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EMPIRICAL MODE DECOMPOSITION BASED

TECHNIQUE APPLIED IN EXPERIMENTAL

BIOSIGNALS

Alexandros Karagiannis

School of Electrical and Computer EngineeringNational Technical University of Athens

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RESPIRATION MONITORING

3

Acceleration Vector

Respiration Mechanism is comprised of

changes in some physical quantitiessuch as :

1. Muscular motion

2. Volume

3. Pressure

4. Flow

Muscular contraction is composed of

1. Low frequency movement related to

the whole contraction (0 - 5 Hz)

2. High frequency component due to

vibrations (2 40Hz)

X,Y,Z components of

acceleration vector

Acceleration

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EMPIRICAL MODE DECOMPOSITIONMethod for processing nonstationary signals and signals produced by nonlinear

processes

Decomposition of the signal into a set of Intrinsic Mode Functions (IMF) which are

defined as

1. Functions with equal number of extrema and zero crossings (or at most

differed by one)

2. Signal must have a zero-mean

Why Empirical Mode Decomposition?

To determine characteristic time/frequency scales for the energy

Nonlinear decomposition method for time series which are generated by an

underlying dynamical system obeying nonlinear equations

Basic Parts of the Empirical Mode Decomposition

1. Interpolation technique (cubic spline)

2. Sifting process to extract and identify intrinsic modes

3. Numerical convergence criteria (mainly to stop the iterative process of identifying

every IMF as well as the whole set of IMFs)

4

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EMPIRICAL MODE DECOMPOSITION ALGORITHM

1. Local maxima and minima of d0(t) = x(t).

2. Interpolate between the maxima and connect them by a cubic spline curve. The

same applies for the minima in order to obtain the upper and lower envelopes

eu(t) and el(t), respectively.

3. Compute the mean of the envelopes m(t):

4. Extract the detail d1 (t) = d0(t)-m(t) (sifting process)

5. Iterate steps 1-4 on the residual until the detail signal dk(t) can be considered an

IMF: c1(t)= d

k(t)

6. Iterate steps 1-5 on the residual rn(t)=x(t) - cn(t) in order to obtain all the IMFs

c1(t),.., cN(t) of the signal.

The procedure terminates when the residual signal is either a constant, a

monotonic slope, or a function with only one extrema.

5

( ) ( )( )

2

u le t e t

m t

!

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EMPIRICAL MODE DECOMPOSITION

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Mathematical Expression of EMD processed signal

Lower order IMFs capture fast oscillation modes while higher order IMFscapture slow oscillation modes

Criteria used for Numerical Convergence

1. The sifting process ends (IMF extraction) when the range of the mean

of the envelopes m(t) is lower than 1 (0.001) of Ci (Candidate IMF)

2. Iteration process ends when the residue r(t) is 10% or lower of the d(t)

IMF set residual

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EMPIRICAL MODE DECOMPOSITION BASED TECHNIQUE

ALGORITHM APPLIED ON BIOSIGNALS

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Apply spectral criteria on i-th IMF

EMD processed Experimental Respiratory Signal

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EMPIRICAL MODE DECOMPOSITION BASED

TECHNIQUE ALGORITHM APPLIED ON BIOSIGNALS

Experimental Procedure

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Respirationsignal sampled

from the mote

Respirationimported for

processing

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EMPIRICAL MODE DECOMPOSITION BASED

TECHNIQUE ALGORITHM APPLIED ON BIOSIGNALS

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1. Analog 2-axis Accelerometer

Experimental Setup

2. Multichannel Sampling of X, Y axes.Data are packed in one

Channel 1Channel 2

(X axis)

Channel 3

(Y axis)

00 FF FF FF FF 10 00 03 00 00 05 07 07 EB 06 0B 05 1F 07 E7 05 FF AC 4B

Source

GroupID

handler

3. Code developed in TinyOS-NesC oriented for event driven

applications.

