 500 experimental results
0510 AM 45
-gt
Comparison with Method Proposed in [1] Underdetermined case
Comparison with Method Proposed in [1] Underdetermined case
[1] Y Li S Amari A Cichocki D W C Ho and S Xie ldquoUnderdetermined blind source separation based on sparse representationrdquo IEEE Transactions on Signal Processing vol 54 p 423ndash437 Feb 2006
0510 AM
Nor
mal
ized
mea
n sq
uare
err
or (N
MSE
) in
mix
ing
mat
rix e
stim
ation
(dB)
Order of the mixing matrices (PxQ)
46
P ndash No of mixturesQ ndash No of sources
Advantages of the Proposed algorithmAdvantages of the Proposed algorithm
Step 1 Convert x in the time domain to the TF domain to get XStep 2 Check the condition
Step 3 If the condition is satisfied then X(k t) is a sample atthe SSP and this sample is kept for mixing matrix estimationotherwise discard the point
Step 4 Repeat Steps 2 to 3 for all the points in the TF planeor until sufficient number of SSPs are obtained
cos
)()(
)()(
tkXItkXR
tkXItkXR T
1) Much simpler constrain the algorithm does not require ldquosingle source zonerdquo
3) The algorithm is extremely simple but effective2) Separation performance is better
0510 AM 47-gt
My Contributions ndash III IV and VMy Contributions ndash III IV and V
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
48
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Mask estimation
Mic 1
Mic P
Mixture in TF domain
Separated signals in TF domain
)( tkX P
)(1 tkX
t
t
k
k
)(1 tkY
)(1 tkY
)( tkYQ
)( tkYQ
QP
0510 AM 49
Mathematical RepresentationMathematical Representation
Q
q
L
lqpqp Pplnslhnx
1
1
0
1)()()(
)()()()()()()( 11 tkSktkSktkSktk QQqq HHHX
)(
)(
)()(
)()(
)(
)( 1
1
1111
tkS
tkS
kHkH
kHkH
tkX
tkX
QPQP
Q
P
)(
)(
)(
)(
)(
)(
)(
)(
)( 11
1
1
11
tkS
kH
kH
tkS
kH
kH
tkS
kH
kH
Q
PQ
Q
q
Pq
q
P
Time domain
Frequency domain
0510 AM 50
P ndash No of mixturesQ ndash No of sources
Single source pointsSingle source pointsInstantaneous mixing
00point at 1 Case 11211111 tkStkStk
)()()(
)()()(
111111
111111
tkSIktkI
tkSRktkR
HX
HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()(
)()()(
222222
222222
tkSIktkI
tkSRktkR
HX
HX
Single source point 2
Real scalar
RealReal
Real scalarReal scalar
Real scalar
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
0510 AM 51
Basic Principle of Single Source Points Detection
Basic Principle of Single Source Points Detection
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
j
H
C
e
cos21
21
UU
UUUUU H
and 20coscos HCH
angle pseudo called is
angleHermitian called is
H The Hermitian angle between the complex
vectors u1 and u2 will remain the same even if the vectors are multiplied by any complex scalars whereas the pseudo angle will change
0510 AM 52
-gt
k
Algorithm for Single Source Points Detection
Algorithm for Single Source Points Detection
t
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)(
)(
)(111
121
111 tkSkH
kH
11
11
j
jr
)(
)(
112
111
tkX
tkX
11
11
j
jr
)(
)(
112
111
tkX
tkX
)( 111 tkX
)( 112 tkX
)(
)(
)(112
122
112 tkSkH
kH θH2
θH1
θH2
rX
rX
)(
)(cos
11
111
tk
tk H
Hq
0510 AM 53
θH1
OR
1k
1k
1t
Clean
Estimated
Mask Estimation by k-means (KM)Mask Estimation by k-means (KM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 54
Clean
Estimated
Mask Estimation by Fuzzy c-means (FCM)Mask Estimation by Fuzzy c-means (FCM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 55
Automatic Detection of Number of SourcesAutomatic Detection of Number of Sources
0510 AM 56
Cluster validation technique
For c = 2 to cmax
Cluster the data into c clustersCalculate the cluster validation index
EndTake c corresponding to the best cluster as the number of sources
-gt
Elimination of Low Energy PointsElimination of Low Energy Points
0510 AM 57
- Blind Separation of Speech Mixtures
- Introduction
- Slide 3
- Slide 4
- Slide 5
- Approaches for BSS of Speech Signals
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Permutation Problem in Frequency Domain BSS
- Motivation
- My Contribution - I
- Algorithm for Solving the Permutation Problem
- Existing Method for Solving the Permutation Problem
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Proposed algorithm Partial separation method (Parallel configuration) Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
- Partial separation method (Parallel configuration)
- Partial separation method (Cascade configuration)
- Advantages of Partial Separation method
- Comparison with Adjacent Bands Correlation Method
- Comparison with DOA method
- My Contribution -II
- Underdetermined Blind Source Separation of Instantaneous Mixtures
- Mathematical Representation of Instantaneous Mixing Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
- Single Source Points in Time-Frequency domain
- Slide 31
- Slide 32
- Scatter Diagram of the Mixtures When Source are Perfectly Sparse
- Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
- Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
- Principle of the Proposed Algorithm for the Detection of Single Source Points
- Slide 39
- Slide 40
- Proposed Algorithm for the Detection of Single Source Points
- Elimination of Outliers
- Slide 43
- Detected Single Source Points Three mixtures
- Comparison with Classical Algorithms for Determined Case
- Comparison with Method Proposed in [1] Underdetermined case
- Advantages of the Proposed algorithm
- My Contributions ndash III IV and V
- Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
- Mathematical Representation
- Single source points
- Basic Principle of Single Source Points Detection
- Algorithm for Single Source Points Detection
- Mask Estimation by k-means (KM)
- Mask Estimation by Fuzzy c-means (FCM)
- Automatic Detection of Number of Sources
- Elimination of Low Energy Points
-
Q
qqq tkStk
1
hX
2Let Q
00point at 1 Case 11211111 tkStkStk
)()( 111111 tkStk hX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()( 222222 tkStk hX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
0510 AM 31
00point at 1 Case 11211111 tkStkStk
)()( 111111 tkStk hX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()( 222222 tkStk hX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
Scalar
ScalarScalar
Scalar
At single source point 1 At single source point 2
111
111
ofDirection )( ofDirection
ofDirection )( ofDirection
hX
hX
tkI
tkR 222
222
ofDirection )( ofDirection
ofDirection )( ofDirection
hX
hX
tkI
tkR
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
0510 AM
1111 ( of Direction ( of Direction tkItkR XX 2222 ( of Direction ( of Direction tkItkR XX 32
Scatter Diagram of the Mixtures When Source are Perfectly Sparse
Scatter Diagram of the Mixtures When Source are Perfectly Sparse
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
22222
11111
2221
1211
22222
11111
kSkSkSkSkS
kSkSkSkSkS
hh
hh
kXkXkXkXkX
kXkXkXkXkX
21
111 h
hh
22
122 h
hh
0 00 0 0
Example
0510 AM 33
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
22222
11111
2221
1211
22222
11111
kSkSkSkSkS
kSkSkSkSkS
hh
hh
kXkXkXkXkX
kXkXkXkXkX
21
111 h
hh
22
122 h
hh
0 00 0 00
Example
Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
0510 AM 34
Scatter Diagram of the Mixtures when Sources are Sparse
Scatter Diagram of the Mixtures when Sources are Sparse
3h
6h
5h
1h4h
2h
0510 AM
No of sources = 6No of mixtures = 2
35
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
3h
6h
5h
1h4h
2h
0510 AM
No of sources = 6No of mixtures = 2
36
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
3h
6h
5h
1h4h
2h
0510 AM
ObjectiveEstimation of the single source points
No of sources = 6No of mixtures = 2
37
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Multi source point
38
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
Multi source point
39
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
Average of 15 pairs of speech utterances of length 10 s each
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
)( ofDirection )( ofDirection tkXItkXR )( ofDirection )( ofDirection tkXItkXR
SSPMSP
40
SSPt
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)()(
)()(
112112
111111
tkXjItkXR
tkXjItkXR
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXI
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXIMSP
)( 111 tkX
)( 112 tkX
cos
)()(
)()(
tkXItkXR
tkXItkXR T
Proposed Algorithm for the Detection of Single Source Points
Proposed Algorithm for the Detection of Single Source Points
0510 AM 41
Elimination of OutliersElimination of Outliers
SSPs detection
Clus
terin
g
Outlier elimination
0510 AM 42
0510 AM
Experimental ResultsExperimental Results
dB6747NMSE
No of mixtures =2 No of sources =6
43
Detected Single Source PointsThree mixtures
Detected Single Source PointsThree mixtures
No of mixtures =3 No of sources =60510 AM 44
Comparison with Classical Algorithms for Determined Case
Comparison with Classical Algorithms for Determined Case
No of mixtures =2No of sources =2
Average of 500 experimental results
0510 AM 45
-gt
Comparison with Method Proposed in [1] Underdetermined case
Comparison with Method Proposed in [1] Underdetermined case
[1] Y Li S Amari A Cichocki D W C Ho and S Xie ldquoUnderdetermined blind source separation based on sparse representationrdquo IEEE Transactions on Signal Processing vol 54 p 423ndash437 Feb 2006
0510 AM
Nor
mal
ized
mea
n sq
uare
err
or (N
MSE
) in
mix
ing
mat
rix e
stim
ation
(dB)
Order of the mixing matrices (PxQ)
46
P ndash No of mixturesQ ndash No of sources
Advantages of the Proposed algorithmAdvantages of the Proposed algorithm
Step 1 Convert x in the time domain to the TF domain to get XStep 2 Check the condition
Step 3 If the condition is satisfied then X(k t) is a sample atthe SSP and this sample is kept for mixing matrix estimationotherwise discard the point
Step 4 Repeat Steps 2 to 3 for all the points in the TF planeor until sufficient number of SSPs are obtained
cos
)()(
)()(
tkXItkXR
tkXItkXR T
1) Much simpler constrain the algorithm does not require ldquosingle source zonerdquo
3) The algorithm is extremely simple but effective2) Separation performance is better
0510 AM 47-gt
My Contributions ndash III IV and VMy Contributions ndash III IV and V
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
48
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Mask estimation
Mic 1
Mic P
Mixture in TF domain
Separated signals in TF domain
)( tkX P
)(1 tkX
t
t
k
k
)(1 tkY
)(1 tkY
)( tkYQ
)( tkYQ
QP
0510 AM 49
Mathematical RepresentationMathematical Representation
Q
q
L
lqpqp Pplnslhnx
1
1
0
1)()()(
)()()()()()()( 11 tkSktkSktkSktk QQqq HHHX
)(
)(
)()(
)()(
)(
)( 1
1
1111
tkS
tkS
kHkH
kHkH
tkX
tkX
QPQP
Q
P
)(
)(
)(
)(
)(
)(
)(
)(
)( 11
1
1
11
tkS
kH
kH
tkS
kH
kH
tkS
kH
kH
Q
PQ
Q
q
Pq
q
P
Time domain
Frequency domain
0510 AM 50
P ndash No of mixturesQ ndash No of sources
Single source pointsSingle source pointsInstantaneous mixing
00point at 1 Case 11211111 tkStkStk
)()()(
)()()(
111111
111111
tkSIktkI
tkSRktkR
HX
HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()(
)()()(
222222
222222
tkSIktkI
tkSRktkR
HX
HX
Single source point 2
Real scalar
RealReal
Real scalarReal scalar
Real scalar
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
0510 AM 51
Basic Principle of Single Source Points Detection
Basic Principle of Single Source Points Detection
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
j
H
C
e
cos21
21
UU
UUUUU H
and 20coscos HCH
angle pseudo called is
angleHermitian called is
H The Hermitian angle between the complex
vectors u1 and u2 will remain the same even if the vectors are multiplied by any complex scalars whereas the pseudo angle will change
0510 AM 52
-gt
k
Algorithm for Single Source Points Detection
Algorithm for Single Source Points Detection
t
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)(
)(
)(111
121
111 tkSkH
kH
11
11
j
jr
)(
)(
112
111
tkX
tkX
11
11
j
jr
)(
)(
112
111
tkX
tkX
)( 111 tkX
)( 112 tkX
)(
)(
)(112
122
112 tkSkH
kH θH2
θH1
θH2
rX
rX
)(
)(cos
11
111
tk
tk H
Hq
0510 AM 53
θH1
OR
1k
1k
1t
Clean
Estimated
Mask Estimation by k-means (KM)Mask Estimation by k-means (KM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 54
Clean
Estimated
Mask Estimation by Fuzzy c-means (FCM)Mask Estimation by Fuzzy c-means (FCM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 55
Automatic Detection of Number of SourcesAutomatic Detection of Number of Sources
0510 AM 56
Cluster validation technique
For c = 2 to cmax
Cluster the data into c clustersCalculate the cluster validation index
EndTake c corresponding to the best cluster as the number of sources
-gt
Elimination of Low Energy PointsElimination of Low Energy Points
0510 AM 57
- Blind Separation of Speech Mixtures
- Introduction
- Slide 3
- Slide 4
- Slide 5
- Approaches for BSS of Speech Signals
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Permutation Problem in Frequency Domain BSS
- Motivation
- My Contribution - I
- Algorithm for Solving the Permutation Problem
- Existing Method for Solving the Permutation Problem
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Proposed algorithm Partial separation method (Parallel configuration) Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
- Partial separation method (Parallel configuration)
- Partial separation method (Cascade configuration)
- Advantages of Partial Separation method
- Comparison with Adjacent Bands Correlation Method
- Comparison with DOA method
- My Contribution -II
- Underdetermined Blind Source Separation of Instantaneous Mixtures
- Mathematical Representation of Instantaneous Mixing Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
- Single Source Points in Time-Frequency domain
- Slide 31
- Slide 32
- Scatter Diagram of the Mixtures When Source are Perfectly Sparse
- Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
- Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
- Principle of the Proposed Algorithm for the Detection of Single Source Points
- Slide 39
- Slide 40
- Proposed Algorithm for the Detection of Single Source Points
- Elimination of Outliers
- Slide 43
- Detected Single Source Points Three mixtures
- Comparison with Classical Algorithms for Determined Case
- Comparison with Method Proposed in [1] Underdetermined case
- Advantages of the Proposed algorithm
- My Contributions ndash III IV and V
- Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
- Mathematical Representation
- Single source points
- Basic Principle of Single Source Points Detection
- Algorithm for Single Source Points Detection
- Mask Estimation by k-means (KM)
- Mask Estimation by Fuzzy c-means (FCM)
- Automatic Detection of Number of Sources
- Elimination of Low Energy Points
-
00point at 1 Case 11211111 tkStkStk
)()( 111111 tkStk hX
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()( 222222 tkStk hX
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2
Scalar
ScalarScalar
Scalar
At single source point 1 At single source point 2
111
111
ofDirection )( ofDirection
ofDirection )( ofDirection
hX
hX
tkI
tkR 222
222
ofDirection )( ofDirection
ofDirection )( ofDirection
hX
hX
tkI
tkR
Single Source Points in Time-Frequency domainSingle Source Points in
Time-Frequency domain
0510 AM
1111 ( of Direction ( of Direction tkItkR XX 2222 ( of Direction ( of Direction tkItkR XX 32
Scatter Diagram of the Mixtures When Source are Perfectly Sparse
Scatter Diagram of the Mixtures When Source are Perfectly Sparse
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
22222
11111
2221
1211
22222
11111
kSkSkSkSkS
kSkSkSkSkS
hh
hh
kXkXkXkXkX
kXkXkXkXkX
21
111 h
hh
22
122 h
hh
0 00 0 0
Example
0510 AM 33
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
22222
11111
2221
1211
22222
11111
kSkSkSkSkS
kSkSkSkSkS
hh
hh
kXkXkXkXkX
kXkXkXkXkX
21
111 h
hh
22
122 h
hh
0 00 0 00
Example
Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
0510 AM 34
Scatter Diagram of the Mixtures when Sources are Sparse
Scatter Diagram of the Mixtures when Sources are Sparse
3h
6h
5h
1h4h
2h
0510 AM
No of sources = 6No of mixtures = 2
35
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
3h
6h
5h
1h4h
2h
0510 AM
No of sources = 6No of mixtures = 2
36
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
3h
6h
5h
1h4h
2h
0510 AM
ObjectiveEstimation of the single source points
No of sources = 6No of mixtures = 2
37
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Multi source point
38
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
Multi source point
39
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
Average of 15 pairs of speech utterances of length 10 s each
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
)( ofDirection )( ofDirection tkXItkXR )( ofDirection )( ofDirection tkXItkXR
SSPMSP
40
SSPt
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)()(
)()(
112112
111111
tkXjItkXR
tkXjItkXR
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXI
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXIMSP
)( 111 tkX
)( 112 tkX
cos
)()(
)()(
tkXItkXR
tkXItkXR T
Proposed Algorithm for the Detection of Single Source Points
Proposed Algorithm for the Detection of Single Source Points
0510 AM 41
Elimination of OutliersElimination of Outliers
SSPs detection
Clus
terin
g
Outlier elimination
0510 AM 42
0510 AM
Experimental ResultsExperimental Results
dB6747NMSE
No of mixtures =2 No of sources =6
43
Detected Single Source PointsThree mixtures
Detected Single Source PointsThree mixtures
No of mixtures =3 No of sources =60510 AM 44
Comparison with Classical Algorithms for Determined Case
Comparison with Classical Algorithms for Determined Case
No of mixtures =2No of sources =2
Average of 500 experimental results
0510 AM 45
-gt
Comparison with Method Proposed in [1] Underdetermined case
Comparison with Method Proposed in [1] Underdetermined case
[1] Y Li S Amari A Cichocki D W C Ho and S Xie ldquoUnderdetermined blind source separation based on sparse representationrdquo IEEE Transactions on Signal Processing vol 54 p 423ndash437 Feb 2006
0510 AM
Nor
mal
ized
mea
n sq
uare
err
or (N
MSE
) in
mix
ing
mat
rix e
stim
ation
(dB)
Order of the mixing matrices (PxQ)
46
P ndash No of mixturesQ ndash No of sources
Advantages of the Proposed algorithmAdvantages of the Proposed algorithm
Step 1 Convert x in the time domain to the TF domain to get XStep 2 Check the condition
Step 3 If the condition is satisfied then X(k t) is a sample atthe SSP and this sample is kept for mixing matrix estimationotherwise discard the point
Step 4 Repeat Steps 2 to 3 for all the points in the TF planeor until sufficient number of SSPs are obtained
cos
)()(
)()(
tkXItkXR
tkXItkXR T
1) Much simpler constrain the algorithm does not require ldquosingle source zonerdquo
3) The algorithm is extremely simple but effective2) Separation performance is better
0510 AM 47-gt
My Contributions ndash III IV and VMy Contributions ndash III IV and V
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
48
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Mask estimation
Mic 1
Mic P
Mixture in TF domain
Separated signals in TF domain
)( tkX P
)(1 tkX
t
t
k
k
)(1 tkY
)(1 tkY
)( tkYQ
)( tkYQ
QP
0510 AM 49
Mathematical RepresentationMathematical Representation
Q
q
L
lqpqp Pplnslhnx
1
1
0
1)()()(
)()()()()()()( 11 tkSktkSktkSktk QQqq HHHX
)(
)(
)()(
)()(
)(
)( 1
1
1111
tkS
tkS
kHkH
kHkH
tkX
tkX
QPQP
Q
P
)(
)(
)(
)(
)(
)(
)(
)(
)( 11
1
1
11
tkS
kH
kH
tkS
kH
kH
tkS
kH
kH
Q
PQ
Q
q
Pq
q
P
Time domain
Frequency domain
0510 AM 50
P ndash No of mixturesQ ndash No of sources
Single source pointsSingle source pointsInstantaneous mixing
00point at 1 Case 11211111 tkStkStk
)()()(
)()()(
111111
111111
tkSIktkI
tkSRktkR
HX
HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()(
)()()(
222222
222222
tkSIktkI
tkSRktkR
HX
HX
Single source point 2
Real scalar
RealReal
Real scalarReal scalar
Real scalar
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
0510 AM 51
Basic Principle of Single Source Points Detection
Basic Principle of Single Source Points Detection
