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
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.
