3.Wavelet Transform(Backup slide-3)
-
Upload
nashid-alam -
Category
Education
-
view
215 -
download
5
Transcript of 3.Wavelet Transform(Backup slide-3)
![Page 1: 3.Wavelet Transform(Backup slide-3)](https://reader031.fdocuments.net/reader031/viewer/2022031912/55a6ca1e1a28ab531d8b4805/html5/thumbnails/1.jpg)
Wavelet Transformation
Department of Computer Science And Engineering
Shahjalal University of Science and Technology
Nashid AlamRegistration No: 2012321028
[email protected] -2 Presentation
(Backup Slides# 3)
Courtesy :
Prof. Fred HamprechtHeidelberg University
Source:https://www.youtube.com/watch?v=DGUuJweHamQ
![Page 2: 3.Wavelet Transform(Backup slide-3)](https://reader031.fdocuments.net/reader031/viewer/2022031912/55a6ca1e1a28ab531d8b4805/html5/thumbnails/2.jpg)
Wavelet
![Page 3: 3.Wavelet Transform(Backup slide-3)](https://reader031.fdocuments.net/reader031/viewer/2022031912/55a6ca1e1a28ab531d8b4805/html5/thumbnails/3.jpg)
Wavelet
Working with wavelet:1. Convolve the signal with wavelet filter(h/g)2. Store the results in coefficients/frequency response
(Result in number is put in the boxes)3. Coefficients/frequency response:
- The representation of the signal in the new domain.
Properties:• Maximum frequency depends on the length of the signal.• Recursive partitioning of the lowest band in subjective to the application.
Details in upcoming slides
![Page 4: 3.Wavelet Transform(Backup slide-3)](https://reader031.fdocuments.net/reader031/viewer/2022031912/55a6ca1e1a28ab531d8b4805/html5/thumbnails/4.jpg)
Good temper resolution in high frequencies
Good frequency resolution in low pass band
OBTAION:
Wavelet
A high pass filter
Temper resolution : A vertical high-resolutionFrequency resolution : The sample frequency divided by the number of samples
O/P of Low Pass Filter High Pass Filter = A Band Pass Result
![Page 5: 3.Wavelet Transform(Backup slide-3)](https://reader031.fdocuments.net/reader031/viewer/2022031912/55a6ca1e1a28ab531d8b4805/html5/thumbnails/5.jpg)
1.A length 8 signal
3.Convolve the signal with the high pass filter
2.Split/divide the signal in two parts
Wavelet
![Page 6: 3.Wavelet Transform(Backup slide-3)](https://reader031.fdocuments.net/reader031/viewer/2022031912/55a6ca1e1a28ab531d8b4805/html5/thumbnails/6.jpg)
To avoid redundancy
Down sample by 2
Wavelet
![Page 7: 3.Wavelet Transform(Backup slide-3)](https://reader031.fdocuments.net/reader031/viewer/2022031912/55a6ca1e1a28ab531d8b4805/html5/thumbnails/7.jpg)
• For perfect low pass filter• Leave everything intact in 0 (zero)
Spectrodensity of the signal at this point
Unit cell
Unit cell is shrunk by half(1/2)
Wavelet
No information loss due to shrinking
First partitioning of lower and higher frequency band
![Page 8: 3.Wavelet Transform(Backup slide-3)](https://reader031.fdocuments.net/reader031/viewer/2022031912/55a6ca1e1a28ab531d8b4805/html5/thumbnails/8.jpg)
Wavelet
Spectrodensity of the signal at this point
For perfect low pass filter For perfect high pass filter
