Matlab inverse FFT from phase/magnitude only

Question

So I have this image 'I'. I take F = fft2(I) to get the 2D fourier transform. To reconstruct it, I could go ifft2(F).

The problem is, I need to reconstruct this image from only the a) magnitude, and b) phase components of F. How can I separate these two components of the fourier transform, and then reconstruct the image from each?

I tried the abs() and angle() functions to get magnitude and phase, but the phase one won't reconstruct properly.

Help?

Answer 1

it's too late to put another answer to this post, but...anyway

@ zhilevan, you can use the codes I have written using mtrw's answer:

image = rgb2gray(imread('pillsetc.png')); 
subplot(131),imshow(image),title('original image');
set(gcf, 'Position', get(0, 'ScreenSize')); % maximize the figure window
%:::::::::::::::::::::
F = fft2(double(image));
F_Mag = abs(F); % has the same magnitude as image, 0 phase 
F_Phase = exp(1i*angle(F)); % has magnitude 1, same phase as image
% OR: F_Phase = cos(angle(F)) + 1i*(sin(angle(F)));
%:::::::::::::::::::::
% reconstruction
I_Mag = log(abs(ifft2(F_Mag*exp(i*0)))+1);
I_Phase = ifft2(F_Phase);
%:::::::::::::::::::::
% Calculate limits for plotting
% To display the images properly using imshow, the color range
% of the plot must the minimum and maximum values in the data.
I_Mag_min = min(min(abs(I_Mag)));
I_Mag_max = max(max(abs(I_Mag)));

I_Phase_min = min(min(abs(I_Phase)));
I_Phase_max = max(max(abs(I_Phase)));
%:::::::::::::::::::::
% Display reconstructed images
% because the magnitude and phase were switched, the image will be complex.
% This means that the magnitude of the image must be taken in order to
% produce a viewable 2-D image.
subplot(132),imshow(abs(I_Mag),[I_Mag_min I_Mag_max]), colormap gray 
title('reconstructed image only by Magnitude');
subplot(133),imshow(abs(I_Phase),[I_Phase_min I_Phase_max]), colormap gray 
title('reconstructed image only by Phase');

Answer 2

You need one matrix with the same magnitude as F and 0 phase, and another with the same phase as F and uniform magnitude. As you noted abs gives you the magnitude. To get the uniform magnitude same phase matrix, you need to use angle to get the phase, and then separate the phase back into real and imaginary parts.

> F_Mag = abs(F); %# has same magnitude as F, 0 phase
> F_Phase = cos(angle(F)) + j*(sin(angle(F)); %# has magnitude 1, same phase as F
> I_Mag = ifft2(F_Mag);
> I_Phase = ifft2(F_Phase);