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
j
H
C
e
cos21
21
UU
UUUUU H
and 20coscos HCH
angle pseudo called is
angleHermitian called is
H The Hermitian angle between the complex
vectors u1 and u2 will remain the same even if the vectors are multiplied by any complex scalars whereas the pseudo angle will change
0510 AM 52
-gt
k
Algorithm for Single Source Points Detection
Algorithm for Single Source Points Detection
t
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)(
)(
)(111
121
111 tkSkH
kH
11
11
j
jr
)(
)(
112
111
tkX
tkX
11
11
j
jr
)(
)(
112
111
tkX
tkX
)( 111 tkX
)( 112 tkX
)(
)(
)(112
122
112 tkSkH
kH θH2
θH1
θH2
rX
rX
)(
)(cos
11
111
tk
tk H
Hq
0510 AM 53
θH1
OR
1k
1k
1t
Clean
Estimated
Mask Estimation by k-means (KM)Mask Estimation by k-means (KM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 54
Clean
Estimated
Mask Estimation by Fuzzy c-means (FCM)Mask Estimation by Fuzzy c-means (FCM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 55
Automatic Detection of Number of SourcesAutomatic Detection of Number of Sources
0510 AM 56
Cluster validation technique
For c = 2 to cmax
Cluster the data into c clustersCalculate the cluster validation index
EndTake c corresponding to the best cluster as the number of sources
-gt
Elimination of Low Energy PointsElimination of Low Energy Points
0510 AM 57
- Blind Separation of Speech Mixtures
- Introduction
- Slide 3
- Slide 4
- Slide 5
- Approaches for BSS of Speech Signals
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Permutation Problem in Frequency Domain BSS
- Motivation
- My Contribution - I
- Algorithm for Solving the Permutation Problem
- Existing Method for Solving the Permutation Problem
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Proposed algorithm Partial separation method (Parallel configuration) Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
- Partial separation method (Parallel configuration)
- Partial separation method (Cascade configuration)
- Advantages of Partial Separation method
- Comparison with Adjacent Bands Correlation Method
- Comparison with DOA method
- My Contribution -II
- Underdetermined Blind Source Separation of Instantaneous Mixtures
- Mathematical Representation of Instantaneous Mixing Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
- Single Source Points in Time-Frequency domain
- Slide 31
- Slide 32
- Scatter Diagram of the Mixtures When Source are Perfectly Sparse
- Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
- Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
- Principle of the Proposed Algorithm for the Detection of Single Source Points
- Slide 39
- Slide 40
- Proposed Algorithm for the Detection of Single Source Points
- Elimination of Outliers
- Slide 43
- Detected Single Source Points Three mixtures
- Comparison with Classical Algorithms for Determined Case
- Comparison with Method Proposed in [1] Underdetermined case
- Advantages of the Proposed algorithm
- My Contributions ndash III IV and V
- Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
- Mathematical Representation
- Single source points
- Basic Principle of Single Source Points Detection
- Algorithm for Single Source Points Detection
- Mask Estimation by k-means (KM)
- Mask Estimation by Fuzzy c-means (FCM)
- Automatic Detection of Number of Sources
- Elimination of Low Energy Points
-
Scatter Diagram of the Mixtures When Source are Perfectly Sparse
Scatter Diagram of the Mixtures When Source are Perfectly Sparse
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
22222
11111
2221
1211
22222
11111
kSkSkSkSkS
kSkSkSkSkS
hh
hh
kXkXkXkXkX
kXkXkXkXkX
21
111 h
hh
22
122 h
hh
0 00 0 0
Example
0510 AM 33
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
22222
11111
2221
1211
22222
11111
kSkSkSkSkS
kSkSkSkSkS
hh
hh
kXkXkXkXkX
kXkXkXkXkX
21
111 h
hh
22
122 h
hh
0 00 0 00
Example
Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
0510 AM 34
Scatter Diagram of the Mixtures when Sources are Sparse
Scatter Diagram of the Mixtures when Sources are Sparse
3h
6h
5h
1h4h
2h
0510 AM
No of sources = 6No of mixtures = 2
35
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
3h
6h
5h
1h4h
2h
0510 AM
No of sources = 6No of mixtures = 2
36
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
3h
6h
5h
1h4h
2h
0510 AM
ObjectiveEstimation of the single source points
No of sources = 6No of mixtures = 2
37
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Multi source point
38
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
Multi source point
39
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
Average of 15 pairs of speech utterances of length 10 s each
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
)( ofDirection )( ofDirection tkXItkXR )( ofDirection )( ofDirection tkXItkXR
SSPMSP
40
SSPt
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)()(
)()(
112112
111111
tkXjItkXR
tkXjItkXR
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXI
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXIMSP
)( 111 tkX
)( 112 tkX
cos
)()(
)()(
tkXItkXR
tkXItkXR T
Proposed Algorithm for the Detection of Single Source Points
Proposed Algorithm for the Detection of Single Source Points
0510 AM 41
Elimination of OutliersElimination of Outliers
SSPs detection
Clus
terin
g
Outlier elimination
0510 AM 42
0510 AM
Experimental ResultsExperimental Results
dB6747NMSE
No of mixtures =2 No of sources =6
43
Detected Single Source PointsThree mixtures
Detected Single Source PointsThree mixtures
No of mixtures =3 No of sources =60510 AM 44
Comparison with Classical Algorithms for Determined Case
Comparison with Classical Algorithms for Determined Case
No of mixtures =2No of sources =2
Average of 500 experimental results
0510 AM 45
-gt
Comparison with Method Proposed in [1] Underdetermined case
Comparison with Method Proposed in [1] Underdetermined case
[1] Y Li S Amari A Cichocki D W C Ho and S Xie ldquoUnderdetermined blind source separation based on sparse representationrdquo IEEE Transactions on Signal Processing vol 54 p 423ndash437 Feb 2006
0510 AM
Nor
mal
ized
mea
n sq
uare
err
or (N
MSE
) in
mix
ing
mat
rix e
stim
ation
(dB)
Order of the mixing matrices (PxQ)
46
P ndash No of mixturesQ ndash No of sources
Advantages of the Proposed algorithmAdvantages of the Proposed algorithm
Step 1 Convert x in the time domain to the TF domain to get XStep 2 Check the condition
Step 3 If the condition is satisfied then X(k t) is a sample atthe SSP and this sample is kept for mixing matrix estimationotherwise discard the point
Step 4 Repeat Steps 2 to 3 for all the points in the TF planeor until sufficient number of SSPs are obtained
cos
)()(
)()(
tkXItkXR
tkXItkXR T
1) Much simpler constrain the algorithm does not require ldquosingle source zonerdquo
3) The algorithm is extremely simple but effective2) Separation performance is better
0510 AM 47-gt
My Contributions ndash III IV and VMy Contributions ndash III IV and V
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
48
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Mask estimation
Mic 1
Mic P
Mixture in TF domain
Separated signals in TF domain
)( tkX P
)(1 tkX
t
t
k
k
)(1 tkY
)(1 tkY
)( tkYQ
)( tkYQ
QP
0510 AM 49
Mathematical RepresentationMathematical Representation
Q
q
L
lqpqp Pplnslhnx
1
1
0
1)()()(
)()()()()()()( 11 tkSktkSktkSktk QQqq HHHX
)(
)(
)()(
)()(
)(
)( 1
1
1111
tkS
tkS
kHkH
kHkH
tkX
tkX
QPQP
Q
P
)(
)(
)(
)(
)(
)(
)(
)(
)( 11
1
1
11
tkS
kH
kH
tkS
kH
kH
tkS
kH
kH
Q
PQ
Q
q
Pq
q
P
Time domain
Frequency domain
0510 AM 50
P ndash No of mixturesQ ndash No of sources
Single source pointsSingle source pointsInstantaneous mixing
00point at 1 Case 11211111 tkStkStk
)()()(
)()()(
111111
111111
tkSIktkI
tkSRktkR
HX
HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()(
)()()(
222222
222222
tkSIktkI
tkSRktkR
HX
HX
Single source point 2
Real scalar
RealReal
Real scalarReal scalar
Real scalar
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
0510 AM 51
Basic Principle of Single Source Points Detection
Basic Principle of Single Source Points Detection
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
j
H
C
e
cos21
21
UU
UUUUU H
and 20coscos HCH
angle pseudo called is
angleHermitian called is
H The Hermitian angle between the complex
vectors u1 and u2 will remain the same even if the vectors are multiplied by any complex scalars whereas the pseudo angle will change
0510 AM 52
-gt
k
Algorithm for Single Source Points Detection
Algorithm for Single Source Points Detection
t
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)(
)(
)(111
121
111 tkSkH
kH
11
11
j
jr
)(
)(
112
111
tkX
tkX
11
11
j
jr
)(
)(
112
111
tkX
tkX
)( 111 tkX
)( 112 tkX
)(
)(
)(112
122
112 tkSkH
kH θH2
θH1
θH2
rX
rX
)(
)(cos
11
111
tk
tk H
Hq
0510 AM 53
θH1
OR
1k
1k
1t
Clean
Estimated
Mask Estimation by k-means (KM)Mask Estimation by k-means (KM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 54
Clean
Estimated
Mask Estimation by Fuzzy c-means (FCM)Mask Estimation by Fuzzy c-means (FCM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 55
Automatic Detection of Number of SourcesAutomatic Detection of Number of Sources
0510 AM 56
Cluster validation technique
For c = 2 to cmax
Cluster the data into c clustersCalculate the cluster validation index
EndTake c corresponding to the best cluster as the number of sources
-gt
Elimination of Low Energy PointsElimination of Low Energy Points
0510 AM 57
- Blind Separation of Speech Mixtures
- Introduction
- Slide 3
- Slide 4
- Slide 5
- Approaches for BSS of Speech Signals
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Permutation Problem in Frequency Domain BSS
- Motivation
- My Contribution - I
- Algorithm for Solving the Permutation Problem
- Existing Method for Solving the Permutation Problem
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Proposed algorithm Partial separation method (Parallel configuration) Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
- Partial separation method (Parallel configuration)
- Partial separation method (Cascade configuration)
- Advantages of Partial Separation method
- Comparison with Adjacent Bands Correlation Method
- Comparison with DOA method
- My Contribution -II
- Underdetermined Blind Source Separation of Instantaneous Mixtures
- Mathematical Representation of Instantaneous Mixing Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
- Single Source Points in Time-Frequency domain
- Slide 31
- Slide 32
- Scatter Diagram of the Mixtures When Source are Perfectly Sparse
- Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
- Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
- Principle of the Proposed Algorithm for the Detection of Single Source Points
- Slide 39
- Slide 40
- Proposed Algorithm for the Detection of Single Source Points
- Elimination of Outliers
- Slide 43
- Detected Single Source Points Three mixtures
- Comparison with Classical Algorithms for Determined Case
- Comparison with Method Proposed in [1] Underdetermined case
- Advantages of the Proposed algorithm
- My Contributions ndash III IV and V
- Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
- Mathematical Representation
- Single source points
- Basic Principle of Single Source Points Detection
- Algorithm for Single Source Points Detection
- Mask Estimation by k-means (KM)
- Mask Estimation by Fuzzy c-means (FCM)
- Automatic Detection of Number of Sources
- Elimination of Low Energy Points
-
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
)5()4()3()2()1(
22222
11111
2221
1211
22222
11111
kSkSkSkSkS
kSkSkSkSkS
hh
hh
kXkXkXkXkX
kXkXkXkXkX
21
111 h
hh
22
122 h
hh
0 00 0 00
Example
Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
0510 AM 34
Scatter Diagram of the Mixtures when Sources are Sparse
Scatter Diagram of the Mixtures when Sources are Sparse
3h
6h
5h
1h4h
2h
0510 AM
No of sources = 6No of mixtures = 2
35
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
3h
6h
5h
1h4h
2h
0510 AM
No of sources = 6No of mixtures = 2
36
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
3h
6h
5h
1h4h
2h
0510 AM
ObjectiveEstimation of the single source points
No of sources = 6No of mixtures = 2
37
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Multi source point
38
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
Multi source point
39
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
Average of 15 pairs of speech utterances of length 10 s each
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
)( ofDirection )( ofDirection tkXItkXR )( ofDirection )( ofDirection tkXItkXR
SSPMSP
40
SSPt
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)()(
)()(
112112
111111
tkXjItkXR
tkXjItkXR
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXI
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXIMSP
)( 111 tkX
)( 112 tkX
cos
)()(
)()(
tkXItkXR
tkXItkXR T
Proposed Algorithm for the Detection of Single Source Points
Proposed Algorithm for the Detection of Single Source Points
0510 AM 41
Elimination of OutliersElimination of Outliers
SSPs detection
Clus
terin
g
Outlier elimination
0510 AM 42
0510 AM
Experimental ResultsExperimental Results
dB6747NMSE
No of mixtures =2 No of sources =6
43
Detected Single Source PointsThree mixtures
Detected Single Source PointsThree mixtures
No of mixtures =3 No of sources =60510 AM 44
Comparison with Classical Algorithms for Determined Case
Comparison with Classical Algorithms for Determined Case
No of mixtures =2No of sources =2
Average of 500 experimental results
0510 AM 45
-gt
Comparison with Method Proposed in [1] Underdetermined case
Comparison with Method Proposed in [1] Underdetermined case
[1] Y Li S Amari A Cichocki D W C Ho and S Xie ldquoUnderdetermined blind source separation based on sparse representationrdquo IEEE Transactions on Signal Processing vol 54 p 423ndash437 Feb 2006
0510 AM
Nor
mal
ized
mea
n sq
uare
err
or (N
MSE
) in
mix
ing
mat
rix e
stim
ation
(dB)
Order of the mixing matrices (PxQ)
46
P ndash No of mixturesQ ndash No of sources
Advantages of the Proposed algorithmAdvantages of the Proposed algorithm
Step 1 Convert x in the time domain to the TF domain to get XStep 2 Check the condition
Step 3 If the condition is satisfied then X(k t) is a sample atthe SSP and this sample is kept for mixing matrix estimationotherwise discard the point
Step 4 Repeat Steps 2 to 3 for all the points in the TF planeor until sufficient number of SSPs are obtained
cos
)()(
)()(
tkXItkXR
tkXItkXR T
1) Much simpler constrain the algorithm does not require ldquosingle source zonerdquo
3) The algorithm is extremely simple but effective2) Separation performance is better
0510 AM 47-gt
My Contributions ndash III IV and VMy Contributions ndash III IV and V
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
48
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Mask estimation
Mic 1
Mic P
Mixture in TF domain
Separated signals in TF domain
)( tkX P
)(1 tkX
t
t
k
k
)(1 tkY
)(1 tkY
)( tkYQ
)( tkYQ
QP
0510 AM 49
Mathematical RepresentationMathematical Representation
Q
q
L
lqpqp Pplnslhnx
1
1
0
1)()()(
)()()()()()()( 11 tkSktkSktkSktk QQqq HHHX
)(
)(
)()(
)()(
)(
)( 1
1
1111
tkS
tkS
kHkH
kHkH
tkX
tkX
QPQP
Q
P
)(
)(
)(
)(
)(
)(
)(
)(
)( 11
1
1
11
tkS
kH
kH
tkS
kH
kH
tkS
kH
kH
Q
PQ
Q
q
Pq
q
P
Time domain
Frequency domain
0510 AM 50
P ndash No of mixturesQ ndash No of sources
Single source pointsSingle source pointsInstantaneous mixing
00point at 1 Case 11211111 tkStkStk
)()()(
)()()(
111111
111111
tkSIktkI
tkSRktkR
HX
HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()(
)()()(
222222
222222
tkSIktkI
tkSRktkR
HX
HX
Single source point 2
Real scalar
RealReal
Real scalarReal scalar
Real scalar
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
0510 AM 51
Basic Principle of Single Source Points Detection
Basic Principle of Single Source Points Detection
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
j
H
C
e
cos21
21
UU
UUUUU H
and 20coscos HCH
angle pseudo called is
angleHermitian called is
H The Hermitian angle between the complex
vectors u1 and u2 will remain the same even if the vectors are multiplied by any complex scalars whereas the pseudo angle will change
0510 AM 52
-gt
k
Algorithm for Single Source Points Detection
Algorithm for Single Source Points Detection
t
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)(
)(
)(111
121
111 tkSkH
kH
11
11
j
jr
)(
)(
112
111
tkX
tkX
11
11
j
jr
)(
)(
112
111
tkX
tkX
)( 111 tkX
)( 112 tkX
)(
)(
)(112
122
112 tkSkH
kH θH2
θH1
θH2
rX
rX
)(
)(cos
11
111
tk
tk H
Hq
0510 AM 53
θH1
OR
1k
1k
1t
Clean
Estimated
Mask Estimation by k-means (KM)Mask Estimation by k-means (KM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 54
Clean
Estimated
Mask Estimation by Fuzzy c-means (FCM)Mask Estimation by Fuzzy c-means (FCM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 55
Automatic Detection of Number of SourcesAutomatic Detection of Number of Sources
0510 AM 56
Cluster validation technique
For c = 2 to cmax
Cluster the data into c clustersCalculate the cluster validation index
EndTake c corresponding to the best cluster as the number of sources
-gt
Elimination of Low Energy PointsElimination of Low Energy Points
0510 AM 57
- Blind Separation of Speech Mixtures
- Introduction
- Slide 3
- Slide 4
- Slide 5
- Approaches for BSS of Speech Signals
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Permutation Problem in Frequency Domain BSS
- Motivation
- My Contribution - I
- Algorithm for Solving the Permutation Problem
- Existing Method for Solving the Permutation Problem
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Proposed algorithm Partial separation method (Parallel configuration) Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
- Partial separation method (Parallel configuration)
- Partial separation method (Cascade configuration)
- Advantages of Partial Separation method
- Comparison with Adjacent Bands Correlation Method
- Comparison with DOA method
- My Contribution -II
- Underdetermined Blind Source Separation of Instantaneous Mixtures
- Mathematical Representation of Instantaneous Mixing Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
- Single Source Points in Time-Frequency domain
- Slide 31
- Slide 32
- Scatter Diagram of the Mixtures When Source are Perfectly Sparse
- Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
- Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
- Principle of the Proposed Algorithm for the Detection of Single Source Points
- Slide 39
- Slide 40
- Proposed Algorithm for the Detection of Single Source Points
- Elimination of Outliers
- Slide 43
- Detected Single Source Points Three mixtures
- Comparison with Classical Algorithms for Determined Case
- Comparison with Method Proposed in [1] Underdetermined case
- Advantages of the Proposed algorithm
- My Contributions ndash III IV and V
- Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
- Mathematical Representation
- Single source points
- Basic Principle of Single Source Points Detection
- Algorithm for Single Source Points Detection
- Mask Estimation by k-means (KM)
- Mask Estimation by Fuzzy c-means (FCM)
- Automatic Detection of Number of Sources
- Elimination of Low Energy Points
-
Scatter Diagram of the Mixtures when Sources are Sparse
Scatter Diagram of the Mixtures when Sources are Sparse
3h
6h
5h
1h4h
2h
0510 AM
No of sources = 6No of mixtures = 2
35
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
3h
6h
5h
1h4h
2h
0510 AM
No of sources = 6No of mixtures = 2
36
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
3h
6h
5h
1h4h
2h
0510 AM
ObjectiveEstimation of the single source points
No of sources = 6No of mixtures = 2
37
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Multi source point
38
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
Multi source point
39
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
Average of 15 pairs of speech utterances of length 10 s each