This works even not for perfect high pass/low pass filter
![Page 9: 3.Wavelet Transform(Backup slide-3)](https://reader031.fdocuments.net/reader031/viewer/2022031912/55a6ca1e1a28ab531d8b4805/html5/thumbnails/9.jpg)
Wavelet
Split the signalAnd
down-sample by 2In high frequency
Details at level 1
![Page 10: 3.Wavelet Transform(Backup slide-3)](https://reader031.fdocuments.net/reader031/viewer/2022031912/55a6ca1e1a28ab531d8b4805/html5/thumbnails/10.jpg)
Wavelet
Split inthe low frequency
Details at level 2
![Page 11: 3.Wavelet Transform(Backup slide-3)](https://reader031.fdocuments.net/reader031/viewer/2022031912/55a6ca1e1a28ab531d8b4805/html5/thumbnails/11.jpg)
Wavelet
Extra Split inthe low frequency
Details at level 3
![Page 12: 3.Wavelet Transform(Backup slide-3)](https://reader031.fdocuments.net/reader031/viewer/2022031912/55a6ca1e1a28ab531d8b4805/html5/thumbnails/12.jpg)
Wavelet
Approximationat level 3
Approximationat level 2
Approximationat level 1
![Page 13: 3.Wavelet Transform(Backup slide-3)](https://reader031.fdocuments.net/reader031/viewer/2022031912/55a6ca1e1a28ab531d8b4805/html5/thumbnails/13.jpg)
Wavelet
Works for Signals of 8 samples
23= 8, Sample=8, level=3.
![Page 14: 3.Wavelet Transform(Backup slide-3)](https://reader031.fdocuments.net/reader031/viewer/2022031912/55a6ca1e1a28ab531d8b4805/html5/thumbnails/14.jpg)
Wavelet
Positive half of the
frequency axis
1
1 2 3 4
![Page 15: 3.Wavelet Transform(Backup slide-3)](https://reader031.fdocuments.net/reader031/viewer/2022031912/55a6ca1e1a28ab531d8b4805/html5/thumbnails/15.jpg)
Wavelet
Positive half of the
frequency axis
2
1 21
1 2 3 4
![Page 16: 3.Wavelet Transform(Backup slide-3)](https://reader031.fdocuments.net/reader031/viewer/2022031912/55a6ca1e1a28ab531d8b4805/html5/thumbnails/16.jpg)
Wavelet
Positive half
of
the frequency axis
31
2
1 21
1 2 3 4
![Page 17: 3.Wavelet Transform(Backup slide-3)](https://reader031.fdocuments.net/reader031/viewer/2022031912/55a6ca1e1a28ab531d8b4805/html5/thumbnails/17.jpg)
Wavelet
Positive half
of
the frequency axis
Details at level 2
Details at level 3
Detailsat
level 1
Approximation
Good frequency resolution in low pass band
![Page 18: 3.Wavelet Transform(Backup slide-3)](https://reader031.fdocuments.net/reader031/viewer/2022031912/55a6ca1e1a28ab531d8b4805/html5/thumbnails/18.jpg)
Wavelet
Filter response/Coefficientof
perfect bandpass filter
Wavelet Behaving
as bandpass
![Page 19: 3.Wavelet Transform(Backup slide-3)](https://reader031.fdocuments.net/reader031/viewer/2022031912/55a6ca1e1a28ab531d8b4805/html5/thumbnails/19.jpg)
Wavelet
Filter response/Coefficientof
Practically used wavelet filter
Collect the low frequencies
High frequencies
Wavelet Behaving
as bandpass
![Page 20: 3.Wavelet Transform(Backup slide-3)](https://reader031.fdocuments.net/reader031/viewer/2022031912/55a6ca1e1a28ab531d8b4805/html5/thumbnails/20.jpg)
Wavelet
Filter response/Coefficientof
Practically used wavelet filter
Modular square ofThese transfer
function Add up to 1.
