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

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');

[Matt J]

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]

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

Answer 1

[Alex Hanes]

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

1. Apply fft
2. Apply fftshift
3. Apply ifft
4. 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);