2-d wavelet analyses on sinograms
DESCRIPTION
2-D Wavelet analyses on sinograms. CSE 5780 Medical Imaging Florida Institute of Technology Fall 2012. FREQUENCY ANALYSIS. Frequency Spectrum Be basically the frequency components (spectral components) of that signal Show what frequencies exists in the signal Fourier Transform (FT) - PowerPoint PPT PresentationTRANSCRIPT
CSE 5780 Medical ImagingFlorida Institute of Technology
Fall 2012
Frequency Spectrum◦ Be basically the frequency components
(spectral components) of that signal◦ Show what frequencies exists in the signal
Fourier Transform (FT) ◦ One way to find the frequency content◦ Tells how much of each frequency exists in a
signal
knN
N
n
WnxkX
1
0
11
knN
N
k
WkXN
nx
1
0
11
1
Nj
N ew2
dtetxfX ftj2
dfefXtx ftj2
0 0.5 1-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0 5 10 15 20 250
50
100
150
Time
Ma
gn
itu
de
Ma
gn
itu
de
Frequency (Hz)0 0.5 1
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0 5 10 15 20 250
50
100
150
TimeM
ag
nit
ud
e
Ma
gn
itu
de
Frequency (Hz)
Different in Time Domain
Frequency: 2 Hz to 20 Hz Frequency: 20 Hz to 2 Hz
Same in Frequency Domain
At what time the frequency components occur? FT can not tell!
At what time the frequency components occur? FT can not tell!
Wavelet decompostion Matlab code : clc; clear all; close all; for indx=1:72 [Y] = dicomread('demo', 'frames',indx); figure(1) subplot(2,3,1),imshow(Y,[]); xlabel('Orginal DICOM image'); A = (fft2(double(Y))); [P,Q]=size(Y);
% step 2: Filtering the image in F-D by gaussian filter H = gausslfilter(P,Q,5*i);% A = H.*single(A); % step 3: Display the results in F-D subplot(2,3,4), imshow(log(1+abs(A)),[]); xlabel('H X Image spectrum (2D fft)'); subplot(2,3,3), imshow(log(1+abs(H)),[]); xlabel('Gaussian Filter)'); % step 4: apply 2D IFFt on each frame(takes the image from frequeency domain to % spatial domain ) A = ifft2(A); % step 5: Display the results in spacial-D subplot(2,3,5), imshow(abs(A),[]); xlabel('Restored DICOM image (2D ifft)'); end pause(5) end
Orginal DICOM image Image spectrum (2D fft)
H X Image spectrum (2D fft)
Gaussian Filter)
Restored DICOM image (2D ifft)
Orginal DICOM image Image spectrum (2D fft)
H X Image spectrum (2D fft)
Gaussian Filter)
Restored DICOM image (2D ifft)
Orginal DICOM image Image spectrum (2D fft)
H X Image spectrum (2D fft)
Gaussian Filter)
Restored DICOM image (2D ifft)
Orginal DICOM image Image spectrum (2D fft)
H X Image spectrum (2D fft)
Gaussian Filter)
Restored DICOM image (2D ifft)
For image processing applications we need wavelets that are two-dimensional.
This problem reduces down to designing 2D filters.
We will focus on a particular class of 2D filters: separable filters (Daubechies wavelets)
LH
HL HH
LENA
high pass
high pass high pass
We can interpret the decomposition as a breakdown of the signal into spatially oriented frequency channels.
Decomposition of frequency support
Arrangement of wavelet representations
Three levels of 2D wavelet decompositions:[Y] = dicomread('demo', 'frames',indx)[a1,h1,v1,d1]=dwt2((Y),'db2'); plotting(a1,h1,v1,d1); [a2,h2,v2,d2]=dwt2((a1),'db2'); plotting(a2,h2,v2,d2);[a3,h3,v3,d3]=dwt2((a2),'db2'); plotting(a3,h3,v3,d3);
d1=zeros(size(d1)); For the first level d2=zeros(size(d2)); For the second level d3=zeros(size(d3)); For the third level
a2=idwt2(a3,h3,v3,d3,'db2'); a1=idwt2(a2,h2,v2,d2,'db2'); recImage=idwt2(a1,h1,v1,d1,'db2');
orginal RECONSTRUCTION