Prevent Loosing
signal/energy
To
Wavelet Behaving
as bandpass
![Page 21: 3.Wavelet Transform(Backup slide-3)](https://reader031.fdocuments.net/reader031/viewer/2022031912/55a6ca1e1a28ab531d8b4805/html5/thumbnails/21.jpg)
Code Fragments to do the task
% Extract the level 1 coefficients.
a1 = appcoef2(wc,s,wname,1);
h1 = detcoef2('h',wc,s,1);
v1 = detcoef2('v',wc,s,1);
d1 = detcoef2('d',wc,s,1);
% Display the decomposition up to level 1 only. ncolors = size(map,1); % Number of colors.
sz = size(X);
cod_a1 = wcodemat(a1,ncolors);
cod_a1 = wkeep(cod_a1, sz/2);
cod_h1 = wcodemat(h1,ncolors);
cod_h1 = wkeep(cod_h1, sz/2);
cod_v1 = wcodemat(v1,ncolors);
cod_v1 = wkeep(cod_v1, sz/2);
cod_d1 = wcodemat(d1,ncolors);
cod_d1 = wkeep(cod_d1, sz/2);
image([cod_a1,cod_h1;cod_v1,cod_d1]);
axis image; set(gca,'XTick',[],'YTick',[]);
title('Single stage decomposition')
colormap(map)
pause
% Here are the reconstructed branches
ra2 = wrcoef2('a',wc,s,wname,2);
rh2 = wrcoef2('h',wc,s,wname,2);
rv2 = wrcoef2('v',wc,s,wname,2);
rd2 = wrcoef2('d',wc,s,wname,2);
Wavelet
![Page 22: 3.Wavelet Transform(Backup slide-3)](https://reader031.fdocuments.net/reader031/viewer/2022031912/55a6ca1e1a28ab531d8b4805/html5/thumbnails/22.jpg)
Wavelet
Transfer function of
The wavelets
Transfer function of
The Scaling function
![Page 23: 3.Wavelet Transform(Backup slide-3)](https://reader031.fdocuments.net/reader031/viewer/2022031912/55a6ca1e1a28ab531d8b4805/html5/thumbnails/23.jpg)
Wavelet
Want to understand The effect of this label
Have to perform convolution
Understand The effect of each this label
![Page 24: 3.Wavelet Transform(Backup slide-3)](https://reader031.fdocuments.net/reader031/viewer/2022031912/55a6ca1e1a28ab531d8b4805/html5/thumbnails/24.jpg)
Wavelet
Graph 01: Transfer functions of the wavelet transforms
Works for Signals more then 8 samples 23= 8, Sample=8, level=3.
Level 1details
Level 2details
Level 3details
Level 4details
Level 5details
Transfer functions of
Approximation:The low pass
result That we keep at
the end
![Page 25: 3.Wavelet Transform(Backup slide-3)](https://reader031.fdocuments.net/reader031/viewer/2022031912/55a6ca1e1a28ab531d8b4805/html5/thumbnails/25.jpg)
Wavelet
Graph 01: Transfer functions of the wavelet transforms
Leveldetails
+ approximation= 1
Property of wavelet
![Page 26: 3.Wavelet Transform(Backup slide-3)](https://reader031.fdocuments.net/reader031/viewer/2022031912/55a6ca1e1a28ab531d8b4805/html5/thumbnails/26.jpg)
Wavelet
Approximation is a sinc- A perfect low pass filter
sincA-sincBA=A frequencyB=A frequency
-A perfect bandpass filter
![Page 27: 3.Wavelet Transform(Backup slide-3)](https://reader031.fdocuments.net/reader031/viewer/2022031912/55a6ca1e1a28ab531d8b4805/html5/thumbnails/27.jpg)
Wavelet
Signal withmore than
eight samplesScenario:
Temper resolution : A vertical high-resolutionFrequency resolution : The sample frequency divided by the number of samples
Temper resolution>Frequency resolution
Increasingfrequency resolution
Decreasestemporal resolution.
