Block-Iterative Fisher Scoring Algorithms for Maximum Penalized Likelihood Image Reconstruction in Emission Tomography

This paper introduces and evaluates a block-iterative fisher scoring (BFS) algorithm. The algorithm provides regularized estimation in tomographic models of projection data with Poisson variability. Regularization is achieved by penalized likelihood with a general quadratic penalty. Local convergence of the block-iterative algorithm is proven under conditions that do not require iteration dependent relaxation. We show that, when the algorithm converges, it converges to the unconstrained maximum penalized likelihood (MPL) solution. Simulation studies demonstrate that, with suitable choice of relaxation parameter and restriction of the algorithm to respect nonnegative constraints, the BFS algorithm provides convergence to the constrained MPL solution. Constrained BFS often attains a maximum penalized likelihood faster than other block-iterative algorithms which are designed for nonnegatively constrained penalized reconstruction.