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
)( ofDirection )( ofDirection tkXItkXR )( ofDirection )( ofDirection tkXItkXR
SSPMSP
40
SSPt
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)()(
)()(
112112
111111
tkXjItkXR
tkXjItkXR
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXI
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXIMSP
)( 111 tkX
)( 112 tkX
cos
)()(
)()(
tkXItkXR
tkXItkXR T
Proposed Algorithm for the Detection of Single Source Points
Proposed Algorithm for the Detection of Single Source Points
0510 AM 41
Elimination of OutliersElimination of Outliers
SSPs detection
Clus
terin
g
Outlier elimination
0510 AM 42
0510 AM
Experimental ResultsExperimental Results
dB6747NMSE
No of mixtures =2 No of sources =6
43
Detected Single Source PointsThree mixtures
Detected Single Source PointsThree mixtures
No of mixtures =3 No of sources =60510 AM 44
Comparison with Classical Algorithms for Determined Case
Comparison with Classical Algorithms for Determined Case
No of mixtures =2No of sources =2
Average of 500 experimental results
0510 AM 45
-gt
Comparison with Method Proposed in [1] Underdetermined case
Comparison with Method Proposed in [1] Underdetermined case
[1] Y Li S Amari A Cichocki D W C Ho and S Xie ldquoUnderdetermined blind source separation based on sparse representationrdquo IEEE Transactions on Signal Processing vol 54 p 423ndash437 Feb 2006
0510 AM
Nor
mal
ized
mea
n sq
uare
err
or (N
MSE
) in
mix
ing
mat
rix e
stim
ation
(dB)
Order of the mixing matrices (PxQ)
46
P ndash No of mixturesQ ndash No of sources
Advantages of the Proposed algorithmAdvantages of the Proposed algorithm
Step 1 Convert x in the time domain to the TF domain to get XStep 2 Check the condition
Step 3 If the condition is satisfied then X(k t) is a sample atthe SSP and this sample is kept for mixing matrix estimationotherwise discard the point
Step 4 Repeat Steps 2 to 3 for all the points in the TF planeor until sufficient number of SSPs are obtained
cos
)()(
)()(
tkXItkXR
tkXItkXR T
1) Much simpler constrain the algorithm does not require ldquosingle source zonerdquo
3) The algorithm is extremely simple but effective2) Separation performance is better
0510 AM 47-gt
My Contributions ndash III IV and VMy Contributions ndash III IV and V
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
48
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Mask estimation
Mic 1
Mic P
Mixture in TF domain
Separated signals in TF domain
)( tkX P
)(1 tkX
t
t
k
k
)(1 tkY
)(1 tkY
)( tkYQ
)( tkYQ
QP
0510 AM 49
Mathematical RepresentationMathematical Representation
Q
q
L
lqpqp Pplnslhnx
1
1
0
1)()()(
)()()()()()()( 11 tkSktkSktkSktk QQqq HHHX
)(
)(
)()(
)()(
)(
)( 1
1
1111
tkS
tkS
kHkH
kHkH
tkX
tkX
QPQP
Q
P
)(
)(
)(
)(
)(
)(
)(
)(
)( 11
1
1
11
tkS
kH
kH
tkS
kH
kH
tkS
kH
kH
Q
PQ
Q
q
Pq
q
P
Time domain
Frequency domain
0510 AM 50
P ndash No of mixturesQ ndash No of sources
Single source pointsSingle source pointsInstantaneous mixing
00point at 1 Case 11211111 tkStkStk
)()()(
)()()(
111111
111111
tkSIktkI
tkSRktkR
HX
HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()(
)()()(
222222
222222
tkSIktkI
tkSRktkR
HX
HX
Single source point 2
Real scalar
RealReal
Real scalarReal scalar
Real scalar
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
0510 AM 51
Basic Principle of Single Source Points Detection
Basic Principle of Single Source Points Detection
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
j
H
C
e
cos21
21
UU
UUUUU H
and 20coscos HCH
angle pseudo called is
angleHermitian called is
H The Hermitian angle between the complex
vectors u1 and u2 will remain the same even if the vectors are multiplied by any complex scalars whereas the pseudo angle will change
0510 AM 52
-gt
k
Algorithm for Single Source Points Detection
Algorithm for Single Source Points Detection
t
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)(
)(
)(111
121
111 tkSkH
kH
11
11
j
jr
)(
)(
112
111
tkX
tkX
11
11
j
jr
)(
)(
112
111
tkX
tkX
)( 111 tkX
)( 112 tkX
)(
)(
)(112
122
112 tkSkH
kH θH2
θH1
θH2
rX
rX
)(
)(cos
11
111
tk
tk H
Hq
0510 AM 53
θH1
OR
1k
1k
1t
Clean
Estimated
Mask Estimation by k-means (KM)Mask Estimation by k-means (KM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 54
Clean
Estimated
Mask Estimation by Fuzzy c-means (FCM)Mask Estimation by Fuzzy c-means (FCM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 55
Automatic Detection of Number of SourcesAutomatic Detection of Number of Sources
0510 AM 56
Cluster validation technique
For c = 2 to cmax
Cluster the data into c clustersCalculate the cluster validation index
EndTake c corresponding to the best cluster as the number of sources
-gt
Elimination of Low Energy PointsElimination of Low Energy Points
0510 AM 57
- Blind Separation of Speech Mixtures
- Introduction
- Slide 3
- Slide 4
- Slide 5
- Approaches for BSS of Speech Signals
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Permutation Problem in Frequency Domain BSS
- Motivation
- My Contribution - I
- Algorithm for Solving the Permutation Problem
- Existing Method for Solving the Permutation Problem
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Proposed algorithm Partial separation method (Parallel configuration) Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
- Partial separation method (Parallel configuration)
- Partial separation method (Cascade configuration)
- Advantages of Partial Separation method
- Comparison with Adjacent Bands Correlation Method
- Comparison with DOA method
- My Contribution -II
- Underdetermined Blind Source Separation of Instantaneous Mixtures
- Mathematical Representation of Instantaneous Mixing Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
- Single Source Points in Time-Frequency domain
- Slide 31
- Slide 32
- Scatter Diagram of the Mixtures When Source are Perfectly Sparse
- Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
- Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
- Principle of the Proposed Algorithm for the Detection of Single Source Points
- Slide 39
- Slide 40
- Proposed Algorithm for the Detection of Single Source Points
- Elimination of Outliers
- Slide 43
- Detected Single Source Points Three mixtures
- Comparison with Classical Algorithms for Determined Case
- Comparison with Method Proposed in [1] Underdetermined case
- Advantages of the Proposed algorithm
- My Contributions ndash III IV and V
- Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
- Mathematical Representation
- Single source points
- Basic Principle of Single Source Points Detection
- Algorithm for Single Source Points Detection
- Mask Estimation by k-means (KM)
- Mask Estimation by Fuzzy c-means (FCM)
- Automatic Detection of Number of Sources
- Elimination of Low Energy Points
-
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
3h
6h
5h
1h4h
2h
0510 AM
No of sources = 6No of mixtures = 2
36
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
3h
6h
5h
1h4h
2h
0510 AM
ObjectiveEstimation of the single source points
No of sources = 6No of mixtures = 2
37
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Multi source point
38
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
Multi source point
39
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
Average of 15 pairs of speech utterances of length 10 s each
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
)( ofDirection )( ofDirection tkXItkXR )( ofDirection )( ofDirection tkXItkXR
SSPMSP
40
SSPt
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)()(
)()(
112112
111111
tkXjItkXR
tkXjItkXR
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXI
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXIMSP
)( 111 tkX
)( 112 tkX
cos
)()(
)()(
tkXItkXR
tkXItkXR T
Proposed Algorithm for the Detection of Single Source Points
Proposed Algorithm for the Detection of Single Source Points
0510 AM 41
Elimination of OutliersElimination of Outliers
SSPs detection
Clus
terin
g
Outlier elimination
0510 AM 42
0510 AM
Experimental ResultsExperimental Results
dB6747NMSE
No of mixtures =2 No of sources =6
43
Detected Single Source PointsThree mixtures
Detected Single Source PointsThree mixtures
No of mixtures =3 No of sources =60510 AM 44
Comparison with Classical Algorithms for Determined Case
Comparison with Classical Algorithms for Determined Case
No of mixtures =2No of sources =2
Average of 500 experimental results
0510 AM 45
-gt
Comparison with Method Proposed in [1] Underdetermined case
Comparison with Method Proposed in [1] Underdetermined case
[1] Y Li S Amari A Cichocki D W C Ho and S Xie ldquoUnderdetermined blind source separation based on sparse representationrdquo IEEE Transactions on Signal Processing vol 54 p 423ndash437 Feb 2006
0510 AM
Nor
mal
ized
mea
n sq
uare
err
or (N
MSE
) in
mix
ing
mat
rix e
stim
ation
(dB)
Order of the mixing matrices (PxQ)
46
P ndash No of mixturesQ ndash No of sources
Advantages of the Proposed algorithmAdvantages of the Proposed algorithm
Step 1 Convert x in the time domain to the TF domain to get XStep 2 Check the condition
Step 3 If the condition is satisfied then X(k t) is a sample atthe SSP and this sample is kept for mixing matrix estimationotherwise discard the point
Step 4 Repeat Steps 2 to 3 for all the points in the TF planeor until sufficient number of SSPs are obtained
cos
)()(
)()(
tkXItkXR
tkXItkXR T
1) Much simpler constrain the algorithm does not require ldquosingle source zonerdquo
3) The algorithm is extremely simple but effective2) Separation performance is better
0510 AM 47-gt
My Contributions ndash III IV and VMy Contributions ndash III IV and V
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
48
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Mask estimation
Mic 1
Mic P
Mixture in TF domain
Separated signals in TF domain
)( tkX P
)(1 tkX
t
t
k
k
)(1 tkY
)(1 tkY
)( tkYQ
)( tkYQ
QP
0510 AM 49
Mathematical RepresentationMathematical Representation
Q
q
L
lqpqp Pplnslhnx
1
1
0
1)()()(
)()()()()()()( 11 tkSktkSktkSktk QQqq HHHX
)(
)(
)()(
)()(
)(
)( 1
1
1111
tkS
tkS
kHkH
kHkH
tkX
tkX
QPQP
Q
P
)(
)(
)(
)(
)(
)(
)(
)(
)( 11
1
1
11
tkS
kH
kH
tkS
kH
kH
tkS
kH
kH
Q
PQ
Q
q
Pq
q
P
Time domain
Frequency domain
0510 AM 50
P ndash No of mixturesQ ndash No of sources
Single source pointsSingle source pointsInstantaneous mixing
00point at 1 Case 11211111 tkStkStk
)()()(
)()()(
111111
111111
tkSIktkI
tkSRktkR
HX
HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()(
)()()(
222222
222222
tkSIktkI
tkSRktkR
HX
HX
Single source point 2
Real scalar
RealReal
Real scalarReal scalar
Real scalar
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
0510 AM 51
Basic Principle of Single Source Points Detection
Basic Principle of Single Source Points Detection
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
j
H
C
e
cos21
21
UU
UUUUU H
and 20coscos HCH
angle pseudo called is
angleHermitian called is
H The Hermitian angle between the complex
vectors u1 and u2 will remain the same even if the vectors are multiplied by any complex scalars whereas the pseudo angle will change
0510 AM 52
-gt
k
Algorithm for Single Source Points Detection
Algorithm for Single Source Points Detection
t
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)(
)(
)(111
121
111 tkSkH
kH
11
11
j
jr
)(
)(
112
111
tkX
tkX
11
11
j
jr
)(
)(
112
111
tkX
tkX
)( 111 tkX
)( 112 tkX
)(
)(
)(112
122
112 tkSkH
kH θH2
θH1
θH2
rX
rX
)(
)(cos
11
111
tk
tk H
Hq
0510 AM 53
θH1
OR
1k
1k
1t
Clean
Estimated
Mask Estimation by k-means (KM)Mask Estimation by k-means (KM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 54
Clean
Estimated
Mask Estimation by Fuzzy c-means (FCM)Mask Estimation by Fuzzy c-means (FCM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 55
Automatic Detection of Number of SourcesAutomatic Detection of Number of Sources
0510 AM 56
Cluster validation technique
For c = 2 to cmax
Cluster the data into c clustersCalculate the cluster validation index
EndTake c corresponding to the best cluster as the number of sources
-gt
Elimination of Low Energy PointsElimination of Low Energy Points
0510 AM 57
- Blind Separation of Speech Mixtures
- Introduction
- Slide 3
- Slide 4
- Slide 5
- Approaches for BSS of Speech Signals
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Permutation Problem in Frequency Domain BSS
- Motivation
- My Contribution - I
- Algorithm for Solving the Permutation Problem
- Existing Method for Solving the Permutation Problem
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Proposed algorithm Partial separation method (Parallel configuration) Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
- Partial separation method (Parallel configuration)
- Partial separation method (Cascade configuration)
- Advantages of Partial Separation method
- Comparison with Adjacent Bands Correlation Method
- Comparison with DOA method
- My Contribution -II
- Underdetermined Blind Source Separation of Instantaneous Mixtures
- Mathematical Representation of Instantaneous Mixing Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
- Single Source Points in Time-Frequency domain
- Slide 31
- Slide 32
- Scatter Diagram of the Mixtures When Source are Perfectly Sparse
- Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
- Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
- Principle of the Proposed Algorithm for the Detection of Single Source Points
- Slide 39
- Slide 40
- Proposed Algorithm for the Detection of Single Source Points
- Elimination of Outliers
- Slide 43
- Detected Single Source Points Three mixtures
- Comparison with Classical Algorithms for Determined Case
- Comparison with Method Proposed in [1] Underdetermined case
- Advantages of the Proposed algorithm
- My Contributions ndash III IV and V
- Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
- Mathematical Representation
- Single source points
- Basic Principle of Single Source Points Detection
- Algorithm for Single Source Points Detection
- Mask Estimation by k-means (KM)
- Mask Estimation by Fuzzy c-means (FCM)
- Automatic Detection of Number of Sources
- Elimination of Low Energy Points
-
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
3h
6h
5h
1h4h
2h
0510 AM
ObjectiveEstimation of the single source points
No of sources = 6No of mixtures = 2
37
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Multi source point
38
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
Multi source point
39
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
Average of 15 pairs of speech utterances of length 10 s each
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
)( ofDirection )( ofDirection tkXItkXR )( ofDirection )( ofDirection tkXItkXR
SSPMSP
40
SSPt
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)()(
)()(
112112
111111
tkXjItkXR
tkXjItkXR
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXI
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXIMSP
)( 111 tkX
)( 112 tkX
cos
)()(
)()(
tkXItkXR
tkXItkXR T
Proposed Algorithm for the Detection of Single Source Points
Proposed Algorithm for the Detection of Single Source Points
0510 AM 41
Elimination of OutliersElimination of Outliers
SSPs detection
Clus
terin
g
Outlier elimination
0510 AM 42
0510 AM
Experimental ResultsExperimental Results
dB6747NMSE
No of mixtures =2 No of sources =6
43
Detected Single Source PointsThree mixtures
Detected Single Source PointsThree mixtures
No of mixtures =3 No of sources =60510 AM 44
Comparison with Classical Algorithms for Determined Case
Comparison with Classical Algorithms for Determined Case
No of mixtures =2No of sources =2
Average of 500 experimental results
0510 AM 45
-gt
Comparison with Method Proposed in [1] Underdetermined case
Comparison with Method Proposed in [1] Underdetermined case
[1] Y Li S Amari A Cichocki D W C Ho and S Xie ldquoUnderdetermined blind source separation based on sparse representationrdquo IEEE Transactions on Signal Processing vol 54 p 423ndash437 Feb 2006
0510 AM
Nor
mal
ized
mea
n sq
uare
err
or (N
MSE
) in
mix
ing
mat
rix e
stim
ation
(dB)
Order of the mixing matrices (PxQ)
46
P ndash No of mixturesQ ndash No of sources
Advantages of the Proposed algorithmAdvantages of the Proposed algorithm
Step 1 Convert x in the time domain to the TF domain to get XStep 2 Check the condition
Step 3 If the condition is satisfied then X(k t) is a sample atthe SSP and this sample is kept for mixing matrix estimationotherwise discard the point
Step 4 Repeat Steps 2 to 3 for all the points in the TF planeor until sufficient number of SSPs are obtained
cos
)()(
)()(
tkXItkXR
tkXItkXR T
1) Much simpler constrain the algorithm does not require ldquosingle source zonerdquo
3) The algorithm is extremely simple but effective2) Separation performance is better
0510 AM 47-gt
My Contributions ndash III IV and VMy Contributions ndash III IV and V
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
48
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Mask estimation
Mic 1
Mic P
Mixture in TF domain
Separated signals in TF domain
)( tkX P
)(1 tkX
t
t
k
k
)(1 tkY
)(1 tkY
)( tkYQ
)( tkYQ
QP
0510 AM 49
Mathematical RepresentationMathematical Representation
Q
q
L
lqpqp Pplnslhnx
1
1
0
1)()()(
)()()()()()()( 11 tkSktkSktkSktk QQqq HHHX
)(
)(
)()(
)()(
)(
)( 1
1
1111
tkS
tkS
kHkH
kHkH
tkX
tkX
QPQP
Q
P
)(
)(
)(
)(
)(
)(
)(
)(
)( 11
1
1
11
tkS
kH
kH
tkS
kH
kH
tkS
kH
kH
Q
PQ
Q
q
Pq
q
P
Time domain
Frequency domain
0510 AM 50
P ndash No of mixturesQ ndash No of sources
Single source pointsSingle source pointsInstantaneous mixing
00point at 1 Case 11211111 tkStkStk
)()()(
)()()(
111111
111111
tkSIktkI
tkSRktkR
HX
HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()(
)()()(
222222
222222
tkSIktkI
tkSRktkR
HX
HX
Single source point 2
Real scalar
RealReal
Real scalarReal scalar
Real scalar
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
0510 AM 51
Basic Principle of Single Source Points Detection
Basic Principle of Single Source Points Detection
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
j
H
C
e
cos21
21
UU
UUUUU H
and 20coscos HCH
angle pseudo called is
angleHermitian called is
H The Hermitian angle between the complex
vectors u1 and u2 will remain the same even if the vectors are multiplied by any complex scalars whereas the pseudo angle will change
0510 AM 52
-gt
k
Algorithm for Single Source Points Detection
Algorithm for Single Source Points Detection
t
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)(
)(
)(111
121
111 tkSkH
kH
11
11
j
jr
)(
)(
112
111
tkX
tkX
11
11
j
jr
)(
)(
112
111
tkX
tkX
)( 111 tkX
)( 112 tkX
)(
)(
)(112
122
112 tkSkH
kH θH2
θH1
θH2
rX
rX
)(
)(cos
11
111
tk
tk H
Hq
0510 AM 53
θH1
OR
1k
1k
1t
Clean
Estimated
Mask Estimation by k-means (KM)Mask Estimation by k-means (KM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 54
Clean
Estimated
Mask Estimation by Fuzzy c-means (FCM)Mask Estimation by Fuzzy c-means (FCM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 55
Automatic Detection of Number of SourcesAutomatic Detection of Number of Sources
0510 AM 56
Cluster validation technique
For c = 2 to cmax
Cluster the data into c clustersCalculate the cluster validation index
EndTake c corresponding to the best cluster as the number of sources
-gt
Elimination of Low Energy PointsElimination of Low Energy Points
0510 AM 57
- Blind Separation of Speech Mixtures
- Introduction
- Slide 3
- Slide 4
- Slide 5
- Approaches for BSS of Speech Signals
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Permutation Problem in Frequency Domain BSS
- Motivation
- My Contribution - I
- Algorithm for Solving the Permutation Problem
- Existing Method for Solving the Permutation Problem
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Proposed algorithm Partial separation method (Parallel configuration) Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
- Partial separation method (Parallel configuration)
