I'm doing an exercise to reconstruct an CT-scan image from its sinogram (given).
From the sinogram, implementing the central slice theorem, I did the 1D FFT (after zero padding)
sino_fft = fftshift(fft(fftshift(sinogram)));
and recover the back-projection through the 2D inverse FFT
backprojection = fftshift(ifft2(fftshift(sino_fft)));
Now I should convert the polar back projection to cartesian coordinate and reconstruct the grayscale image. I'm not sure how do it. backprojection is a double complex, so I converted into x-y with
theta = 0:180/(size(backprojection,1)-1):180;
[x,y] = pol2cart(theta,abs(backprojection));
and at this point I have a scattered data set. The hint from the exercise is to sum iteratively from all the angles to get the recovered image. But I don't understand. Just do image = x+y? In this case I get an empty gray image.
Edit after @Christoph Rackwitz comment:
If I remove the inner fftshift from sino_fft and backprojection I get a splitted fourier transform.
while with my code I get a centered fourier transform.
