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? 

Answers: 

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);