A new Fourier method for fan beam reconstruction

For parallel beam geometry the Fourier reconstruction works via the central slice theorem. For fan beam geometry the central slice theorem in its simple form does not exist. This paper introduces a generalized central slice theorem for fan beam geometry. Using this method the frequency plane is filled by adding up the contributions from all projections individually. Thereby the values in the Fourier plane are directly calculated for Cartesian coordinates such avoiding the interpolation from polar to Cartesian coordinates in the frequency domain. The new approach has been implemented and tested. This method is appropriate for the short scan case where the scanning covers less than 360°. It works for arbitrary ray-sampling schemes including equally spaced collinear detectors, equiangular rays and circle cameras as used for PET and SPECT systems