Date: Dec 27, 2012 10:54 AM
Author: Wojtek
Subject: Strange object position after IFFT2

Hello. I'm working with the Projection Slice Theorem (but it is not important in this case). I have a set of vectors that are projections of my object at different angles (cuts from bmp 2d images). I calculate fft of these vectors:

my_vector = double(image_cut) ;
my_fft = fftshift(fft(my_vector)) ;

so that now I have 1D Fourier Transform with 0 freq. at the center. Now I put that vector into a 2d matrix (named "my_spectrum"), which will be my 2D Fourier domain. I place vector so that it's center is in the centre of the matrix (where 0 freq should be). In this way I put all the vectors - every one of them is placed in the same way, just the angle is different - I get a star-like shape of my spectrum.
Now I calculate IFFT2 from so created 2D spectrum:

my_reconstruction = ifft2(ifftshift(my_spectrum)) ;

so first I ifftshift to place 0 freq. in the corners, then I ifft2. According to the theory, I should get my initial object this way. And I think (not sure) that I get it but in a very strange way. My object should me more or less a circle. It's difficult to explain what is wrong so I will link to the image:

As you can see the ifft2 worked wrong. Instead of a circle I have 4 halves - and as I suspect these are halves of my circle. These halves are placed in such way, that no fftshift is possible - and there should be no need to use fftshift on the reconstructed image. What could I do wrong? What kind of mistake may lead to such reconstruction?
I will be very grateful for your help, I'm fighting with this for too long... I can give more details if needed!

PS What is also strange is the fact, that after changing from
my_reconstruction = ifft2(ifftshift(my_spectrum)) ; to
my_reconstruction = ifft2(my_spectrum) ;
there is no difference in the reconstructed image.