![Page 28: 3.Wavelet Transform(Backup slide-3)](https://reader031.fdocuments.net/reader031/viewer/2022031912/55a6ca1e1a28ab531d8b4805/html5/thumbnails/28.jpg)
Discrete Wavelet Transform(DWT)
![Page 29: 3.Wavelet Transform(Backup slide-3)](https://reader031.fdocuments.net/reader031/viewer/2022031912/55a6ca1e1a28ab531d8b4805/html5/thumbnails/29.jpg)
Discrete Wavelet Transform(DWT)
Requires a wavelet ,Ψ(t), such that:- It scales and shifts
from an orthonormal basis of the square integral function.
)2/)2((2
1)(, jt
jt n
jnj
Scale Shift
Denote Wavelet
j and n both are integer
nmjlmlnj ., ,, To offer an orthonormal basis:)(, tnj
Orthonormal basis: A vector space basis for the space it spans.
.
.
![Page 30: 3.Wavelet Transform(Backup slide-3)](https://reader031.fdocuments.net/reader031/viewer/2022031912/55a6ca1e1a28ab531d8b4805/html5/thumbnails/30.jpg)
Discrete Wavelet Transform(DWT)
Basis Function
Wavelets,ΨBasis function : An element of a particular basis for a function space
Scaling Function,Ψ
![Page 31: 3.Wavelet Transform(Backup slide-3)](https://reader031.fdocuments.net/reader031/viewer/2022031912/55a6ca1e1a28ab531d8b4805/html5/thumbnails/31.jpg)
Discrete Wavelet Transform(DWT)
With each label:By shifting-
+
+
-
Shift
Inter-product is zero
Wavelets are orthogonal
![Page 32: 3.Wavelet Transform(Backup slide-3)](https://reader031.fdocuments.net/reader031/viewer/2022031912/55a6ca1e1a28ab531d8b4805/html5/thumbnails/32.jpg)
Discrete Wavelet Transform(DWT)
Details at level 1 Scale factor , j =2, 22 =4
![Page 33: 3.Wavelet Transform(Backup slide-3)](https://reader031.fdocuments.net/reader031/viewer/2022031912/55a6ca1e1a28ab531d8b4805/html5/thumbnails/33.jpg)
Discrete Wavelet Transform(DWT)
Details at level 2
Scale factor , j =1, 21 =2
![Page 34: 3.Wavelet Transform(Backup slide-3)](https://reader031.fdocuments.net/reader031/viewer/2022031912/55a6ca1e1a28ab531d8b4805/html5/thumbnails/34.jpg)
Discrete Wavelet Transform(DWT)
Details at level 3
Scale factor , j =0, 20 =1
![Page 35: 3.Wavelet Transform(Backup slide-3)](https://reader031.fdocuments.net/reader031/viewer/2022031912/55a6ca1e1a28ab531d8b4805/html5/thumbnails/35.jpg)
Discrete Wavelet Transform(DWT)
ApproximationLow
frequency
No Scale factor
![Page 36: 3.Wavelet Transform(Backup slide-3)](https://reader031.fdocuments.net/reader031/viewer/2022031912/55a6ca1e1a28ab531d8b4805/html5/thumbnails/36.jpg)
Daubchies’ Wavelet (DW)
![Page 37: 3.Wavelet Transform(Backup slide-3)](https://reader031.fdocuments.net/reader031/viewer/2022031912/55a6ca1e1a28ab531d8b4805/html5/thumbnails/37.jpg)
Daubchies’ Wavelet (DW)
•H()=high pass filter•D4=Daubchies’ Tap 4 Filter•Not symmetrical
Initial shape
![Page 38: 3.Wavelet Transform(Backup slide-3)](https://reader031.fdocuments.net/reader031/viewer/2022031912/55a6ca1e1a28ab531d8b4805/html5/thumbnails/38.jpg)
![Page 39: 3.Wavelet Transform(Backup slide-3)](https://reader031.fdocuments.net/reader031/viewer/2022031912/55a6ca1e1a28ab531d8b4805/html5/thumbnails/39.jpg)
Backward transformation of Wavelets
Opposite of forward transformationMirror the forward transformation on the right hand sideReplace the down-sampling by up-sampling.