- Partial separation method (Cascade configuration)
- Advantages of Partial Separation method
- Comparison with Adjacent Bands Correlation Method
- Comparison with DOA method
- My Contribution -II
- Underdetermined Blind Source Separation of Instantaneous Mixtures
- Mathematical Representation of Instantaneous Mixing Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
- Single Source Points in Time-Frequency domain
- Slide 31
- Slide 32
- Scatter Diagram of the Mixtures When Source are Perfectly Sparse
- Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
- Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
- Principle of the Proposed Algorithm for the Detection of Single Source Points
- Slide 39
- Slide 40
- Proposed Algorithm for the Detection of Single Source Points
- Elimination of Outliers
- Slide 43
- Detected Single Source Points Three mixtures
- Comparison with Classical Algorithms for Determined Case
- Comparison with Method Proposed in [1] Underdetermined case
- Advantages of the Proposed algorithm
- My Contributions ndash III IV and V
- Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
- Mathematical Representation
- Single source points
- Basic Principle of Single Source Points Detection
- Algorithm for Single Source Points Detection
- Mask Estimation by k-means (KM)
- Mask Estimation by Fuzzy c-means (FCM)
- Automatic Detection of Number of Sources
- Elimination of Low Energy Points
-
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Multi source point
38
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
Multi source point
39
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
Average of 15 pairs of speech utterances of length 10 s each
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
)( ofDirection )( ofDirection tkXItkXR )( ofDirection )( ofDirection tkXItkXR
SSPMSP
40
SSPt
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)()(
)()(
112112
111111
tkXjItkXR
tkXjItkXR
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXI
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXIMSP
)( 111 tkX
)( 112 tkX
cos
)()(
)()(
tkXItkXR
tkXItkXR T
Proposed Algorithm for the Detection of Single Source Points
Proposed Algorithm for the Detection of Single Source Points
0510 AM 41
Elimination of OutliersElimination of Outliers
SSPs detection
Clus
terin
g
Outlier elimination
0510 AM 42
0510 AM
Experimental ResultsExperimental Results
dB6747NMSE
No of mixtures =2 No of sources =6
43
Detected Single Source PointsThree mixtures
Detected Single Source PointsThree mixtures
No of mixtures =3 No of sources =60510 AM 44
Comparison with Classical Algorithms for Determined Case
Comparison with Classical Algorithms for Determined Case
No of mixtures =2No of sources =2
Average of 500 experimental results
0510 AM 45
-gt
Comparison with Method Proposed in [1] Underdetermined case
Comparison with Method Proposed in [1] Underdetermined case
[1] Y Li S Amari A Cichocki D W C Ho and S Xie ldquoUnderdetermined blind source separation based on sparse representationrdquo IEEE Transactions on Signal Processing vol 54 p 423ndash437 Feb 2006
0510 AM
Nor
mal
ized
mea
n sq
uare
err
or (N
MSE
) in
mix
ing
mat
rix e
stim
ation
(dB)
Order of the mixing matrices (PxQ)
46
P ndash No of mixturesQ ndash No of sources
Advantages of the Proposed algorithmAdvantages of the Proposed algorithm
Step 1 Convert x in the time domain to the TF domain to get XStep 2 Check the condition
Step 3 If the condition is satisfied then X(k t) is a sample atthe SSP and this sample is kept for mixing matrix estimationotherwise discard the point
Step 4 Repeat Steps 2 to 3 for all the points in the TF planeor until sufficient number of SSPs are obtained
cos
)()(
)()(
tkXItkXR
tkXItkXR T
1) Much simpler constrain the algorithm does not require ldquosingle source zonerdquo
3) The algorithm is extremely simple but effective2) Separation performance is better
0510 AM 47-gt
My Contributions ndash III IV and VMy Contributions ndash III IV and V
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
48
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Mask estimation
Mic 1
Mic P
Mixture in TF domain
Separated signals in TF domain
)( tkX P
)(1 tkX
t
t
k
k
)(1 tkY
)(1 tkY
)( tkYQ
)( tkYQ
QP
0510 AM 49
Mathematical RepresentationMathematical Representation
Q
q
L
lqpqp Pplnslhnx
1
1
0
1)()()(
)()()()()()()( 11 tkSktkSktkSktk QQqq HHHX
)(
)(
)()(
)()(
)(
)( 1
1
1111
tkS
tkS
kHkH
kHkH
tkX
tkX
QPQP
Q
P
)(
)(
)(
)(
)(
)(
)(
)(
)( 11
1
1
11
tkS
kH
kH
tkS
kH
kH
tkS
kH
kH
Q
PQ
Q
q
Pq
q
P
Time domain
Frequency domain
0510 AM 50
P ndash No of mixturesQ ndash No of sources
Single source pointsSingle source pointsInstantaneous mixing
00point at 1 Case 11211111 tkStkStk
)()()(
)()()(
111111
111111
tkSIktkI
tkSRktkR
HX
HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()(
)()()(
222222
222222
tkSIktkI
tkSRktkR
HX
HX
Single source point 2
Real scalar
RealReal
Real scalarReal scalar
Real scalar
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
0510 AM 51
Basic Principle of Single Source Points Detection
Basic Principle of Single Source Points Detection
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
j
H
C
e
cos21
21
UU
UUUUU H
and 20coscos HCH
angle pseudo called is
angleHermitian called is
H The Hermitian angle between the complex
vectors u1 and u2 will remain the same even if the vectors are multiplied by any complex scalars whereas the pseudo angle will change
0510 AM 52
-gt
k
Algorithm for Single Source Points Detection
Algorithm for Single Source Points Detection
t
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)(
)(
)(111
121
111 tkSkH
kH
11
11
j
jr
)(
)(
112
111
tkX
tkX
11
11
j
jr
)(
)(
112
111
tkX
tkX
)( 111 tkX
)( 112 tkX
)(
)(
)(112
122
112 tkSkH
kH θH2
θH1
θH2
rX
rX
)(
)(cos
11
111
tk
tk H
Hq
0510 AM 53
θH1
OR
1k
1k
1t
Clean
Estimated
Mask Estimation by k-means (KM)Mask Estimation by k-means (KM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 54
Clean
Estimated
Mask Estimation by Fuzzy c-means (FCM)Mask Estimation by Fuzzy c-means (FCM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 55
Automatic Detection of Number of SourcesAutomatic Detection of Number of Sources
0510 AM 56
Cluster validation technique
For c = 2 to cmax
Cluster the data into c clustersCalculate the cluster validation index
EndTake c corresponding to the best cluster as the number of sources
-gt
Elimination of Low Energy PointsElimination of Low Energy Points
0510 AM 57
- Blind Separation of Speech Mixtures
- Introduction
- Slide 3
- Slide 4
- Slide 5
- Approaches for BSS of Speech Signals
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Permutation Problem in Frequency Domain BSS
- Motivation
- My Contribution - I
- Algorithm for Solving the Permutation Problem
- Existing Method for Solving the Permutation Problem
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Proposed algorithm Partial separation method (Parallel configuration) Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
- Partial separation method (Parallel configuration)
- Partial separation method (Cascade configuration)
- Advantages of Partial Separation method
- Comparison with Adjacent Bands Correlation Method
- Comparison with DOA method
- My Contribution -II
- Underdetermined Blind Source Separation of Instantaneous Mixtures
- Mathematical Representation of Instantaneous Mixing Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
- Single Source Points in Time-Frequency domain
- Slide 31
- Slide 32
- Scatter Diagram of the Mixtures When Source are Perfectly Sparse
- Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
- Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
- Principle of the Proposed Algorithm for the Detection of Single Source Points
- Slide 39
- Slide 40
- Proposed Algorithm for the Detection of Single Source Points
- Elimination of Outliers
- Slide 43
- Detected Single Source Points Three mixtures
- Comparison with Classical Algorithms for Determined Case
- Comparison with Method Proposed in [1] Underdetermined case
- Advantages of the Proposed algorithm
- My Contributions ndash III IV and V
- Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
- Mathematical Representation
- Single source points
- Basic Principle of Single Source Points Detection
- Algorithm for Single Source Points Detection
- Mask Estimation by k-means (KM)
- Mask Estimation by Fuzzy c-means (FCM)
- Automatic Detection of Number of Sources
- Elimination of Low Energy Points
-
00point At 1 Case 11211111 tkStkStk
)()(
)()(
111111
111111
tkSItkI
tkSRtkR
hX
hX
Single source point 1
00point At 2 Case 22222122 tkStkStk
)()(
)()(
222222
222222
tkSItkI
tkSRtkR
hX
hX
Single source point 2Scalar
ScalarScalar
Scalar
00point At 3 Case 33233133 tkStkStk
)()()(
)()()(
3322331133
3322331133
tkSItkSItkI
tkSRtkSRtkR
hhX
hhX
)()()( 3322331133 tkStkStk hhX
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
Multi source point
39
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
Average of 15 pairs of speech utterances of length 10 s each
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
)( ofDirection )( ofDirection tkXItkXR )( ofDirection )( ofDirection tkXItkXR
SSPMSP
40
SSPt
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)()(
)()(
112112
111111
tkXjItkXR
tkXjItkXR
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXI
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXIMSP
)( 111 tkX
)( 112 tkX
cos
)()(
)()(
tkXItkXR
tkXItkXR T
Proposed Algorithm for the Detection of Single Source Points
Proposed Algorithm for the Detection of Single Source Points
0510 AM 41
Elimination of OutliersElimination of Outliers
SSPs detection
Clus
terin
g
Outlier elimination
0510 AM 42
0510 AM
Experimental ResultsExperimental Results
dB6747NMSE
No of mixtures =2 No of sources =6
43
Detected Single Source PointsThree mixtures
Detected Single Source PointsThree mixtures
No of mixtures =3 No of sources =60510 AM 44
Comparison with Classical Algorithms for Determined Case
Comparison with Classical Algorithms for Determined Case
No of mixtures =2No of sources =2
Average of 500 experimental results
0510 AM 45
-gt
Comparison with Method Proposed in [1] Underdetermined case
Comparison with Method Proposed in [1] Underdetermined case
[1] Y Li S Amari A Cichocki D W C Ho and S Xie ldquoUnderdetermined blind source separation based on sparse representationrdquo IEEE Transactions on Signal Processing vol 54 p 423ndash437 Feb 2006
0510 AM
Nor
mal
ized
mea
n sq
uare
err
or (N
MSE
) in
mix
ing
mat
rix e
stim
ation
(dB)
Order of the mixing matrices (PxQ)
46
P ndash No of mixturesQ ndash No of sources
Advantages of the Proposed algorithmAdvantages of the Proposed algorithm
Step 1 Convert x in the time domain to the TF domain to get XStep 2 Check the condition
Step 3 If the condition is satisfied then X(k t) is a sample atthe SSP and this sample is kept for mixing matrix estimationotherwise discard the point
Step 4 Repeat Steps 2 to 3 for all the points in the TF planeor until sufficient number of SSPs are obtained
cos
)()(
)()(
tkXItkXR
tkXItkXR T
1) Much simpler constrain the algorithm does not require ldquosingle source zonerdquo
3) The algorithm is extremely simple but effective2) Separation performance is better
0510 AM 47-gt
My Contributions ndash III IV and VMy Contributions ndash III IV and V
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
48
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Mask estimation
Mic 1
Mic P
Mixture in TF domain
Separated signals in TF domain
)( tkX P
)(1 tkX
t
t
k
k
)(1 tkY
)(1 tkY
)( tkYQ
)( tkYQ
QP
0510 AM 49
Mathematical RepresentationMathematical Representation
Q
q
L
lqpqp Pplnslhnx
1
1
0
1)()()(
)()()()()()()( 11 tkSktkSktkSktk QQqq HHHX
)(
)(
)()(
)()(
)(
)( 1
1
1111
tkS
tkS
kHkH
kHkH
tkX
tkX
QPQP
Q
P
)(
)(
)(
)(
)(
)(
)(
)(
)( 11
1
1
11
tkS
kH
kH
tkS
kH
kH
tkS
kH
kH
Q
PQ
Q
q
Pq
q
P
Time domain
Frequency domain
0510 AM 50
P ndash No of mixturesQ ndash No of sources
Single source pointsSingle source pointsInstantaneous mixing
00point at 1 Case 11211111 tkStkStk
)()()(
)()()(
111111
111111
tkSIktkI
tkSRktkR
HX
HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()(
)()()(
222222
222222
tkSIktkI
tkSRktkR
HX
HX
Single source point 2
Real scalar
RealReal
Real scalarReal scalar
Real scalar
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
0510 AM 51
Basic Principle of Single Source Points Detection
Basic Principle of Single Source Points Detection
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
j
H
C
e
cos21
21
UU
UUUUU H
and 20coscos HCH
angle pseudo called is
angleHermitian called is
H The Hermitian angle between the complex
vectors u1 and u2 will remain the same even if the vectors are multiplied by any complex scalars whereas the pseudo angle will change
0510 AM 52
-gt
k
Algorithm for Single Source Points Detection
Algorithm for Single Source Points Detection
t
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)(
)(
)(111
121
111 tkSkH
kH
11
11
j
jr
)(
)(
112
111
tkX
tkX
11
11
j
jr
)(
)(
112
111
tkX
tkX
)( 111 tkX
)( 112 tkX
)(
)(
)(112
122
112 tkSkH
kH θH2
θH1
θH2
rX
rX
)(
)(cos
11
111
tk
tk H
Hq
0510 AM 53
θH1
OR
1k
1k
1t
Clean
Estimated
Mask Estimation by k-means (KM)Mask Estimation by k-means (KM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 54
Clean
Estimated
Mask Estimation by Fuzzy c-means (FCM)Mask Estimation by Fuzzy c-means (FCM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 55
Automatic Detection of Number of SourcesAutomatic Detection of Number of Sources
0510 AM 56
Cluster validation technique
For c = 2 to cmax
Cluster the data into c clustersCalculate the cluster validation index
EndTake c corresponding to the best cluster as the number of sources
-gt
Elimination of Low Energy PointsElimination of Low Energy Points
0510 AM 57
- Blind Separation of Speech Mixtures
- Introduction
- Slide 3
- Slide 4
- Slide 5
- Approaches for BSS of Speech Signals
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Permutation Problem in Frequency Domain BSS
- Motivation
- My Contribution - I
- Algorithm for Solving the Permutation Problem
- Existing Method for Solving the Permutation Problem
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Proposed algorithm Partial separation method (Parallel configuration) Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
- Partial separation method (Parallel configuration)
- Partial separation method (Cascade configuration)
- Advantages of Partial Separation method
- Comparison with Adjacent Bands Correlation Method
- Comparison with DOA method
- My Contribution -II
- Underdetermined Blind Source Separation of Instantaneous Mixtures
- Mathematical Representation of Instantaneous Mixing Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
- Single Source Points in Time-Frequency domain
- Slide 31
- Slide 32
- Scatter Diagram of the Mixtures When Source are Perfectly Sparse
- Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
- Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
- Principle of the Proposed Algorithm for the Detection of Single Source Points
- Slide 39
- Slide 40
- Proposed Algorithm for the Detection of Single Source Points
- Elimination of Outliers
- Slide 43
- Detected Single Source Points Three mixtures
- Comparison with Classical Algorithms for Determined Case
- Comparison with Method Proposed in [1] Underdetermined case
- Advantages of the Proposed algorithm
- My Contributions ndash III IV and V
- Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
- Mathematical Representation
- Single source points
- Basic Principle of Single Source Points Detection
- Algorithm for Single Source Points Detection
- Mask Estimation by k-means (KM)
- Mask Estimation by Fuzzy c-means (FCM)
- Automatic Detection of Number of Sources
- Elimination of Low Energy Points
-
)(
)(
)(
)( ifonly and if
)( ofDirection )( ofDirection
332
332
331
331
3333
tkSI
tkSR
tkSI
tkSR
tkXItkXR
Average of 15 pairs of speech utterances of length 10 s each
0510 AM
Principle of the Proposed Algorithm for the Detection of Single Source Points
Principle of the Proposed Algorithm for the Detection of Single Source Points
)( ofDirection )( ofDirection tkXItkXR )( ofDirection )( ofDirection tkXItkXR
SSPMSP
40
SSPt
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)()(
)()(
112112
111111
tkXjItkXR
tkXjItkXR
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXI
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXIMSP
)( 111 tkX
)( 112 tkX
cos
)()(
)()(
tkXItkXR
tkXItkXR T
Proposed Algorithm for the Detection of Single Source Points
Proposed Algorithm for the Detection of Single Source Points
0510 AM 41
Elimination of OutliersElimination of Outliers
SSPs detection
Clus
terin
g
Outlier elimination
0510 AM 42
0510 AM
Experimental ResultsExperimental Results
dB6747NMSE
No of mixtures =2 No of sources =6
43
Detected Single Source PointsThree mixtures
Detected Single Source PointsThree mixtures
No of mixtures =3 No of sources =60510 AM 44
Comparison with Classical Algorithms for Determined Case
Comparison with Classical Algorithms for Determined Case
No of mixtures =2No of sources =2
Average of 500 experimental results
0510 AM 45
-gt
Comparison with Method Proposed in [1] Underdetermined case
Comparison with Method Proposed in [1] Underdetermined case
[1] Y Li S Amari A Cichocki D W C Ho and S Xie ldquoUnderdetermined blind source separation based on sparse representationrdquo IEEE Transactions on Signal Processing vol 54 p 423ndash437 Feb 2006
0510 AM
Nor
mal
ized
mea
n sq
uare
err
or (N
MSE
) in
mix
ing
mat
rix e
stim
ation
(dB)
Order of the mixing matrices (PxQ)
46
P ndash No of mixturesQ ndash No of sources
Advantages of the Proposed algorithmAdvantages of the Proposed algorithm
Step 1 Convert x in the time domain to the TF domain to get XStep 2 Check the condition
Step 3 If the condition is satisfied then X(k t) is a sample atthe SSP and this sample is kept for mixing matrix estimationotherwise discard the point
Step 4 Repeat Steps 2 to 3 for all the points in the TF planeor until sufficient number of SSPs are obtained
cos
)()(
)()(
tkXItkXR
tkXItkXR T
1) Much simpler constrain the algorithm does not require ldquosingle source zonerdquo
3) The algorithm is extremely simple but effective2) Separation performance is better
0510 AM 47-gt
My Contributions ndash III IV and VMy Contributions ndash III IV and V
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
48
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Mask estimation
Mic 1
Mic P
Mixture in TF domain
Separated signals in TF domain
)( tkX P
)(1 tkX
t
t
k
k
)(1 tkY
)(1 tkY
)( tkYQ
)( tkYQ
QP
0510 AM 49
Mathematical RepresentationMathematical Representation
Q
q
L
lqpqp Pplnslhnx
1
1
0
1)()()(
)()()()()()()( 11 tkSktkSktkSktk QQqq HHHX
)(
)(
)()(
)()(
)(
)( 1
1
1111
tkS
tkS
kHkH
kHkH
tkX
tkX
QPQP
Q
P
)(
)(
)(
)(
)(
)(
)(
)(
)( 11
1
1
11
tkS
kH
kH
tkS
kH
kH
tkS
kH
kH
Q
PQ
Q
q
Pq
q
P
Time domain
Frequency domain
0510 AM 50
P ndash No of mixturesQ ndash No of sources
Single source pointsSingle source pointsInstantaneous mixing
00point at 1 Case 11211111 tkStkStk
)()()(
)()()(
111111
111111
tkSIktkI
tkSRktkR
HX
HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()(
)()()(
222222
222222
tkSIktkI
tkSRktkR
HX
HX
Single source point 2
Real scalar
RealReal
Real scalarReal scalar
Real scalar
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
0510 AM 51
Basic Principle of Single Source Points Detection
Basic Principle of Single Source Points Detection
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
j
H
C
e
cos21
21
UU
UUUUU H
and 20coscos HCH
angle pseudo called is
angleHermitian called is
H The Hermitian angle between the complex
vectors u1 and u2 will remain the same even if the vectors are multiplied by any complex scalars whereas the pseudo angle will change
0510 AM 52
-gt
k
Algorithm for Single Source Points Detection
Algorithm for Single Source Points Detection