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EMPIRICAL MODE DECOMPOSITION BASED TECHNIQUE

ALGORITHM APPLIED ON BIOSIGNAL

Processing Procedure1. Respiration signals were monitored in X,Y axes by measuring the

acceleration

2. Application of the EMD on each axis signal

3. Application of the spectral criteria on each IMF of 2-axes respiratory

signal

3. Evaluation of the EMD based technique was aided by metricscomputation (Cross Correlation Coefficients)

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data

EMD

Set of

IMF

Apply Spectral Criteria on

the IMF set

SelectIMF

Partial Signal

Reconstruction

Metric for overall

performance

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Application of EMD based technique in both X,Y axes signal from the 2-axis

accelerometer.

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EMPIRICAL MODE DECOMPOSITION BASED TECHNIQUE

ALGORITHM APPLIED ON BIOSIGNAL

Original Y axis signal

Lower order IMFs

Higher order IMFs

Residual signal

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EMPIRICAL MODE DECOMPOSITION BASED TECHNIQUE

ALGORITHM APPLIED ON BIOSIGNALS

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1. Decision Stage for the selection of appropriate IMFs computes the mean

power of the N max power peaks in order to have a smoother estimate

and more precise view of the power spectral density of each IMF

2. Axis components (X,Y,Z) magnitude is closely related to the measurement

point selection

3. Y axis component is significantly higher compared to X axis component inmeasurement point 1 and the opposite stands for measurement point 2

X,Y axes components.

Experimental Results

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EMPIRICAL MODE DECOMPOSITION BASED TECHNIQUE

ALGORITHM APPLIED ON BIOSIGNALS

Experimental Results

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1. Adaptive power threshold criterion (based on the max mean power and

minimum mean power of each IMF) produces a smaller number of IMFs

suitable for partial signal reconstruction. Rigid power thresholds (based on

the minimum of mean power of all IMFs) produce greater IMF set.

2. Different frequency ranges and power thresholds result in different IMF

sets.3. IMF sets produced by the adaptive power threshold stage suitable for

partial signal reconstruction have smaller correlation with the original axis

signal without compromising the characteristics of the signal. (Trade Off)

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EMPIRICAL MODE DECOMPOSITION BASED TECHNIQUE

ALGORITHM APPLIED ON BIOSIGNALS

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Experimental Results1. High frequency denoising due to removal from the IMF set of the lower

order IMFs is accomplished without altering the characteristic attributes

of the signal

2. Adaptive power threshold stage is more effective in filtering after the partial

signal reconstruction rather than rigid power thresholds. This is due to the

smaller IMF sets.

Measurement

point 2

X axis

Measurement

point 2

Y axis

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EMPIRICAL MODE DECOMPOSITION BASED TECHNIQUE

ALGORITHM APPLIED ON BIOSIGNALS

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Conclusions1. Empirical Mode Decomposition based technique that utilize the decomposition of

the signal to IMFs in order to apply a Partial Signal Reconstruction process

2. The proposed technique tries to identify and use at the partial signal

reconstruction stage those IMFs that may have a physical meaning.

3. Two stage process of the technique Decision based on the spectral

characteristics of the IMFs (frequency, power)

4. IMFs that satisfy conditions (frequency criterion, power criterion) are considered

for Partial Signal Reconstruction. The others are excluded.

5. Different conditions set by the criteria produce different IMF sets for the Partial

Signal Reconstruction

6. Mode mixing problem does not affect significantly the decision stage because ofthe disparate scales of the IMFs of the EMD processed respiratory signals.

7. EMD demands high computational and memory resources. A preprocessing stage

prior to the application of the technique reduce time and resource demands

without compromising signal quality

8. Future work : MIT-BIH records to apply the technique, lung sounds, Weighed

Partial Signal Reconstruction, Implementation on sensor network node level .

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Thank you

Metamorphosis by M.S.Escher