Signal
Wavelettransform
of the Signal
Wavelettransform
of the Signal
Signal
![Page 40: 3.Wavelet Transform(Backup slide-3)](https://reader031.fdocuments.net/reader031/viewer/2022031912/55a6ca1e1a28ab531d8b4805/html5/thumbnails/40.jpg)
2D Wavelet Transform
Scaling function Wavelet
2Πk1 =ω1
2Πk2 =ω2
Low pass filter
![Page 41: 3.Wavelet Transform(Backup slide-3)](https://reader031.fdocuments.net/reader031/viewer/2022031912/55a6ca1e1a28ab531d8b4805/html5/thumbnails/41.jpg)
2D Wavelet Transform
High pass filter
Scaling function Wavelet
![Page 42: 3.Wavelet Transform(Backup slide-3)](https://reader031.fdocuments.net/reader031/viewer/2022031912/55a6ca1e1a28ab531d8b4805/html5/thumbnails/42.jpg)
Use Separable Transform
2D Wavelet Transform
Originalimage
![Page 43: 3.Wavelet Transform(Backup slide-3)](https://reader031.fdocuments.net/reader031/viewer/2022031912/55a6ca1e1a28ab531d8b4805/html5/thumbnails/43.jpg)
hx = High pass filter(X-direction)
gx = low pass filter(X-direction)
Use Separable Transform
2D Wavelet Transform
![Page 44: 3.Wavelet Transform(Backup slide-3)](https://reader031.fdocuments.net/reader031/viewer/2022031912/55a6ca1e1a28ab531d8b4805/html5/thumbnails/44.jpg)
hxy = High pass filter(y-direction)
Use Separable Transform
2D Wavelet Transform
![Page 45: 3.Wavelet Transform(Backup slide-3)](https://reader031.fdocuments.net/reader031/viewer/2022031912/55a6ca1e1a28ab531d8b4805/html5/thumbnails/45.jpg)
gy = low pass filter(y-direction)
Use Separable Transform
2D Wavelet Transform
![Page 46: 3.Wavelet Transform(Backup slide-3)](https://reader031.fdocuments.net/reader031/viewer/2022031912/55a6ca1e1a28ab531d8b4805/html5/thumbnails/46.jpg)
Use Separable Transform
2D Wavelet Transform
Further split
![Page 47: 3.Wavelet Transform(Backup slide-3)](https://reader031.fdocuments.net/reader031/viewer/2022031912/55a6ca1e1a28ab531d8b4805/html5/thumbnails/47.jpg)
Use Separable Transform
2D Wavelet Transform
hy = High pass filter(y-direction)
![Page 48: 3.Wavelet Transform(Backup slide-3)](https://reader031.fdocuments.net/reader031/viewer/2022031912/55a6ca1e1a28ab531d8b4805/html5/thumbnails/48.jpg)
Use Separable Transform
2D Wavelet Transform
hy = Low pass filter(y-direction)
![Page 49: 3.Wavelet Transform(Backup slide-3)](https://reader031.fdocuments.net/reader031/viewer/2022031912/55a6ca1e1a28ab531d8b4805/html5/thumbnails/49.jpg)
Use Separable Transform
2D Wavelet Transform
Four region:
Blue= Diagonal Details at label 1
Green=Horizontal Details at label 1
Purple=vertical details at label 1
Yellow= Approximation at Label 1(Low pass in both x and y direction)
![Page 50: 3.Wavelet Transform(Backup slide-3)](https://reader031.fdocuments.net/reader031/viewer/2022031912/55a6ca1e1a28ab531d8b4805/html5/thumbnails/50.jpg)
Use Separable Transform
2D Wavelet Transform
Doing the above steps recursively:Take the current approximation
![Page 51: 3.Wavelet Transform(Backup slide-3)](https://reader031.fdocuments.net/reader031/viewer/2022031912/55a6ca1e1a28ab531d8b4805/html5/thumbnails/51.jpg)
Use Separable Transform
