A comparison of POCS algorithms for tomographic reconstruction under noise and limited view

Abstract

We present in this work a comparison among four algorithms for transmission tomography. The algorithms are based on the formalism of POCS (Projection onto Convex Sets): ART (Algebraic Reconstruction Technique), SIRT (Simultaneous Iterative Reconstruction Technique), sequential POCS and parallel POCS. We found that the use of adequate a priori knowledge about the solutions, expressed by convex sets restrictions, particularly in the case of the last algorithm, is an efficient way to reduce the variations on the solutions due to the ill-conditioning of the reconstruction problem, not only due to the noise in the projections, but also due to limited view reconstruction.