How can I restore my image back from the Fourier Spectrum - matlab

Question

I've taken the following image:
PandaNoise.bmp and tried to remove the periodic noise by focusing on its Fourier spectrum. Commented lines are the ones I'm not sure about. I can't get it back to the image plane. What am I doing wrong here?
panda = imread('PandaNoise.bmp');
fpanda = fft2(panda); % 2d fast fourier transform
fpanda = fftshift(fpanda); % center FFT
fpanda = abs(fpanda); % get magnitude
fpanda = log(1 + fpanda); % use log to expand range of dark pixels into bright region
fpanda = mat2gray(fpanda); % scale image from 0 to 1
figure; imshow(fpanda,[]); % show the picture
zpanda = fpanda;
zpanda(fpanda<0.5)=0;
zpanda(fpanda>0.5)=1;
%img = ifft2(zpanda);
%img = ifftshift(img);
%img = exp(1-img);
%img = abs(img);

Answer 1

Here is an example of how to work with the complex Fourier transform. We can take the log modulus for display, but don't change the original Fourier transform matrix, since the phase information that we throw away with abs is very important.
% Load data
panda = imread('https://i.stack.imgur.com/9SlW5.png');
panda = im2double(panda);
% Forward transform
fpanda = fft2(panda);
% Prepare FT for display -- don't change fpanda!
fd = fftshift(fpanda);
fd = log(1 + abs(fd));
figure; imshow(fd,[]); % show the picture
% From here we learn that we should keep the central 1/5th along both axes
% Low-pass filter
sz = size(fpanda);
center = floor(sz/2)+1;
half_width = ceil(sz/10)-1;
filter = zeros(sz);
filter(center(1)+(-half_width(1):half_width(1)),...
center(2)+(-half_width(2):half_width(2))) = 1;
filter = ifftshift(filter); % The origin should be on the top-left, like that of fpanda.
fpanda = fpanda .* filter;
% Inverse transform
newpanda = ifft2(fpanda);
figure; imshow(newpanda);
After computing the ifft2, newpanda is supposed to be purely real-valued if we designed the filter correctly (i.e. perfectly symmetric around the origin). Any imaginary component still present should be purely numerical innacuracy. MATLAB will detect that the input to ifft2 is conjugate symmetric, and return a purely real result. Octave will not, and you would have to do newpanda=real(newpanda) to avoid warnings from imshow.