2D Wavelet Transform
Doing the above steps recursively:1. Take the current approximation2. And further split it up
![Page 52: 3.Wavelet Transform(Backup slide-3)](https://reader031.fdocuments.net/reader031/viewer/2022031912/55a6ca1e1a28ab531d8b4805/html5/thumbnails/52.jpg)
Use Separable Transform
2D Wavelet Transform
Doing the above steps recursively:1. Take the current approximation2. And further split it up
![Page 53: 3.Wavelet Transform(Backup slide-3)](https://reader031.fdocuments.net/reader031/viewer/2022031912/55a6ca1e1a28ab531d8b4805/html5/thumbnails/53.jpg)
Use Separable Transform
2D Wavelet Transform
New approximation
Doing the above steps recursively:1. Take the current approximation2. And further split it up3. Getting new approximation
![Page 54: 3.Wavelet Transform(Backup slide-3)](https://reader031.fdocuments.net/reader031/viewer/2022031912/55a6ca1e1a28ab531d8b4805/html5/thumbnails/54.jpg)
Use Separable Transform
2D Wavelet Transform
Diagonal Details
Horizontal Details
vertical details
Approximation(can be furtherdecomposed)
In summary
![Page 55: 3.Wavelet Transform(Backup slide-3)](https://reader031.fdocuments.net/reader031/viewer/2022031912/55a6ca1e1a28ab531d8b4805/html5/thumbnails/55.jpg)
Use Separable Transform
2D Wavelet Transform
In summary
Approximation(can be furtherdecomposed)
![Page 56: 3.Wavelet Transform(Backup slide-3)](https://reader031.fdocuments.net/reader031/viewer/2022031912/55a6ca1e1a28ab531d8b4805/html5/thumbnails/56.jpg)
Use Separable Transform
2D Wavelet Transform
Visualization
Label ofapproximation
HorizontalDetails
HorizontalDetails
VerticalDetails
DiagonalDetails
VerticalDetails
DiagonalDetails
![Page 57: 3.Wavelet Transform(Backup slide-3)](https://reader031.fdocuments.net/reader031/viewer/2022031912/55a6ca1e1a28ab531d8b4805/html5/thumbnails/57.jpg)
Use Separable Transform
2D Wavelet Transform
VisualizationLabel of approximation:• Very strong low pass filter• Few pixels
![Page 58: 3.Wavelet Transform(Backup slide-3)](https://reader031.fdocuments.net/reader031/viewer/2022031912/55a6ca1e1a28ab531d8b4805/html5/thumbnails/58.jpg)
Use Separable Transform
2D Wavelet Transform
Visualization
Details in
Various Scale
![Page 59: 3.Wavelet Transform(Backup slide-3)](https://reader031.fdocuments.net/reader031/viewer/2022031912/55a6ca1e1a28ab531d8b4805/html5/thumbnails/59.jpg)
Use Separable Transform
2D Wavelet Transform
Visualization
vertical details ->Shoulder
Horizontal Details ->Edges
Diagonal Details
![Page 60: 3.Wavelet Transform(Backup slide-3)](https://reader031.fdocuments.net/reader031/viewer/2022031912/55a6ca1e1a28ab531d8b4805/html5/thumbnails/60.jpg)
Use Separable Transform
2D Wavelet Transform
More precise
Visualization
Original image:Gray square on a Black Background
Diagonal Details
Horizontal Details(row by row)
Vertical details(column by column)
![Page 61: 3.Wavelet Transform(Backup slide-3)](https://reader031.fdocuments.net/reader031/viewer/2022031912/55a6ca1e1a28ab531d8b4805/html5/thumbnails/61.jpg)
Use Separable Transform
2D Wavelet Transform
