Optimal block-size selection for iterative reconstruction of images from projections

Abstract

Statistical methods are preferred for reconstruction of images from projections when the signal-to-noise ratio is low or data is sparse. Likelihoods resulting from statistical formulation are usually nonlinear. Simultaneous iterative methods such as the conjugate gradient (CG), and point iterative methods such as Gauss-Seidel (GS) have been the most popular methods used for maximization of likelihoods. Simultaneous and point iterative methods are special cases of group iterative methods (GIM) with trivial block choices. It has been shown for similar problems that GIMs with nontrivial block choices may provide faster convergence, however, an optimal block selection rule has not been presented. We propose an optimal block-size selection method for GIMs, and demonstrate its usefulness on a positron emission tomography (PET) image reconstruction application.