t
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)(
)(
)(111
121
111 tkSkH
kH
11
11
j
jr
)(
)(
112
111
tkX
tkX
11
11
j
jr
)(
)(
112
111
tkX
tkX
)( 111 tkX
)( 112 tkX
)(
)(
)(112
122
112 tkSkH
kH θH2
θH1
θH2
rX
rX
)(
)(cos
11
111
tk
tk H
Hq
0510 AM 53
θH1
OR
1k
1k
1t
Clean
Estimated
Mask Estimation by k-means (KM)Mask Estimation by k-means (KM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 54
Clean
Estimated
Mask Estimation by Fuzzy c-means (FCM)Mask Estimation by Fuzzy c-means (FCM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 55
Automatic Detection of Number of SourcesAutomatic Detection of Number of Sources
0510 AM 56
Cluster validation technique
For c = 2 to cmax
Cluster the data into c clustersCalculate the cluster validation index
EndTake c corresponding to the best cluster as the number of sources
-gt
Elimination of Low Energy PointsElimination of Low Energy Points
0510 AM 57
- Blind Separation of Speech Mixtures
- Introduction
- Slide 3
- Slide 4
- Slide 5
- Approaches for BSS of Speech Signals
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Permutation Problem in Frequency Domain BSS
- Motivation
- My Contribution - I
- Algorithm for Solving the Permutation Problem
- Existing Method for Solving the Permutation Problem
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Proposed algorithm Partial separation method (Parallel configuration) Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
- Partial separation method (Parallel configuration)
- Partial separation method (Cascade configuration)
- Advantages of Partial Separation method
- Comparison with Adjacent Bands Correlation Method
- Comparison with DOA method
- My Contribution -II
- Underdetermined Blind Source Separation of Instantaneous Mixtures
- Mathematical Representation of Instantaneous Mixing Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
- Single Source Points in Time-Frequency domain
- Slide 31
- Slide 32
- Scatter Diagram of the Mixtures When Source are Perfectly Sparse
- Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
- Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
- Principle of the Proposed Algorithm for the Detection of Single Source Points
- Slide 39
- Slide 40
- Proposed Algorithm for the Detection of Single Source Points
- Elimination of Outliers
- Slide 43
- Detected Single Source Points Three mixtures
- Comparison with Classical Algorithms for Determined Case
- Comparison with Method Proposed in [1] Underdetermined case
- Advantages of the Proposed algorithm
- My Contributions ndash III IV and V
- Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
- Mathematical Representation
- Single source points
- Basic Principle of Single Source Points Detection
- Algorithm for Single Source Points Detection
- Mask Estimation by k-means (KM)
- Mask Estimation by Fuzzy c-means (FCM)
- Automatic Detection of Number of Sources
- Elimination of Low Energy Points
-
SSPt
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)()(
)()(
112112
111111
tkXjItkXR
tkXjItkXR
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXI
)(
)(
112
111
tkXR
tkXR
)(
)(
112
111
tkXI
tkXIMSP
)( 111 tkX
)( 112 tkX
cos
)()(
)()(
tkXItkXR
tkXItkXR T
Proposed Algorithm for the Detection of Single Source Points
Proposed Algorithm for the Detection of Single Source Points
0510 AM 41
Elimination of OutliersElimination of Outliers
SSPs detection
Clus
terin
g
Outlier elimination
0510 AM 42
0510 AM
Experimental ResultsExperimental Results
dB6747NMSE
No of mixtures =2 No of sources =6
43
Detected Single Source PointsThree mixtures
Detected Single Source PointsThree mixtures
No of mixtures =3 No of sources =60510 AM 44
Comparison with Classical Algorithms for Determined Case
Comparison with Classical Algorithms for Determined Case
No of mixtures =2No of sources =2
Average of 500 experimental results
0510 AM 45
-gt
Comparison with Method Proposed in [1] Underdetermined case
Comparison with Method Proposed in [1] Underdetermined case
[1] Y Li S Amari A Cichocki D W C Ho and S Xie ldquoUnderdetermined blind source separation based on sparse representationrdquo IEEE Transactions on Signal Processing vol 54 p 423ndash437 Feb 2006
0510 AM
Nor
mal
ized
mea
n sq
uare
err
or (N
MSE
) in
mix
ing
mat
rix e
stim
ation
(dB)
Order of the mixing matrices (PxQ)
46
P ndash No of mixturesQ ndash No of sources
Advantages of the Proposed algorithmAdvantages of the Proposed algorithm
Step 1 Convert x in the time domain to the TF domain to get XStep 2 Check the condition
Step 3 If the condition is satisfied then X(k t) is a sample atthe SSP and this sample is kept for mixing matrix estimationotherwise discard the point
Step 4 Repeat Steps 2 to 3 for all the points in the TF planeor until sufficient number of SSPs are obtained
cos
)()(
)()(
tkXItkXR
tkXItkXR T
1) Much simpler constrain the algorithm does not require ldquosingle source zonerdquo
3) The algorithm is extremely simple but effective2) Separation performance is better
0510 AM 47-gt
My Contributions ndash III IV and VMy Contributions ndash III IV and V
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
48
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Mask estimation
Mic 1
Mic P
Mixture in TF domain
Separated signals in TF domain
)( tkX P
)(1 tkX
t
t
k
k
)(1 tkY
)(1 tkY
)( tkYQ
)( tkYQ
QP
0510 AM 49
Mathematical RepresentationMathematical Representation
Q
q
L
lqpqp Pplnslhnx
1
1
0
1)()()(
)()()()()()()( 11 tkSktkSktkSktk QQqq HHHX
)(
)(
)()(
)()(
)(
)( 1
1
1111
tkS
tkS
kHkH
kHkH
tkX
tkX
QPQP
Q
P
)(
)(
)(
)(
)(
)(
)(
)(
)( 11
1
1
11
tkS
kH
kH
tkS
kH
kH
tkS
kH
kH
Q
PQ
Q
q
Pq
q
P
Time domain
Frequency domain
0510 AM 50
P ndash No of mixturesQ ndash No of sources
Single source pointsSingle source pointsInstantaneous mixing
00point at 1 Case 11211111 tkStkStk
)()()(
)()()(
111111
111111
tkSIktkI
tkSRktkR
HX
HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()(
)()()(
222222
222222
tkSIktkI
tkSRktkR
HX
HX
Single source point 2
Real scalar
RealReal
Real scalarReal scalar
Real scalar
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
0510 AM 51
Basic Principle of Single Source Points Detection
Basic Principle of Single Source Points Detection
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
j
H
C
e
cos21
21
UU
UUUUU H
and 20coscos HCH
angle pseudo called is
angleHermitian called is
H The Hermitian angle between the complex
vectors u1 and u2 will remain the same even if the vectors are multiplied by any complex scalars whereas the pseudo angle will change
0510 AM 52
-gt
k
Algorithm for Single Source Points Detection
Algorithm for Single Source Points Detection
t
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)(
)(
)(111
121
111 tkSkH
kH
11
11
j
jr
)(
)(
112
111
tkX
tkX
11
11
j
jr
)(
)(
112
111
tkX
tkX
)( 111 tkX
)( 112 tkX
)(
)(
)(112
122
112 tkSkH
kH θH2
θH1
θH2
rX
rX
)(
)(cos
11
111
tk
tk H
Hq
0510 AM 53
θH1
OR
1k
1k
1t
Clean
Estimated
Mask Estimation by k-means (KM)Mask Estimation by k-means (KM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 54
Clean
Estimated
Mask Estimation by Fuzzy c-means (FCM)Mask Estimation by Fuzzy c-means (FCM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 55
Automatic Detection of Number of SourcesAutomatic Detection of Number of Sources
0510 AM 56
Cluster validation technique
For c = 2 to cmax
Cluster the data into c clustersCalculate the cluster validation index
EndTake c corresponding to the best cluster as the number of sources
-gt
Elimination of Low Energy PointsElimination of Low Energy Points
0510 AM 57
- Blind Separation of Speech Mixtures
- Introduction
- Slide 3
- Slide 4
- Slide 5
- Approaches for BSS of Speech Signals
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Permutation Problem in Frequency Domain BSS
- Motivation
- My Contribution - I
- Algorithm for Solving the Permutation Problem
- Existing Method for Solving the Permutation Problem
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Proposed algorithm Partial separation method (Parallel configuration) Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
- Partial separation method (Parallel configuration)
- Partial separation method (Cascade configuration)
- Advantages of Partial Separation method
- Comparison with Adjacent Bands Correlation Method
- Comparison with DOA method
- My Contribution -II
- Underdetermined Blind Source Separation of Instantaneous Mixtures
- Mathematical Representation of Instantaneous Mixing Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
- Single Source Points in Time-Frequency domain
- Slide 31
- Slide 32
- Scatter Diagram of the Mixtures When Source are Perfectly Sparse
- Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
- Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
- Principle of the Proposed Algorithm for the Detection of Single Source Points
- Slide 39
- Slide 40
- Proposed Algorithm for the Detection of Single Source Points
- Elimination of Outliers
- Slide 43
- Detected Single Source Points Three mixtures
- Comparison with Classical Algorithms for Determined Case
- Comparison with Method Proposed in [1] Underdetermined case
- Advantages of the Proposed algorithm
- My Contributions ndash III IV and V
- Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
- Mathematical Representation
- Single source points
- Basic Principle of Single Source Points Detection
- Algorithm for Single Source Points Detection
- Mask Estimation by k-means (KM)
- Mask Estimation by Fuzzy c-means (FCM)
- Automatic Detection of Number of Sources
- Elimination of Low Energy Points
-
Elimination of OutliersElimination of Outliers
SSPs detection
Clus
terin
g
Outlier elimination
0510 AM 42
0510 AM
Experimental ResultsExperimental Results
dB6747NMSE
No of mixtures =2 No of sources =6
43
Detected Single Source PointsThree mixtures
Detected Single Source PointsThree mixtures
No of mixtures =3 No of sources =60510 AM 44
Comparison with Classical Algorithms for Determined Case
Comparison with Classical Algorithms for Determined Case
No of mixtures =2No of sources =2
Average of 500 experimental results
0510 AM 45
-gt
Comparison with Method Proposed in [1] Underdetermined case
Comparison with Method Proposed in [1] Underdetermined case
[1] Y Li S Amari A Cichocki D W C Ho and S Xie ldquoUnderdetermined blind source separation based on sparse representationrdquo IEEE Transactions on Signal Processing vol 54 p 423ndash437 Feb 2006
0510 AM
Nor
mal
ized
mea
n sq
uare
err
or (N
MSE
) in
mix
ing
mat
rix e
stim
ation
(dB)
Order of the mixing matrices (PxQ)
46
P ndash No of mixturesQ ndash No of sources
Advantages of the Proposed algorithmAdvantages of the Proposed algorithm
Step 1 Convert x in the time domain to the TF domain to get XStep 2 Check the condition
Step 3 If the condition is satisfied then X(k t) is a sample atthe SSP and this sample is kept for mixing matrix estimationotherwise discard the point
Step 4 Repeat Steps 2 to 3 for all the points in the TF planeor until sufficient number of SSPs are obtained
cos
)()(
)()(
tkXItkXR
tkXItkXR T
1) Much simpler constrain the algorithm does not require ldquosingle source zonerdquo
3) The algorithm is extremely simple but effective2) Separation performance is better
0510 AM 47-gt
My Contributions ndash III IV and VMy Contributions ndash III IV and V
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
48
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Mask estimation
Mic 1
Mic P
Mixture in TF domain
Separated signals in TF domain
)( tkX P
)(1 tkX
t
t
k
k
)(1 tkY
)(1 tkY
)( tkYQ
)( tkYQ
QP
0510 AM 49
Mathematical RepresentationMathematical Representation
Q
q
L
lqpqp Pplnslhnx
1
1
0
1)()()(
)()()()()()()( 11 tkSktkSktkSktk QQqq HHHX
)(
)(
)()(
)()(
)(
)( 1
1
1111
tkS
tkS
kHkH
kHkH
tkX
tkX
QPQP
Q
P
)(
)(
)(
)(
)(
)(
)(
)(
)( 11
1
1
11
tkS
kH
kH
tkS
kH
kH
tkS
kH
kH
Q
PQ
Q
q
Pq
q
P
Time domain
Frequency domain
0510 AM 50
P ndash No of mixturesQ ndash No of sources
Single source pointsSingle source pointsInstantaneous mixing
00point at 1 Case 11211111 tkStkStk
)()()(
)()()(
111111
111111
tkSIktkI
tkSRktkR
HX
HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()(
)()()(
222222
222222
tkSIktkI
tkSRktkR
HX
HX
Single source point 2
Real scalar
RealReal
Real scalarReal scalar
Real scalar
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
0510 AM 51
Basic Principle of Single Source Points Detection
Basic Principle of Single Source Points Detection
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
j
H
C
e
cos21
21
UU
UUUUU H
and 20coscos HCH
angle pseudo called is
angleHermitian called is
H The Hermitian angle between the complex
vectors u1 and u2 will remain the same even if the vectors are multiplied by any complex scalars whereas the pseudo angle will change
0510 AM 52
-gt
k
Algorithm for Single Source Points Detection
Algorithm for Single Source Points Detection
t
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)(
)(
)(111
121
111 tkSkH
kH
11
11
j
jr
)(
)(
112
111
tkX
tkX
11
11
j
jr
)(
)(
112
111
tkX
tkX
)( 111 tkX
)( 112 tkX
)(
)(
)(112
122
112 tkSkH
kH θH2
θH1
θH2
rX
rX
)(
)(cos
11
111
tk
tk H
Hq
0510 AM 53
θH1
OR
1k
1k
1t
Clean
Estimated
Mask Estimation by k-means (KM)Mask Estimation by k-means (KM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 54
Clean
Estimated
Mask Estimation by Fuzzy c-means (FCM)Mask Estimation by Fuzzy c-means (FCM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 55
Automatic Detection of Number of SourcesAutomatic Detection of Number of Sources
0510 AM 56
Cluster validation technique
For c = 2 to cmax
Cluster the data into c clustersCalculate the cluster validation index
EndTake c corresponding to the best cluster as the number of sources
-gt
Elimination of Low Energy PointsElimination of Low Energy Points
0510 AM 57
- Blind Separation of Speech Mixtures
- Introduction
- Slide 3
- Slide 4
- Slide 5
- Approaches for BSS of Speech Signals
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Permutation Problem in Frequency Domain BSS
- Motivation
- My Contribution - I
- Algorithm for Solving the Permutation Problem
- Existing Method for Solving the Permutation Problem
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Proposed algorithm Partial separation method (Parallel configuration) Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
- Partial separation method (Parallel configuration)
- Partial separation method (Cascade configuration)
- Advantages of Partial Separation method
- Comparison with Adjacent Bands Correlation Method
- Comparison with DOA method
- My Contribution -II
- Underdetermined Blind Source Separation of Instantaneous Mixtures
- Mathematical Representation of Instantaneous Mixing Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
- Single Source Points in Time-Frequency domain
- Slide 31
- Slide 32
- Scatter Diagram of the Mixtures When Source are Perfectly Sparse
- Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
- Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
- Principle of the Proposed Algorithm for the Detection of Single Source Points
- Slide 39
- Slide 40
- Proposed Algorithm for the Detection of Single Source Points
- Elimination of Outliers
- Slide 43
- Detected Single Source Points Three mixtures
- Comparison with Classical Algorithms for Determined Case
- Comparison with Method Proposed in [1] Underdetermined case
- Advantages of the Proposed algorithm
- My Contributions ndash III IV and V
- Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
- Mathematical Representation
- Single source points
- Basic Principle of Single Source Points Detection
- Algorithm for Single Source Points Detection
- Mask Estimation by k-means (KM)
- Mask Estimation by Fuzzy c-means (FCM)
- Automatic Detection of Number of Sources
- Elimination of Low Energy Points
-
0510 AM
Experimental ResultsExperimental Results
dB6747NMSE
No of mixtures =2 No of sources =6
43
Detected Single Source PointsThree mixtures
Detected Single Source PointsThree mixtures
No of mixtures =3 No of sources =60510 AM 44
Comparison with Classical Algorithms for Determined Case
Comparison with Classical Algorithms for Determined Case
No of mixtures =2No of sources =2
Average of 500 experimental results
0510 AM 45
-gt
Comparison with Method Proposed in [1] Underdetermined case
Comparison with Method Proposed in [1] Underdetermined case
[1] Y Li S Amari A Cichocki D W C Ho and S Xie ldquoUnderdetermined blind source separation based on sparse representationrdquo IEEE Transactions on Signal Processing vol 54 p 423ndash437 Feb 2006
0510 AM
Nor
mal
ized
mea
n sq
uare
err
or (N
MSE
) in
mix
ing
mat
rix e
stim
ation
(dB)
Order of the mixing matrices (PxQ)
46
P ndash No of mixturesQ ndash No of sources
Advantages of the Proposed algorithmAdvantages of the Proposed algorithm
Step 1 Convert x in the time domain to the TF domain to get XStep 2 Check the condition
Step 3 If the condition is satisfied then X(k t) is a sample atthe SSP and this sample is kept for mixing matrix estimationotherwise discard the point
Step 4 Repeat Steps 2 to 3 for all the points in the TF planeor until sufficient number of SSPs are obtained
cos
)()(
)()(
tkXItkXR
tkXItkXR T
1) Much simpler constrain the algorithm does not require ldquosingle source zonerdquo
3) The algorithm is extremely simple but effective2) Separation performance is better
0510 AM 47-gt
My Contributions ndash III IV and VMy Contributions ndash III IV and V
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
48
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Mask estimation
Mic 1
Mic P
Mixture in TF domain
Separated signals in TF domain
)( tkX P
)(1 tkX
t
t
k
k
)(1 tkY
)(1 tkY
)( tkYQ
)( tkYQ
QP
0510 AM 49
Mathematical RepresentationMathematical Representation
Q
q
L
lqpqp Pplnslhnx
1
1
0
1)()()(
)()()()()()()( 11 tkSktkSktkSktk QQqq HHHX
)(
)(
)()(
)()(
)(
)( 1
1
1111
tkS
tkS
kHkH
kHkH
tkX
tkX
QPQP
Q
P
)(
)(
)(
)(
)(
)(
)(
)(
)( 11
1
1
11
tkS
kH
kH
tkS
kH
kH
tkS
kH
kH
Q
PQ
Q
q
Pq
q
P
Time domain
Frequency domain
0510 AM 50
P ndash No of mixturesQ ndash No of sources
Single source pointsSingle source pointsInstantaneous mixing
00point at 1 Case 11211111 tkStkStk
)()()(
)()()(
111111
111111
tkSIktkI
tkSRktkR
HX
HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()(
)()()(
222222
222222
tkSIktkI
tkSRktkR
HX
HX
Single source point 2
Real scalar
RealReal
Real scalarReal scalar
Real scalar
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
0510 AM 51
Basic Principle of Single Source Points Detection
Basic Principle of Single Source Points Detection
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
j
H
C
e
cos21
21
UU
UUUUU H
and 20coscos HCH
angle pseudo called is
angleHermitian called is
H The Hermitian angle between the complex
vectors u1 and u2 will remain the same even if the vectors are multiplied by any complex scalars whereas the pseudo angle will change
0510 AM 52
-gt
k
Algorithm for Single Source Points Detection
Algorithm for Single Source Points Detection
t
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)(
)(
)(111
121
111 tkSkH
kH
11
11
j
jr
)(
)(
112
111
tkX
tkX
11
11
j
jr
)(
)(
112
111
tkX
tkX
)( 111 tkX
)( 112 tkX
)(
)(
)(112
122
112 tkSkH
kH θH2
θH1
θH2
rX
rX
)(
)(cos
11
111
tk
tk H
Hq
0510 AM 53
θH1
OR
1k
1k
1t
Clean
Estimated
Mask Estimation by k-means (KM)Mask Estimation by k-means (KM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 54
Clean
Estimated
Mask Estimation by Fuzzy c-means (FCM)Mask Estimation by Fuzzy c-means (FCM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 55
Automatic Detection of Number of SourcesAutomatic Detection of Number of Sources
0510 AM 56
Cluster validation technique
For c = 2 to cmax
Cluster the data into c clustersCalculate the cluster validation index
EndTake c corresponding to the best cluster as the number of sources
-gt
Elimination of Low Energy PointsElimination of Low Energy Points
0510 AM 57
