Unable to convert image back to time domain using IFFT!!

Question

Rupika Raj 2022-9-22

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1810025-unable-to-convert-image-back-to-time-domain-using-ifft

回答： Alex Hanes 2022-10-25

Hi,

I've been using MATLAB to analyse the properties of image in frequency domain. For this i used the cameraman.jpg image. i was able to find its FFT but unfortunately i am unable to convert the image back to original. can anyone please help!?

I have added the code and images below.

Thanks in advance!

img = imread('cameraman.tif');
figure;
imshow(img, []);
title('Input Image');
imRef = fftshift(fft((img),[],1),1);
imRef = fftshift(fft(imRef,[],2),2);
kspace = squeeze(sqrt(sum(abs(imRef).^2, 4)));   
figure;
imshow(log(kspace), []); 
title('Input kspace');
shifted_127(127,:) = circshift(kspace(127,:),5); % shifted 5+1 places
shifted = kspace ;
shifted(127,:) = shifted_127(127,:);
figure;
imshow(log(shifted), []);
title('Shifted kspace');
imRef1 = ifftshift(ifft(shifted,[],1),1);
imRef1 = ifftshift(ifft(imRef1,[],2),2);
kspace1 = squeeze(sqrt(sum(abs(imRef1).^2, 4)));  
figure;
imshow(kspace1,[]);
title('Out image');

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Matt J 2022-9-22

编辑：Matt J 2022-9-22

It's not clear why you think the original image should be recoverable. In particular, when creating kspace, all phase information is discarded.

Rupika Raj 2022-9-22

编辑：Rupika Raj 2022-9-22

I want to know how the image gets affected if i shift some values of a line in kspace.

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Answer 1

Alex Hanes 2022-10-25

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1810025-unable-to-convert-image-back-to-time-domain-using-ifft#answer_1082553

在 MATLAB Online 中打开

The ifft() and ifftshift() function do not commute. Look at the series of steps you took (working outwards):

Apply fft
Apply fftshift
Apply ifft
Apply ifftshift

Instead, you need to swap the order of steps 3 and 4 since the order of function operations matters. You can convince yourself of this using a simple sine function:

% Create a sine function:
t = (0:0.01:25)'; 
y1 = sin(t); 
yFFT = fftshift(fft(y1));         % Calculate DFT, then fftshift
y2 = real(ifftshift(ifft(yFFT))); % Apply ifft, then ifftshift
y3 = real(ifft(ifftshift(yFFT))); % Apply ifftshift, then ifft
% See if y1 matches y2, y3:
diff1 = y1 - y2; % Calculate Difference
diff2 = y1 - y3; % Calculate Difference
 
% Set Values = 0 if < eps: 
diff1(abs(diff1) <= 10.*eps) = 0; 
diff2(abs(diff2) <= 10.*eps) = 0; 
% Get Number of Non-zero Differences:
N1 = nnz(diff1); 
N2 = nnz(diff2); 
figure(1); clf; zoom on; hold on; 
plot(t,y1,'k-','LineWidth',2); 
plot(t,y2,'b-','LineWidth',2); 
plot(t,y3,'r--','LineWidth',2); 