Iterative Gerchberg-Papoulis algorithm for fan-beam tomography

Abstract

In tomography from a small number of projections it is necessary to apply the algorithms that allow to use prior information about the solution. The Gerchberg-Papoulis algorithm (G-P), based on the central slice theorem in Fourier space, is known as one of the most effective iterative methods for few-projection tomography in parallel scanning geometries. This algorithm has not been studied for fan-beam geometries, because a central slice theorem is lacking. In this paper, we state a recently developed central slice theorem for fan-beam geometries, and on this basis we develop a new iterative G-P algorithm. In numerical simulation two versions are investigated.We study how additive random noise in the projections influences the accuracy of the reconstructions, and we give regularization criteria for suppressing random noise in the measurements.