- Blind Separation of Speech Mixtures
- Introduction
- Slide 3
- Slide 4
- Slide 5
- Approaches for BSS of Speech Signals
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Permutation Problem in Frequency Domain BSS
- Motivation
- My Contribution - I
- Algorithm for Solving the Permutation Problem
- Existing Method for Solving the Permutation Problem
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Proposed algorithm Partial separation method (Parallel configuration) Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
- Partial separation method (Parallel configuration)
- Partial separation method (Cascade configuration)
- Advantages of Partial Separation method
- Comparison with Adjacent Bands Correlation Method
- Comparison with DOA method
- My Contribution -II
- Underdetermined Blind Source Separation of Instantaneous Mixtures
- Mathematical Representation of Instantaneous Mixing Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
- Single Source Points in Time-Frequency domain
- Slide 31
- Slide 32
- Scatter Diagram of the Mixtures When Source are Perfectly Sparse
- Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
- Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
- Principle of the Proposed Algorithm for the Detection of Single Source Points
- Slide 39
- Slide 40
- Proposed Algorithm for the Detection of Single Source Points
- Elimination of Outliers
- Slide 43
- Detected Single Source Points Three mixtures
- Comparison with Classical Algorithms for Determined Case
- Comparison with Method Proposed in [1] Underdetermined case
- Advantages of the Proposed algorithm
- My Contributions ndash III IV and V
- Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
- Mathematical Representation
- Single source points
- Basic Principle of Single Source Points Detection
- Algorithm for Single Source Points Detection
- Mask Estimation by k-means (KM)
- Mask Estimation by Fuzzy c-means (FCM)
- Automatic Detection of Number of Sources
- Elimination of Low Energy Points
-
Detected Single Source PointsThree mixtures
Detected Single Source PointsThree mixtures
No of mixtures =3 No of sources =60510 AM 44
Comparison with Classical Algorithms for Determined Case
Comparison with Classical Algorithms for Determined Case
No of mixtures =2No of sources =2
Average of 500 experimental results
0510 AM 45
-gt
Comparison with Method Proposed in [1] Underdetermined case
Comparison with Method Proposed in [1] Underdetermined case
[1] Y Li S Amari A Cichocki D W C Ho and S Xie ldquoUnderdetermined blind source separation based on sparse representationrdquo IEEE Transactions on Signal Processing vol 54 p 423ndash437 Feb 2006
0510 AM
Nor
mal
ized
mea
n sq
uare
err
or (N
MSE
) in
mix
ing
mat
rix e
stim
ation
(dB)
Order of the mixing matrices (PxQ)
46
P ndash No of mixturesQ ndash No of sources
Advantages of the Proposed algorithmAdvantages of the Proposed algorithm
Step 1 Convert x in the time domain to the TF domain to get XStep 2 Check the condition
Step 3 If the condition is satisfied then X(k t) is a sample atthe SSP and this sample is kept for mixing matrix estimationotherwise discard the point
Step 4 Repeat Steps 2 to 3 for all the points in the TF planeor until sufficient number of SSPs are obtained
cos
)()(
)()(
tkXItkXR
tkXItkXR T
1) Much simpler constrain the algorithm does not require ldquosingle source zonerdquo
3) The algorithm is extremely simple but effective2) Separation performance is better
0510 AM 47-gt
My Contributions ndash III IV and VMy Contributions ndash III IV and V
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
48
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Mask estimation
Mic 1
Mic P
Mixture in TF domain
Separated signals in TF domain
)( tkX P
)(1 tkX
t
t
k
k
)(1 tkY
)(1 tkY
)( tkYQ
)( tkYQ
QP
0510 AM 49
Mathematical RepresentationMathematical Representation
Q
q
L
lqpqp Pplnslhnx
1
1
0
1)()()(
)()()()()()()( 11 tkSktkSktkSktk QQqq HHHX
)(
)(
)()(
)()(
)(
)( 1
1
1111
tkS
tkS
kHkH
kHkH
tkX
tkX
QPQP
Q
P
)(
)(
)(
)(
)(
)(
)(
)(
)( 11
1
1
11
tkS
kH
kH
tkS
kH
kH
tkS
kH
kH
Q
PQ
Q
q
Pq
q
P
Time domain
Frequency domain
0510 AM 50
P ndash No of mixturesQ ndash No of sources
Single source pointsSingle source pointsInstantaneous mixing
00point at 1 Case 11211111 tkStkStk
)()()(
)()()(
111111
111111
tkSIktkI
tkSRktkR
HX
HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()(
)()()(
222222
222222
tkSIktkI
tkSRktkR
HX
HX
Single source point 2
Real scalar
RealReal
Real scalarReal scalar
Real scalar
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
0510 AM 51
Basic Principle of Single Source Points Detection
Basic Principle of Single Source Points Detection
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
j
H
C
e
cos21
21
UU
UUUUU H
and 20coscos HCH
angle pseudo called is
angleHermitian called is
H The Hermitian angle between the complex
vectors u1 and u2 will remain the same even if the vectors are multiplied by any complex scalars whereas the pseudo angle will change
0510 AM 52
-gt
k
Algorithm for Single Source Points Detection
Algorithm for Single Source Points Detection
t
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)(
)(
)(111
121
111 tkSkH
kH
11
11
j
jr
)(
)(
112
111
tkX
tkX
11
11
j
jr
)(
)(
112
111
tkX
tkX
)( 111 tkX
)( 112 tkX
)(
)(
)(112
122
112 tkSkH
kH θH2
θH1
θH2
rX
rX
)(
)(cos
11
111
tk
tk H
Hq
0510 AM 53
θH1
OR
1k
1k
1t
Clean
Estimated
Mask Estimation by k-means (KM)Mask Estimation by k-means (KM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 54
Clean
Estimated
Mask Estimation by Fuzzy c-means (FCM)Mask Estimation by Fuzzy c-means (FCM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 55
Automatic Detection of Number of SourcesAutomatic Detection of Number of Sources
0510 AM 56
Cluster validation technique
For c = 2 to cmax
Cluster the data into c clustersCalculate the cluster validation index
EndTake c corresponding to the best cluster as the number of sources
-gt
Elimination of Low Energy PointsElimination of Low Energy Points
0510 AM 57
- Blind Separation of Speech Mixtures
- Introduction
- Slide 3
- Slide 4
- Slide 5
- Approaches for BSS of Speech Signals
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Permutation Problem in Frequency Domain BSS
- Motivation
- My Contribution - I
- Algorithm for Solving the Permutation Problem
- Existing Method for Solving the Permutation Problem
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Proposed algorithm Partial separation method (Parallel configuration) Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
- Partial separation method (Parallel configuration)
- Partial separation method (Cascade configuration)
- Advantages of Partial Separation method
- Comparison with Adjacent Bands Correlation Method
- Comparison with DOA method
- My Contribution -II
- Underdetermined Blind Source Separation of Instantaneous Mixtures
- Mathematical Representation of Instantaneous Mixing Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
- Single Source Points in Time-Frequency domain
- Slide 31
- Slide 32
- Scatter Diagram of the Mixtures When Source are Perfectly Sparse
- Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
- Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
- Principle of the Proposed Algorithm for the Detection of Single Source Points
- Slide 39
- Slide 40
- Proposed Algorithm for the Detection of Single Source Points
- Elimination of Outliers
- Slide 43
- Detected Single Source Points Three mixtures
- Comparison with Classical Algorithms for Determined Case
- Comparison with Method Proposed in [1] Underdetermined case
- Advantages of the Proposed algorithm
- My Contributions ndash III IV and V
- Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
- Mathematical Representation
- Single source points
- Basic Principle of Single Source Points Detection
- Algorithm for Single Source Points Detection
- Mask Estimation by k-means (KM)
- Mask Estimation by Fuzzy c-means (FCM)
- Automatic Detection of Number of Sources
- Elimination of Low Energy Points
-
Comparison with Classical Algorithms for Determined Case
Comparison with Classical Algorithms for Determined Case
No of mixtures =2No of sources =2
Average of 500 experimental results
0510 AM 45
-gt
Comparison with Method Proposed in [1] Underdetermined case
Comparison with Method Proposed in [1] Underdetermined case
[1] Y Li S Amari A Cichocki D W C Ho and S Xie ldquoUnderdetermined blind source separation based on sparse representationrdquo IEEE Transactions on Signal Processing vol 54 p 423ndash437 Feb 2006
0510 AM
Nor
mal
ized
mea
n sq
uare
err
or (N
MSE
) in
mix
ing
mat
rix e
stim
ation
(dB)
Order of the mixing matrices (PxQ)
46
P ndash No of mixturesQ ndash No of sources
Advantages of the Proposed algorithmAdvantages of the Proposed algorithm
Step 1 Convert x in the time domain to the TF domain to get XStep 2 Check the condition
Step 3 If the condition is satisfied then X(k t) is a sample atthe SSP and this sample is kept for mixing matrix estimationotherwise discard the point
Step 4 Repeat Steps 2 to 3 for all the points in the TF planeor until sufficient number of SSPs are obtained
cos
)()(
)()(
tkXItkXR
tkXItkXR T
1) Much simpler constrain the algorithm does not require ldquosingle source zonerdquo
3) The algorithm is extremely simple but effective2) Separation performance is better
0510 AM 47-gt
My Contributions ndash III IV and VMy Contributions ndash III IV and V
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
48
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Mask estimation
Mic 1
Mic P
Mixture in TF domain
Separated signals in TF domain
)( tkX P
)(1 tkX
t
t
k
k
)(1 tkY
)(1 tkY
)( tkYQ
)( tkYQ
QP
0510 AM 49
Mathematical RepresentationMathematical Representation
Q
q
L
lqpqp Pplnslhnx
1
1
0
1)()()(
)()()()()()()( 11 tkSktkSktkSktk QQqq HHHX
)(
)(
)()(
)()(
)(
)( 1
1
1111
tkS
tkS
kHkH
kHkH
tkX
tkX
QPQP
Q
P
)(
)(
)(
)(
)(
)(
)(
)(
)( 11
1
1
11
tkS
kH
kH
tkS
kH
kH
tkS
kH
kH
Q
PQ
Q
q
Pq
q
P
Time domain
Frequency domain
0510 AM 50
P ndash No of mixturesQ ndash No of sources
Single source pointsSingle source pointsInstantaneous mixing
00point at 1 Case 11211111 tkStkStk
)()()(
)()()(
111111
111111
tkSIktkI
tkSRktkR
HX
HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()(
)()()(
222222
222222
tkSIktkI
tkSRktkR
HX
HX
Single source point 2
Real scalar
RealReal
Real scalarReal scalar
Real scalar
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
0510 AM 51
Basic Principle of Single Source Points Detection
Basic Principle of Single Source Points Detection
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
j
H
C
e
cos21
21
UU
UUUUU H
and 20coscos HCH
angle pseudo called is
angleHermitian called is
H The Hermitian angle between the complex
vectors u1 and u2 will remain the same even if the vectors are multiplied by any complex scalars whereas the pseudo angle will change
0510 AM 52
-gt
k
Algorithm for Single Source Points Detection
Algorithm for Single Source Points Detection
t
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)(
)(
)(111
121
111 tkSkH
kH
11
11
j
jr
)(
)(
112
111
tkX
tkX
11
11
j
jr
)(
)(
112
111
tkX
tkX
)( 111 tkX
)( 112 tkX
)(
)(
)(112
122
112 tkSkH
kH θH2
θH1
θH2
rX
rX
)(
)(cos
11
111
tk
tk H
Hq
0510 AM 53
θH1
OR
1k
1k
1t
Clean
Estimated
Mask Estimation by k-means (KM)Mask Estimation by k-means (KM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 54
Clean
Estimated
Mask Estimation by Fuzzy c-means (FCM)Mask Estimation by Fuzzy c-means (FCM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 55
Automatic Detection of Number of SourcesAutomatic Detection of Number of Sources
0510 AM 56
Cluster validation technique
For c = 2 to cmax
Cluster the data into c clustersCalculate the cluster validation index
EndTake c corresponding to the best cluster as the number of sources
-gt
Elimination of Low Energy PointsElimination of Low Energy Points
0510 AM 57
- Blind Separation of Speech Mixtures
- Introduction
- Slide 3
- Slide 4
- Slide 5
- Approaches for BSS of Speech Signals
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Permutation Problem in Frequency Domain BSS
- Motivation
- My Contribution - I
- Algorithm for Solving the Permutation Problem
- Existing Method for Solving the Permutation Problem
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Proposed algorithm Partial separation method (Parallel configuration) Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
- Partial separation method (Parallel configuration)
- Partial separation method (Cascade configuration)
- Advantages of Partial Separation method
- Comparison with Adjacent Bands Correlation Method
- Comparison with DOA method
- My Contribution -II
- Underdetermined Blind Source Separation of Instantaneous Mixtures
- Mathematical Representation of Instantaneous Mixing Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
- Single Source Points in Time-Frequency domain
- Slide 31
- Slide 32
- Scatter Diagram of the Mixtures When Source are Perfectly Sparse
- Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
- Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
- Principle of the Proposed Algorithm for the Detection of Single Source Points
- Slide 39
- Slide 40
- Proposed Algorithm for the Detection of Single Source Points
- Elimination of Outliers
- Slide 43
- Detected Single Source Points Three mixtures
- Comparison with Classical Algorithms for Determined Case
- Comparison with Method Proposed in [1] Underdetermined case
- Advantages of the Proposed algorithm
- My Contributions ndash III IV and V
- Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
- Mathematical Representation
- Single source points
- Basic Principle of Single Source Points Detection
- Algorithm for Single Source Points Detection
- Mask Estimation by k-means (KM)
- Mask Estimation by Fuzzy c-means (FCM)
- Automatic Detection of Number of Sources
- Elimination of Low Energy Points
-
Comparison with Method Proposed in [1] Underdetermined case
Comparison with Method Proposed in [1] Underdetermined case
[1] Y Li S Amari A Cichocki D W C Ho and S Xie ldquoUnderdetermined blind source separation based on sparse representationrdquo IEEE Transactions on Signal Processing vol 54 p 423ndash437 Feb 2006
0510 AM
Nor
mal
ized
mea
n sq
uare
err
or (N
MSE
) in
mix
ing
mat
rix e
stim
ation
(dB)
Order of the mixing matrices (PxQ)
46
P ndash No of mixturesQ ndash No of sources
Advantages of the Proposed algorithmAdvantages of the Proposed algorithm
Step 1 Convert x in the time domain to the TF domain to get XStep 2 Check the condition
Step 3 If the condition is satisfied then X(k t) is a sample atthe SSP and this sample is kept for mixing matrix estimationotherwise discard the point
Step 4 Repeat Steps 2 to 3 for all the points in the TF planeor until sufficient number of SSPs are obtained
cos
)()(
)()(
tkXItkXR
tkXItkXR T
1) Much simpler constrain the algorithm does not require ldquosingle source zonerdquo
3) The algorithm is extremely simple but effective2) Separation performance is better
0510 AM 47-gt
My Contributions ndash III IV and VMy Contributions ndash III IV and V
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
48
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Mask estimation
Mic 1
Mic P
Mixture in TF domain
Separated signals in TF domain
)( tkX P
)(1 tkX
t
t
k
k
)(1 tkY
)(1 tkY
)( tkYQ
)( tkYQ
QP
0510 AM 49
Mathematical RepresentationMathematical Representation
Q
q
L
lqpqp Pplnslhnx
1
1
0
1)()()(
)()()()()()()( 11 tkSktkSktkSktk QQqq HHHX
)(
)(
)()(
)()(
)(
)( 1
1
1111
tkS
tkS
kHkH
kHkH
tkX
tkX
QPQP
Q
P
)(
)(
)(
)(
)(
)(
)(
)(
)( 11
1
1
11
tkS
kH
kH
tkS
kH
kH
tkS
kH
kH
Q
PQ
Q
q
Pq
q
P
Time domain
Frequency domain
0510 AM 50
P ndash No of mixturesQ ndash No of sources
Single source pointsSingle source pointsInstantaneous mixing
00point at 1 Case 11211111 tkStkStk
)()()(
)()()(
111111
111111
tkSIktkI
tkSRktkR
HX
HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()(
)()()(
222222
222222
tkSIktkI
tkSRktkR
HX
HX
Single source point 2
Real scalar
RealReal
Real scalarReal scalar
Real scalar
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
0510 AM 51
Basic Principle of Single Source Points Detection
Basic Principle of Single Source Points Detection
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
j
H
C
e
cos21
21
UU
UUUUU H
and 20coscos HCH
angle pseudo called is
angleHermitian called is
H The Hermitian angle between the complex
vectors u1 and u2 will remain the same even if the vectors are multiplied by any complex scalars whereas the pseudo angle will change
0510 AM 52
-gt
k
Algorithm for Single Source Points Detection
Algorithm for Single Source Points Detection
t
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)(
)(
)(111
121
111 tkSkH
kH
11
11
j
jr
)(
)(
112
111
tkX
tkX
11
11
j
jr
)(
)(
112
111
tkX
tkX
)( 111 tkX
)( 112 tkX
)(
)(
)(112
122
112 tkSkH
kH θH2
θH1
θH2
rX
rX
)(
)(cos
11
111
tk
tk H
Hq
0510 AM 53
θH1
OR
1k
1k
1t
Clean
Estimated
Mask Estimation by k-means (KM)Mask Estimation by k-means (KM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 54
Clean
Estimated
Mask Estimation by Fuzzy c-means (FCM)Mask Estimation by Fuzzy c-means (FCM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 55
Automatic Detection of Number of SourcesAutomatic Detection of Number of Sources
0510 AM 56
Cluster validation technique
For c = 2 to cmax
Cluster the data into c clustersCalculate the cluster validation index
EndTake c corresponding to the best cluster as the number of sources
-gt
Elimination of Low Energy PointsElimination of Low Energy Points
0510 AM 57
- Blind Separation of Speech Mixtures
- Introduction
- Slide 3
- Slide 4
- Slide 5
- Approaches for BSS of Speech Signals
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Permutation Problem in Frequency Domain BSS
- Motivation
- My Contribution - I
- Algorithm for Solving the Permutation Problem
- Existing Method for Solving the Permutation Problem
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Proposed algorithm Partial separation method (Parallel configuration) Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
- Partial separation method (Parallel configuration)
- Partial separation method (Cascade configuration)
- Advantages of Partial Separation method
- Comparison with Adjacent Bands Correlation Method
- Comparison with DOA method
- My Contribution -II
- Underdetermined Blind Source Separation of Instantaneous Mixtures
- Mathematical Representation of Instantaneous Mixing Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
- Single Source Points in Time-Frequency domain
- Slide 31
- Slide 32
- Scatter Diagram of the Mixtures When Source are Perfectly Sparse
- Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
- Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
- Principle of the Proposed Algorithm for the Detection of Single Source Points
- Slide 39
- Slide 40
- Proposed Algorithm for the Detection of Single Source Points
- Elimination of Outliers
- Slide 43
- Detected Single Source Points Three mixtures
- Comparison with Classical Algorithms for Determined Case
- Comparison with Method Proposed in [1] Underdetermined case
- Advantages of the Proposed algorithm
- My Contributions ndash III IV and V
- Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
- Mathematical Representation
- Single source points
- Basic Principle of Single Source Points Detection
- Algorithm for Single Source Points Detection
- Mask Estimation by k-means (KM)
- Mask Estimation by Fuzzy c-means (FCM)
- Automatic Detection of Number of Sources
- Elimination of Low Energy Points
-
Advantages of the Proposed algorithmAdvantages of the Proposed algorithm
Step 1 Convert x in the time domain to the TF domain to get XStep 2 Check the condition
Step 3 If the condition is satisfied then X(k t) is a sample atthe SSP and this sample is kept for mixing matrix estimationotherwise discard the point
