I need to perform tomographic reconstruction of an axially symmetric object. Because of the axial symmetry only one projection of the object (one angle) was taken. I implemented the filtered back-projection algorithm in MATLAB. However, when I run this algorithm on a synthetic image which has circular symmetry, but with added noise to its projection, I get a lot of noise in the reconstruction, especially in the center of the reconstruction.
Is there a way to modify the filtered back-projection algorithm so that the noise in the reconstruction will be reduced while this reduction will not result in loss of information ?? or is the filtered back-projection algorithm just doesn't work for a noisy image which has circular symmetry and as a result the reconstruction is performed with only one projection ?? (I must add that I added the noise to the synthetic image projection in a symmetric image).