How to reconstruct an image from Real and Imaginary part?

Hi everyone,

I am very new to Matlab and image processing. I have an image of phantom('Modified Shepp-Logan',200).Then, I use Fourier transformation to extract the Real and the Imaginary. After all, I want to modify the Real part as well as the Imaginary part by multiply each of them with a weighting score.

The out put is look like this.

I would like to ask how do I do that?

Thank you

Answer 1

[Walter Roberson]

filename = 'cameraman.tif';
img = imread(filename);
fimg = fft2(img);
sfimg = fftshift(fftshift(fimg,2),1);
rsf = real(sfimg);
isf = imag(sfimg);
contour(rsf)
title('fft2 real part'); colorbar

contour(isf)
title('fft2 imaginary part'); colorbar

real_weights = rand(size(rsf));
real_weights = real_weights + flipud(real_weights) + fliplr(real_weights)  + fliplr(flipud(real_weights));
imag_weights = rand(size(isf));
imag_weights = imag_weights + flipud(imag_weights) + fliplr(imag_weights) + fliplr(flipud(imag_weights));
contour(real_weights);
title('real weights'); colorbar();

contour(imag_weights);
title('imaginary weights'); colorbar();

mod_sreal = rsf .* real_weights;
mod_simag = isf .* imag_weights;
mod_real = fftshift(fftshift(mod_sreal,2),1);
mod_imag = fftshift(fftshift(mod_simag,2),1);
reconstructed_fimg = complex(mod_real, mod_imag);
reconstructed_img = ifft2(reconstructed_fimg);
whos

  Name                      Size               Bytes  Class     Attributes

  filename                  1x13                  26  char                
  fimg                    256x256            1048576  double    complex   
  imag_weights            256x256             524288  double              
  img                     256x256              65536  uint8               
  isf                     256x256             524288  double              
  mod_imag                256x256             524288  double              
  mod_real                256x256             524288  double              
  mod_simag               256x256             524288  double              
  mod_sreal               256x256             524288  double              
  real_weights            256x256             524288  double              
  reconstructed_fimg      256x256            1048576  double    complex   
  reconstructed_img       256x256            1048576  double    complex   
  rsf                     256x256             524288  double              
  sfimg                   256x256            1048576  double    complex   

  rr8 = uint8(real(reconstructed_img));
  ri8 = uint8(imag(reconstructed_img));
  imshow(rr8)
  title('reconstructed after weights, real part')

  imshow(ri8)
  title('reconstructed after weights, imag part')

I fftshift the fft2 results in order to center the ffts; in theory the result should be symmetric.

I then construct random weights. The random weights must maintain the symmetric nature of the shifted data. The bit where I sum flipped versions of the weights is an attempt to get back a matrix that is symmetric against both diagonals. It looks like I did not succeed -- if I had succeeded then there would be no imaginary components in the reconstructed image.

[Peter Phan]

Oh, it worked for me.

Really thanks

Actually, why don;t you just give me only :

reconstructed_fimg = complex(realpart, imagpart);

reconstructed_img = ifft2(reconstructed_fimg);

Then it work fine to me :)

Thank you so much for your help