Step 4 Repeat Steps 2 to 3 for all the points in the TF planeor until sufficient number of SSPs are obtained
cos
)()(
)()(
tkXItkXR
tkXItkXR T
1) Much simpler constrain the algorithm does not require ldquosingle source zonerdquo
3) The algorithm is extremely simple but effective2) Separation performance is better
0510 AM 47-gt
My Contributions ndash III IV and VMy Contributions ndash III IV and V
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
48
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Mask estimation
Mic 1
Mic P
Mixture in TF domain
Separated signals in TF domain
)( tkX P
)(1 tkX
t
t
k
k
)(1 tkY
)(1 tkY
)( tkYQ
)( tkYQ
QP
0510 AM 49
Mathematical RepresentationMathematical Representation
Q
q
L
lqpqp Pplnslhnx
1
1
0
1)()()(
)()()()()()()( 11 tkSktkSktkSktk QQqq HHHX
)(
)(
)()(
)()(
)(
)( 1
1
1111
tkS
tkS
kHkH
kHkH
tkX
tkX
QPQP
Q
P
)(
)(
)(
)(
)(
)(
)(
)(
)( 11
1
1
11
tkS
kH
kH
tkS
kH
kH
tkS
kH
kH
Q
PQ
Q
q
Pq
q
P
Time domain
Frequency domain
0510 AM 50
P ndash No of mixturesQ ndash No of sources
Single source pointsSingle source pointsInstantaneous mixing
00point at 1 Case 11211111 tkStkStk
)()()(
)()()(
111111
111111
tkSIktkI
tkSRktkR
HX
HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()(
)()()(
222222
222222
tkSIktkI
tkSRktkR
HX
HX
Single source point 2
Real scalar
RealReal
Real scalarReal scalar
Real scalar
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
0510 AM 51
Basic Principle of Single Source Points Detection
Basic Principle of Single Source Points Detection
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
j
H
C
e
cos21
21
UU
UUUUU H
and 20coscos HCH
angle pseudo called is
angleHermitian called is
H The Hermitian angle between the complex
vectors u1 and u2 will remain the same even if the vectors are multiplied by any complex scalars whereas the pseudo angle will change
0510 AM 52
-gt
k
Algorithm for Single Source Points Detection
Algorithm for Single Source Points Detection
t
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)(
)(
)(111
121
111 tkSkH
kH
11
11
j
jr
)(
)(
112
111
tkX
tkX
11
11
j
jr
)(
)(
112
111
tkX
tkX
)( 111 tkX
)( 112 tkX
)(
)(
)(112
122
112 tkSkH
kH θH2
θH1
θH2
rX
rX
)(
)(cos
11
111
tk
tk H
Hq
0510 AM 53
θH1
OR
1k
1k
1t
Clean
Estimated
Mask Estimation by k-means (KM)Mask Estimation by k-means (KM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 54
Clean
Estimated
Mask Estimation by Fuzzy c-means (FCM)Mask Estimation by Fuzzy c-means (FCM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 55
Automatic Detection of Number of SourcesAutomatic Detection of Number of Sources
0510 AM 56
Cluster validation technique
For c = 2 to cmax
Cluster the data into c clustersCalculate the cluster validation index
EndTake c corresponding to the best cluster as the number of sources
-gt
Elimination of Low Energy PointsElimination of Low Energy Points
0510 AM 57
- Blind Separation of Speech Mixtures
- Introduction
- Slide 3
- Slide 4
- Slide 5
- Approaches for BSS of Speech Signals
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Permutation Problem in Frequency Domain BSS
- Motivation
- My Contribution - I
- Algorithm for Solving the Permutation Problem
- Existing Method for Solving the Permutation Problem
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Proposed algorithm Partial separation method (Parallel configuration) Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
- Partial separation method (Parallel configuration)
- Partial separation method (Cascade configuration)
- Advantages of Partial Separation method
- Comparison with Adjacent Bands Correlation Method
- Comparison with DOA method
- My Contribution -II
- Underdetermined Blind Source Separation of Instantaneous Mixtures
- Mathematical Representation of Instantaneous Mixing Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
- Single Source Points in Time-Frequency domain
- Slide 31
- Slide 32
- Scatter Diagram of the Mixtures When Source are Perfectly Sparse
- Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
- Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
- Principle of the Proposed Algorithm for the Detection of Single Source Points
- Slide 39
- Slide 40
- Proposed Algorithm for the Detection of Single Source Points
- Elimination of Outliers
- Slide 43
- Detected Single Source Points Three mixtures
- Comparison with Classical Algorithms for Determined Case
- Comparison with Method Proposed in [1] Underdetermined case
- Advantages of the Proposed algorithm
- My Contributions ndash III IV and V
- Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
- Mathematical Representation
- Single source points
- Basic Principle of Single Source Points Detection
- Algorithm for Single Source Points Detection
- Mask Estimation by k-means (KM)
- Mask Estimation by Fuzzy c-means (FCM)
- Automatic Detection of Number of Sources
- Elimination of Low Energy Points
-
My Contributions ndash III IV and VMy Contributions ndash III IV and V
0510 AM0510 AM
mixtures ge sources mixtures ge sources
mixtures lt sources mixtures lt sources
BSS
Determined Overdetermined
Underdetermined
Instantaneous
Instantaneous
Convolutive
Convolutive
Frequency domain
Frequency domain
Time domain
Time domain
Mixing matrix estimation
Frequency bin-wise separation
Frequency bin-wise separation
Permutation problem
Permutation problem
Source estimation
Automatic detection of no of sources
48
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Mask estimation
Mic 1
Mic P
Mixture in TF domain
Separated signals in TF domain
)( tkX P
)(1 tkX
t
t
k
k
)(1 tkY
)(1 tkY
)( tkYQ
)( tkYQ
QP
0510 AM 49
Mathematical RepresentationMathematical Representation
Q
q
L
lqpqp Pplnslhnx
1
1
0
1)()()(
)()()()()()()( 11 tkSktkSktkSktk QQqq HHHX
)(
)(
)()(
)()(
)(
)( 1
1
1111
tkS
tkS
kHkH
kHkH
tkX
tkX
QPQP
Q
P
)(
)(
)(
)(
)(
)(
)(
)(
)( 11
1
1
11
tkS
kH
kH
tkS
kH
kH
tkS
kH
kH
Q
PQ
Q
q
Pq
q
P
Time domain
Frequency domain
0510 AM 50
P ndash No of mixturesQ ndash No of sources
Single source pointsSingle source pointsInstantaneous mixing
00point at 1 Case 11211111 tkStkStk
)()()(
)()()(
111111
111111
tkSIktkI
tkSRktkR
HX
HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()(
)()()(
222222
222222
tkSIktkI
tkSRktkR
HX
HX
Single source point 2
Real scalar
RealReal
Real scalarReal scalar
Real scalar
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
0510 AM 51
Basic Principle of Single Source Points Detection
Basic Principle of Single Source Points Detection
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
j
H
C
e
cos21
21
UU
UUUUU H
and 20coscos HCH
angle pseudo called is
angleHermitian called is
H The Hermitian angle between the complex
vectors u1 and u2 will remain the same even if the vectors are multiplied by any complex scalars whereas the pseudo angle will change
0510 AM 52
-gt
k
Algorithm for Single Source Points Detection
Algorithm for Single Source Points Detection
t
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)(
)(
)(111
121
111 tkSkH
kH
11
11
j
jr
)(
)(
112
111
tkX
tkX
11
11
j
jr
)(
)(
112
111
tkX
tkX
)( 111 tkX
)( 112 tkX
)(
)(
)(112
122
112 tkSkH
kH θH2
θH1
θH2
rX
rX
)(
)(cos
11
111
tk
tk H
Hq
0510 AM 53
θH1
OR
1k
1k
1t
Clean
Estimated
Mask Estimation by k-means (KM)Mask Estimation by k-means (KM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 54
Clean
Estimated
Mask Estimation by Fuzzy c-means (FCM)Mask Estimation by Fuzzy c-means (FCM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 55
Automatic Detection of Number of SourcesAutomatic Detection of Number of Sources
0510 AM 56
Cluster validation technique
For c = 2 to cmax
Cluster the data into c clustersCalculate the cluster validation index
EndTake c corresponding to the best cluster as the number of sources
-gt
Elimination of Low Energy PointsElimination of Low Energy Points
0510 AM 57
- Blind Separation of Speech Mixtures
- Introduction
- Slide 3
- Slide 4
- Slide 5
- Approaches for BSS of Speech Signals
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Permutation Problem in Frequency Domain BSS
- Motivation
- My Contribution - I
- Algorithm for Solving the Permutation Problem
- Existing Method for Solving the Permutation Problem
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Proposed algorithm Partial separation method (Parallel configuration) Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
- Partial separation method (Parallel configuration)
- Partial separation method (Cascade configuration)
- Advantages of Partial Separation method
- Comparison with Adjacent Bands Correlation Method
- Comparison with DOA method
- My Contribution -II
- Underdetermined Blind Source Separation of Instantaneous Mixtures
- Mathematical Representation of Instantaneous Mixing Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
- Single Source Points in Time-Frequency domain
- Slide 31
- Slide 32
- Scatter Diagram of the Mixtures When Source are Perfectly Sparse
- Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
- Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
- Principle of the Proposed Algorithm for the Detection of Single Source Points
- Slide 39
- Slide 40
- Proposed Algorithm for the Detection of Single Source Points
- Elimination of Outliers
- Slide 43
- Detected Single Source Points Three mixtures
- Comparison with Classical Algorithms for Determined Case
- Comparison with Method Proposed in [1] Underdetermined case
- Advantages of the Proposed algorithm
- My Contributions ndash III IV and V
- Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
- Mathematical Representation
- Single source points
- Basic Principle of Single Source Points Detection
- Algorithm for Single Source Points Detection
- Mask Estimation by k-means (KM)
- Mask Estimation by Fuzzy c-means (FCM)
- Automatic Detection of Number of Sources
- Elimination of Low Energy Points
-
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking
Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
Mask estimation
Mic 1
Mic P
Mixture in TF domain
Separated signals in TF domain
)( tkX P
)(1 tkX
t
t
k
k
)(1 tkY
)(1 tkY
)( tkYQ
)( tkYQ
QP
0510 AM 49
Mathematical RepresentationMathematical Representation
Q
q
L
lqpqp Pplnslhnx
1
1
0
1)()()(
)()()()()()()( 11 tkSktkSktkSktk QQqq HHHX
)(
)(
)()(
)()(
)(
)( 1
1
1111
tkS
tkS
kHkH
kHkH
tkX
tkX
QPQP
Q
P
)(
)(
)(
)(
)(
)(
)(
)(
)( 11
1
1
11
tkS
kH
kH
tkS
kH
kH
tkS
kH
kH
Q
PQ
Q
q
Pq
q
P
Time domain
Frequency domain
0510 AM 50
P ndash No of mixturesQ ndash No of sources
Single source pointsSingle source pointsInstantaneous mixing
00point at 1 Case 11211111 tkStkStk
)()()(
)()()(
111111
111111
tkSIktkI
tkSRktkR
HX
HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()(
)()()(
222222
222222
tkSIktkI
tkSRktkR
HX
HX
Single source point 2
Real scalar
RealReal
Real scalarReal scalar
Real scalar
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
0510 AM 51
Basic Principle of Single Source Points Detection
Basic Principle of Single Source Points Detection
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
j
H
C
e
cos21
21
UU
UUUUU H
and 20coscos HCH
angle pseudo called is
angleHermitian called is
H The Hermitian angle between the complex
vectors u1 and u2 will remain the same even if the vectors are multiplied by any complex scalars whereas the pseudo angle will change
0510 AM 52
-gt
k
Algorithm for Single Source Points Detection
Algorithm for Single Source Points Detection
t
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)(
)(
)(111
121
111 tkSkH
kH
11
11
j
jr
)(
)(
112
111
tkX
tkX
11
11
j
jr
)(
)(
112
111
tkX
tkX
)( 111 tkX
)( 112 tkX
)(
)(
)(112
122
112 tkSkH
kH θH2
θH1
θH2
rX
rX
)(
)(cos
11
111
tk
tk H
Hq
0510 AM 53
θH1
OR
1k
1k
1t
Clean
Estimated
Mask Estimation by k-means (KM)Mask Estimation by k-means (KM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 54
Clean
Estimated
Mask Estimation by Fuzzy c-means (FCM)Mask Estimation by Fuzzy c-means (FCM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 55
Automatic Detection of Number of SourcesAutomatic Detection of Number of Sources
0510 AM 56
Cluster validation technique
For c = 2 to cmax
Cluster the data into c clustersCalculate the cluster validation index
EndTake c corresponding to the best cluster as the number of sources
-gt
Elimination of Low Energy PointsElimination of Low Energy Points
0510 AM 57
- Blind Separation of Speech Mixtures
- Introduction
- Slide 3
- Slide 4
- Slide 5
- Approaches for BSS of Speech Signals
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Permutation Problem in Frequency Domain BSS
- Motivation
- My Contribution - I
- Algorithm for Solving the Permutation Problem
- Existing Method for Solving the Permutation Problem
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Proposed algorithm Partial separation method (Parallel configuration) Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
- Partial separation method (Parallel configuration)
- Partial separation method (Cascade configuration)
- Advantages of Partial Separation method
- Comparison with Adjacent Bands Correlation Method
- Comparison with DOA method
- My Contribution -II
- Underdetermined Blind Source Separation of Instantaneous Mixtures
- Mathematical Representation of Instantaneous Mixing Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
- Single Source Points in Time-Frequency domain
- Slide 31
- Slide 32
- Scatter Diagram of the Mixtures When Source are Perfectly Sparse
- Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
- Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
- Principle of the Proposed Algorithm for the Detection of Single Source Points
- Slide 39
- Slide 40
- Proposed Algorithm for the Detection of Single Source Points
- Elimination of Outliers
- Slide 43
- Detected Single Source Points Three mixtures
- Comparison with Classical Algorithms for Determined Case
- Comparison with Method Proposed in [1] Underdetermined case
- Advantages of the Proposed algorithm
- My Contributions ndash III IV and V
- Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
- Mathematical Representation
- Single source points
- Basic Principle of Single Source Points Detection
- Algorithm for Single Source Points Detection
- Mask Estimation by k-means (KM)
- Mask Estimation by Fuzzy c-means (FCM)
- Automatic Detection of Number of Sources
- Elimination of Low Energy Points
-
Mathematical RepresentationMathematical Representation
Q
q
L
lqpqp Pplnslhnx
1
1
0
1)()()(
)()()()()()()( 11 tkSktkSktkSktk QQqq HHHX
)(
)(
)()(
)()(
)(
)( 1
1
1111
tkS
tkS
kHkH
kHkH
tkX
tkX
QPQP
Q
P
)(
)(
)(
)(
)(
)(
)(
)(
)( 11
1
1
11
tkS
kH
kH
tkS
kH
kH
tkS
kH
kH
Q
PQ
Q
q
Pq
q
P
Time domain
Frequency domain
0510 AM 50
P ndash No of mixturesQ ndash No of sources
Single source pointsSingle source pointsInstantaneous mixing
00point at 1 Case 11211111 tkStkStk
)()()(
)()()(
111111
111111
tkSIktkI
tkSRktkR
HX
HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()(
)()()(
222222
222222
tkSIktkI
tkSRktkR
HX
HX
Single source point 2
Real scalar
RealReal
Real scalarReal scalar
Real scalar
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
0510 AM 51
Basic Principle of Single Source Points Detection
Basic Principle of Single Source Points Detection
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
j
H
C
e
cos21
21
UU
UUUUU H
and 20coscos HCH
angle pseudo called is
angleHermitian called is
H The Hermitian angle between the complex
vectors u1 and u2 will remain the same even if the vectors are multiplied by any complex scalars whereas the pseudo angle will change
0510 AM 52
-gt
k
Algorithm for Single Source Points Detection
Algorithm for Single Source Points Detection
t
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)(
)(
)(111
121
111 tkSkH
kH
11
11
j
jr
)(
)(
112
111
tkX
tkX
11
11
j
jr
)(
)(
112
111
tkX
tkX
)( 111 tkX
)( 112 tkX
)(
)(
)(112
122
112 tkSkH
kH θH2
θH1
θH2
rX
rX
)(
)(cos
11
111
tk
tk H
Hq
0510 AM 53
θH1
OR
1k
1k
1t
Clean
Estimated
Mask Estimation by k-means (KM)Mask Estimation by k-means (KM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 54
Clean
Estimated
Mask Estimation by Fuzzy c-means (FCM)Mask Estimation by Fuzzy c-means (FCM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 55
Automatic Detection of Number of SourcesAutomatic Detection of Number of Sources
0510 AM 56
Cluster validation technique
For c = 2 to cmax
Cluster the data into c clustersCalculate the cluster validation index
EndTake c corresponding to the best cluster as the number of sources
-gt
Elimination of Low Energy PointsElimination of Low Energy Points
0510 AM 57
- Blind Separation of Speech Mixtures
- Introduction
- Slide 3
- Slide 4
- Slide 5
- Approaches for BSS of Speech Signals
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Permutation Problem in Frequency Domain BSS
- Motivation
- My Contribution - I
- Algorithm for Solving the Permutation Problem
- Existing Method for Solving the Permutation Problem
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Proposed algorithm Partial separation method (Parallel configuration) Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
- Partial separation method (Parallel configuration)
- Partial separation method (Cascade configuration)
- Advantages of Partial Separation method
- Comparison with Adjacent Bands Correlation Method
- Comparison with DOA method
- My Contribution -II
- Underdetermined Blind Source Separation of Instantaneous Mixtures
- Mathematical Representation of Instantaneous Mixing Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
- Single Source Points in Time-Frequency domain
- Slide 31
- Slide 32
- Scatter Diagram of the Mixtures When Source are Perfectly Sparse
- Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
- Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
- Principle of the Proposed Algorithm for the Detection of Single Source Points
- Slide 39
- Slide 40
- Proposed Algorithm for the Detection of Single Source Points
- Elimination of Outliers
- Slide 43
- Detected Single Source Points Three mixtures
- Comparison with Classical Algorithms for Determined Case
- Comparison with Method Proposed in [1] Underdetermined case
- Advantages of the Proposed algorithm
- My Contributions ndash III IV and V
- Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
- Mathematical Representation
- Single source points
- Basic Principle of Single Source Points Detection
- Algorithm for Single Source Points Detection
- Mask Estimation by k-means (KM)
- Mask Estimation by Fuzzy c-means (FCM)
- Automatic Detection of Number of Sources
- Elimination of Low Energy Points
-
Single source pointsSingle source pointsInstantaneous mixing
00point at 1 Case 11211111 tkStkStk
)()()(
)()()(
111111
111111
tkSIktkI
tkSRktkR
HX
HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()(
)()()(
222222
222222
tkSIktkI
tkSRktkR
HX
HX
Single source point 2
Real scalar
RealReal
Real scalarReal scalar
Real scalar
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
0510 AM 51
Basic Principle of Single Source Points Detection
Basic Principle of Single Source Points Detection
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
j
H
C
e
cos21
21
UU
UUUUU H
and 20coscos HCH
angle pseudo called is
angleHermitian called is
H The Hermitian angle between the complex
vectors u1 and u2 will remain the same even if the vectors are multiplied by any complex scalars whereas the pseudo angle will change
0510 AM 52
-gt
k
Algorithm for Single Source Points Detection
Algorithm for Single Source Points Detection
t
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)(
)(
)(111
121
111 tkSkH
kH
11
11
j
jr
)(
)(
112
111
tkX
tkX
11
11
j
jr
)(
)(
112
111
tkX
tkX
)( 111 tkX
)( 112 tkX
)(
)(
)(112
122
112 tkSkH
kH θH2
θH1
θH2
rX
rX
)(
)(cos
11
111
tk
tk H
Hq
0510 AM 53
θH1
OR
1k
1k
1t
Clean
Estimated
Mask Estimation by k-means (KM)Mask Estimation by k-means (KM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 54