Toy of original image
![Page 62: 3.Wavelet Transform(Backup slide-3)](https://reader031.fdocuments.net/reader031/viewer/2022031912/55a6ca1e1a28ab531d8b4805/html5/thumbnails/62.jpg)
Use Separable Transform
2D Wavelet Transform
Decomposition at Label 4
Original image
![Page 63: 3.Wavelet Transform(Backup slide-3)](https://reader031.fdocuments.net/reader031/viewer/2022031912/55a6ca1e1a28ab531d8b4805/html5/thumbnails/63.jpg)
Use Separable Transform
2D Wavelet Transform
Decomposition at Label 4
Original image(with diagonal details areas indicated)
Diagonal Details
![Page 64: 3.Wavelet Transform(Backup slide-3)](https://reader031.fdocuments.net/reader031/viewer/2022031912/55a6ca1e1a28ab531d8b4805/html5/thumbnails/64.jpg)
Use Separable Transform
2D Wavelet Transform
Vertical Details
Decomposition at Label 4
Original image(with Vertical details areas indicated)
![Page 65: 3.Wavelet Transform(Backup slide-3)](https://reader031.fdocuments.net/reader031/viewer/2022031912/55a6ca1e1a28ab531d8b4805/html5/thumbnails/65.jpg)
Experimental Results
![Page 66: 3.Wavelet Transform(Backup slide-3)](https://reader031.fdocuments.net/reader031/viewer/2022031912/55a6ca1e1a28ab531d8b4805/html5/thumbnails/66.jpg)
Experimental Results
DWT
1.Original Image(Malignent_mdb238) 2.Decomposition at Label 4
2.Decomposition at Label 1 3.Decomposition at Label 2 3.Decomposition at Label 3
![Page 67: 3.Wavelet Transform(Backup slide-3)](https://reader031.fdocuments.net/reader031/viewer/2022031912/55a6ca1e1a28ab531d8b4805/html5/thumbnails/67.jpg)
Experimental Results
DWT
1.Original Image(Malignent_mdb238) 2.Decomposition at Label 4
![Page 68: 3.Wavelet Transform(Backup slide-3)](https://reader031.fdocuments.net/reader031/viewer/2022031912/55a6ca1e1a28ab531d8b4805/html5/thumbnails/68.jpg)
Experimental Results
1.Original Image(Benign_mdb252)
2.Decomposition at Label 4
2.Decomposition at Label 1 3.Decomposition at Label 2 3.Decomposition at Label 3
DWT
![Page 69: 3.Wavelet Transform(Backup slide-3)](https://reader031.fdocuments.net/reader031/viewer/2022031912/55a6ca1e1a28ab531d8b4805/html5/thumbnails/69.jpg)
Experimental Results
1.Original Image(Malignent_mdb253.jpg) 2.Decomposition at Label 4
2.Decomposition at Label 1 3.Decomposition at Label 2 3.Decomposition at Label 3
![Page 70: 3.Wavelet Transform(Backup slide-3)](https://reader031.fdocuments.net/reader031/viewer/2022031912/55a6ca1e1a28ab531d8b4805/html5/thumbnails/70.jpg)
CT vs. DWT
DWT Target Goal:1.Applying a DWT to decompose a digital mammogram into different subbands.
2.The low-pass wavelet band is removed (set to zero) and the remaining coefficients are enhanced.
3.The inverse wavelet transform is applied to recoverthe enhanced mammogram containing microcalcifications [7].
7. Wang T. C and Karayiannis N. B.: Detection of Microcalcifications in Digital Mammograms Using Wavelets, IEEETransaction on Medical Imaging, vol. 17, no. 4, (1989) pp. 498-509
The results obtained by the Contourlet Transformation (CT)are compared with
The well-known method based on the discrete wavelet transform