Fan-beam tomography iterative algorithm based on Fourier transform

In tomography with a small number of views (i.e., optical tomography) there is a big demand for the algorithms able to adapt and efficiently use different types of a priori information about the solution. The Gerchberg-Papoulis algorithm (G-P) is known as one of the best iterative methods of a limited data tomography with parallel arrangement of projections because of its wide range of constraints it is capable to embed into processing steps. The G-P algorithm is based on the theorem of the central slice in Fourier space for parallel geometry of scanning and intensive interpolation in both image and frequency domains. In fan-beam geometry such algorithm has not been investigated, because of the central slice theorem lacking. In this paper recently developed theorem of the central slice is stated for fan-beam geometry, and on its basis the new iterative G-P algorithm is developed.