Clean
Estimated
Mask Estimation by Fuzzy c-means (FCM)Mask Estimation by Fuzzy c-means (FCM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 55
Automatic Detection of Number of SourcesAutomatic Detection of Number of Sources
0510 AM 56
Cluster validation technique
For c = 2 to cmax
Cluster the data into c clustersCalculate the cluster validation index
EndTake c corresponding to the best cluster as the number of sources
-gt
Elimination of Low Energy PointsElimination of Low Energy Points
0510 AM 57
- Blind Separation of Speech Mixtures
- Introduction
- Slide 3
- Slide 4
- Slide 5
- Approaches for BSS of Speech Signals
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Permutation Problem in Frequency Domain BSS
- Motivation
- My Contribution - I
- Algorithm for Solving the Permutation Problem
- Existing Method for Solving the Permutation Problem
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Proposed algorithm Partial separation method (Parallel configuration) Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
- Partial separation method (Parallel configuration)
- Partial separation method (Cascade configuration)
- Advantages of Partial Separation method
- Comparison with Adjacent Bands Correlation Method
- Comparison with DOA method
- My Contribution -II
- Underdetermined Blind Source Separation of Instantaneous Mixtures
- Mathematical Representation of Instantaneous Mixing Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
- Single Source Points in Time-Frequency domain
- Slide 31
- Slide 32
- Scatter Diagram of the Mixtures When Source are Perfectly Sparse
- Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
- Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
- Principle of the Proposed Algorithm for the Detection of Single Source Points
- Slide 39
- Slide 40
- Proposed Algorithm for the Detection of Single Source Points
- Elimination of Outliers
- Slide 43
- Detected Single Source Points Three mixtures
- Comparison with Classical Algorithms for Determined Case
- Comparison with Method Proposed in [1] Underdetermined case
- Advantages of the Proposed algorithm
- My Contributions ndash III IV and V
- Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
- Mathematical Representation
- Single source points
- Basic Principle of Single Source Points Detection
- Algorithm for Single Source Points Detection
- Mask Estimation by k-means (KM)
- Mask Estimation by Fuzzy c-means (FCM)
- Automatic Detection of Number of Sources
- Elimination of Low Energy Points
-
Basic Principle of Single Source Points Detection
Basic Principle of Single Source Points Detection
Convolutive mixing
00point at 1 Case 11211111 tkStkStk
)()()( 111111 tkSktk HX
Single source point 1
00point at 2 Case 22222122 tkStkStk
)()()( 222222 tkSktk HX
Single source point 2
Complex scalar
Complex
Complex
Complex scalar
j
H
C
e
cos21
21
UU
UUUUU H
and 20coscos HCH
angle pseudo called is
angleHermitian called is
H The Hermitian angle between the complex
vectors u1 and u2 will remain the same even if the vectors are multiplied by any complex scalars whereas the pseudo angle will change
0510 AM 52
-gt
k
Algorithm for Single Source Points Detection
Algorithm for Single Source Points Detection
t
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)(
)(
)(111
121
111 tkSkH
kH
11
11
j
jr
)(
)(
112
111
tkX
tkX
11
11
j
jr
)(
)(
112
111
tkX
tkX
)( 111 tkX
)( 112 tkX
)(
)(
)(112
122
112 tkSkH
kH θH2
θH1
θH2
rX
rX
)(
)(cos
11
111
tk
tk H
Hq
0510 AM 53
θH1
OR
1k
1k
1t
Clean
Estimated
Mask Estimation by k-means (KM)Mask Estimation by k-means (KM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 54
Clean
Estimated
Mask Estimation by Fuzzy c-means (FCM)Mask Estimation by Fuzzy c-means (FCM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 55
Automatic Detection of Number of SourcesAutomatic Detection of Number of Sources
0510 AM 56
Cluster validation technique
For c = 2 to cmax
Cluster the data into c clustersCalculate the cluster validation index
EndTake c corresponding to the best cluster as the number of sources
-gt
Elimination of Low Energy PointsElimination of Low Energy Points
0510 AM 57
- Blind Separation of Speech Mixtures
- Introduction
- Slide 3
- Slide 4
- Slide 5
- Approaches for BSS of Speech Signals
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Permutation Problem in Frequency Domain BSS
- Motivation
- My Contribution - I
- Algorithm for Solving the Permutation Problem
- Existing Method for Solving the Permutation Problem
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Proposed algorithm Partial separation method (Parallel configuration) Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
- Partial separation method (Parallel configuration)
- Partial separation method (Cascade configuration)
- Advantages of Partial Separation method
- Comparison with Adjacent Bands Correlation Method
- Comparison with DOA method
- My Contribution -II
- Underdetermined Blind Source Separation of Instantaneous Mixtures
- Mathematical Representation of Instantaneous Mixing Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
- Single Source Points in Time-Frequency domain
- Slide 31
- Slide 32
- Scatter Diagram of the Mixtures When Source are Perfectly Sparse
- Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
- Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
- Principle of the Proposed Algorithm for the Detection of Single Source Points
- Slide 39
- Slide 40
- Proposed Algorithm for the Detection of Single Source Points
- Elimination of Outliers
- Slide 43
- Detected Single Source Points Three mixtures
- Comparison with Classical Algorithms for Determined Case
- Comparison with Method Proposed in [1] Underdetermined case
- Advantages of the Proposed algorithm
- My Contributions ndash III IV and V
- Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
- Mathematical Representation
- Single source points
- Basic Principle of Single Source Points Detection
- Algorithm for Single Source Points Detection
- Mask Estimation by k-means (KM)
- Mask Estimation by Fuzzy c-means (FCM)
- Automatic Detection of Number of Sources
- Elimination of Low Energy Points
-
k
Algorithm for Single Source Points Detection
Algorithm for Single Source Points Detection
t
k
tkX 1
tkX 22x
1x
)( 111 tkX
)( 112 tkX
)(
)(
)(111
121
111 tkSkH
kH
11
11
j
jr
)(
)(
112
111
tkX
tkX
11
11
j
jr
)(
)(
112
111
tkX
tkX
)( 111 tkX
)( 112 tkX
)(
)(
)(112
122
112 tkSkH
kH θH2
θH1
θH2
rX
rX
)(
)(cos
11
111
tk
tk H
Hq
0510 AM 53
θH1
OR
1k
1k
1t
Clean
Estimated
Mask Estimation by k-means (KM)Mask Estimation by k-means (KM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 54
Clean
Estimated
Mask Estimation by Fuzzy c-means (FCM)Mask Estimation by Fuzzy c-means (FCM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 55
Automatic Detection of Number of SourcesAutomatic Detection of Number of Sources
0510 AM 56
Cluster validation technique
For c = 2 to cmax
Cluster the data into c clustersCalculate the cluster validation index
EndTake c corresponding to the best cluster as the number of sources
-gt
Elimination of Low Energy PointsElimination of Low Energy Points
0510 AM 57
- Blind Separation of Speech Mixtures
- Introduction
- Slide 3
- Slide 4
- Slide 5
- Approaches for BSS of Speech Signals
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Permutation Problem in Frequency Domain BSS
- Motivation
- My Contribution - I
- Algorithm for Solving the Permutation Problem
- Existing Method for Solving the Permutation Problem
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Proposed algorithm Partial separation method (Parallel configuration) Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
- Partial separation method (Parallel configuration)
- Partial separation method (Cascade configuration)
- Advantages of Partial Separation method
- Comparison with Adjacent Bands Correlation Method
- Comparison with DOA method
- My Contribution -II
- Underdetermined Blind Source Separation of Instantaneous Mixtures
- Mathematical Representation of Instantaneous Mixing Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
- Single Source Points in Time-Frequency domain
- Slide 31
- Slide 32
- Scatter Diagram of the Mixtures When Source are Perfectly Sparse
- Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
- Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
- Principle of the Proposed Algorithm for the Detection of Single Source Points
- Slide 39
- Slide 40
- Proposed Algorithm for the Detection of Single Source Points
- Elimination of Outliers
- Slide 43
- Detected Single Source Points Three mixtures
- Comparison with Classical Algorithms for Determined Case
- Comparison with Method Proposed in [1] Underdetermined case
- Advantages of the Proposed algorithm
- My Contributions ndash III IV and V
- Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
- Mathematical Representation
- Single source points
- Basic Principle of Single Source Points Detection
- Algorithm for Single Source Points Detection
- Mask Estimation by k-means (KM)
- Mask Estimation by Fuzzy c-means (FCM)
- Automatic Detection of Number of Sources
- Elimination of Low Energy Points
-
Clean
Estimated
Mask Estimation by k-means (KM)Mask Estimation by k-means (KM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 54
Clean
Estimated
Mask Estimation by Fuzzy c-means (FCM)Mask Estimation by Fuzzy c-means (FCM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 55
Automatic Detection of Number of SourcesAutomatic Detection of Number of Sources
0510 AM 56
Cluster validation technique
For c = 2 to cmax
Cluster the data into c clustersCalculate the cluster validation index
EndTake c corresponding to the best cluster as the number of sources
-gt
Elimination of Low Energy PointsElimination of Low Energy Points
0510 AM 57
- Blind Separation of Speech Mixtures
- Introduction
- Slide 3
- Slide 4
- Slide 5
- Approaches for BSS of Speech Signals
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Permutation Problem in Frequency Domain BSS
- Motivation
- My Contribution - I
- Algorithm for Solving the Permutation Problem
- Existing Method for Solving the Permutation Problem
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Proposed algorithm Partial separation method (Parallel configuration) Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
- Partial separation method (Parallel configuration)
- Partial separation method (Cascade configuration)
- Advantages of Partial Separation method
- Comparison with Adjacent Bands Correlation Method
- Comparison with DOA method
- My Contribution -II
- Underdetermined Blind Source Separation of Instantaneous Mixtures
- Mathematical Representation of Instantaneous Mixing Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
- Single Source Points in Time-Frequency domain
- Slide 31
- Slide 32
- Scatter Diagram of the Mixtures When Source are Perfectly Sparse
- Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
- Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
- Principle of the Proposed Algorithm for the Detection of Single Source Points
- Slide 39
- Slide 40
- Proposed Algorithm for the Detection of Single Source Points
- Elimination of Outliers
- Slide 43
- Detected Single Source Points Three mixtures
- Comparison with Classical Algorithms for Determined Case
- Comparison with Method Proposed in [1] Underdetermined case
- Advantages of the Proposed algorithm
- My Contributions ndash III IV and V
- Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
- Mathematical Representation
- Single source points
- Basic Principle of Single Source Points Detection
- Algorithm for Single Source Points Detection
- Mask Estimation by k-means (KM)
- Mask Estimation by Fuzzy c-means (FCM)
- Automatic Detection of Number of Sources
- Elimination of Low Energy Points
-
Clean
Estimated
Mask Estimation by Fuzzy c-means (FCM)Mask Estimation by Fuzzy c-means (FCM)
QqttkXtkMtkY pqq 1)()()(
0510 AM 55
Automatic Detection of Number of SourcesAutomatic Detection of Number of Sources
0510 AM 56
Cluster validation technique
For c = 2 to cmax
Cluster the data into c clustersCalculate the cluster validation index
EndTake c corresponding to the best cluster as the number of sources
-gt
Elimination of Low Energy PointsElimination of Low Energy Points
0510 AM 57
- Blind Separation of Speech Mixtures
- Introduction
- Slide 3
- Slide 4
- Slide 5
- Approaches for BSS of Speech Signals
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Permutation Problem in Frequency Domain BSS
- Motivation
- My Contribution - I
- Algorithm for Solving the Permutation Problem
- Existing Method for Solving the Permutation Problem
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Proposed algorithm Partial separation method (Parallel configuration) Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
- Partial separation method (Parallel configuration)
- Partial separation method (Cascade configuration)
- Advantages of Partial Separation method
- Comparison with Adjacent Bands Correlation Method
- Comparison with DOA method
- My Contribution -II
- Underdetermined Blind Source Separation of Instantaneous Mixtures
- Mathematical Representation of Instantaneous Mixing Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
- Single Source Points in Time-Frequency domain
- Slide 31
- Slide 32
- Scatter Diagram of the Mixtures When Source are Perfectly Sparse
- Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
- Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
- Principle of the Proposed Algorithm for the Detection of Single Source Points
- Slide 39
- Slide 40
- Proposed Algorithm for the Detection of Single Source Points
- Elimination of Outliers
- Slide 43
- Detected Single Source Points Three mixtures
- Comparison with Classical Algorithms for Determined Case
- Comparison with Method Proposed in [1] Underdetermined case
- Advantages of the Proposed algorithm
- My Contributions ndash III IV and V
- Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
- Mathematical Representation
- Single source points
- Basic Principle of Single Source Points Detection
- Algorithm for Single Source Points Detection
- Mask Estimation by k-means (KM)
- Mask Estimation by Fuzzy c-means (FCM)
- Automatic Detection of Number of Sources
- Elimination of Low Energy Points
-
Automatic Detection of Number of SourcesAutomatic Detection of Number of Sources
0510 AM 56
Cluster validation technique
For c = 2 to cmax
Cluster the data into c clustersCalculate the cluster validation index
EndTake c corresponding to the best cluster as the number of sources
-gt
Elimination of Low Energy PointsElimination of Low Energy Points
0510 AM 57
- Blind Separation of Speech Mixtures
- Introduction
- Slide 3
- Slide 4
- Slide 5
- Approaches for BSS of Speech Signals
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Permutation Problem in Frequency Domain BSS
- Motivation
- My Contribution - I
- Algorithm for Solving the Permutation Problem
- Existing Method for Solving the Permutation Problem
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Proposed algorithm Partial separation method (Parallel configuration) Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
- Partial separation method (Parallel configuration)
- Partial separation method (Cascade configuration)
- Advantages of Partial Separation method
- Comparison with Adjacent Bands Correlation Method
- Comparison with DOA method
- My Contribution -II
- Underdetermined Blind Source Separation of Instantaneous Mixtures
- Mathematical Representation of Instantaneous Mixing Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
- Single Source Points in Time-Frequency domain
- Slide 31
- Slide 32
- Scatter Diagram of the Mixtures When Source are Perfectly Sparse
- Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
- Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
- Principle of the Proposed Algorithm for the Detection of Single Source Points
- Slide 39
- Slide 40
- Proposed Algorithm for the Detection of Single Source Points
- Elimination of Outliers
- Slide 43
- Detected Single Source Points Three mixtures
- Comparison with Classical Algorithms for Determined Case
- Comparison with Method Proposed in [1] Underdetermined case
- Advantages of the Proposed algorithm
- My Contributions ndash III IV and V
- Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
- Mathematical Representation
- Single source points
- Basic Principle of Single Source Points Detection
- Algorithm for Single Source Points Detection
- Mask Estimation by k-means (KM)
- Mask Estimation by Fuzzy c-means (FCM)
- Automatic Detection of Number of Sources
- Elimination of Low Energy Points
-
Elimination of Low Energy PointsElimination of Low Energy Points
0510 AM 57
- Blind Separation of Speech Mixtures
- Introduction
- Slide 3
- Slide 4
- Slide 5
- Approaches for BSS of Speech Signals
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Permutation Problem in Frequency Domain BSS
- Motivation
- My Contribution - I
- Algorithm for Solving the Permutation Problem
- Existing Method for Solving the Permutation Problem
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Proposed algorithm Partial separation method (Parallel configuration) Reference V G Reju S N Koh and I Y Soon ldquoPartial separation method for solving permutation problem in frequency domain blind source separation of speech signalsrdquo Neurocomputing Vol 71 NO 10ndash12 June 2008 pp 2098ndash2112
- Partial separation method (Parallel configuration)
- Partial separation method (Cascade configuration)
- Advantages of Partial Separation method
- Comparison with Adjacent Bands Correlation Method
- Comparison with DOA method
- My Contribution -II
- Underdetermined Blind Source Separation of Instantaneous Mixtures
- Mathematical Representation of Instantaneous Mixing Reference V G Reju S N Koh and I Y Soon ldquoAn algorithm for mixing matrix estimation in instantaneous blind source separationrdquo Signal Processing Vol 89 Issue 9 September 2009 pp 1762ndash1773
- Single Source Points in Time-Frequency domain
- Slide 31
- Slide 32
- Scatter Diagram of the Mixtures When Source are Perfectly Sparse
- Scatter Diagram of the Mixtures When Source are Not Perfectly Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse
- Scatter Diagram of the Mixtures when Sources are Sparse After Clustering
- Scatter Diagram of the Mixtures when Sources are Not Perfectly Sparse
- Principle of the Proposed Algorithm for the Detection of Single Source Points
- Slide 39
- Slide 40
- Proposed Algorithm for the Detection of Single Source Points
- Elimination of Outliers
- Slide 43
- Detected Single Source Points Three mixtures
- Comparison with Classical Algorithms for Determined Case
- Comparison with Method Proposed in [1] Underdetermined case
- Advantages of the Proposed algorithm
- My Contributions ndash III IV and V
- Underdetermined Convolutive Blind Source Separation via Time-Frequency Masking Reference V G Reju S N Koh and I Y Soon ldquoUnderdetermined Convolutive Blind Source Separation via Time- Frequency Maskingrdquo IEEE Transactions on Audio Speech and Language Processing Vol 18 NO 1 Jan 2010 pp 101ndash116
- Mathematical Representation
- Single source points
- Basic Principle of Single Source Points Detection
- Algorithm for Single Source Points Detection
- Mask Estimation by k-means (KM)
- Mask Estimation by Fuzzy c-means (FCM)
- Automatic Detection of Number of Sources
- Elimination of Low Energy Points
-
![Blind Source Separation of Convolutive Mixtures of Speech ...maki/reprint/Makino/sm05ieice1640-1655.pdf · Blind source separation (BSS) [1]–[3] is an approach for estimating source](https://static.fdocuments.net/doc/165x107/5e497388391cea583a5234cc/blind-source-separation-of-convolutive-mixtures-of-speech-makireprintmakinosm05ieice1640-1655pdf.jpg)
