Globally convergent Newton-SOR method for statistical image reconstruction

Abstract

Develops a new fast iterative method to minimize a general convex cost function over the nonnegative orthant for tomographic image reconstruction. The new method is based on the inexact Newton method where the convex cost function is approximated by a quadratic function at each iteration step and the quadratic cost is decreased using the projected successive overrelaxation (SOR) method. To assure the global convergence property of the Newton method, the authors introduce the trust region and the line search techniques. The resulting method can be applied to arbitrary convex cost function in a unified way and its global convergence is mathematically assured. The method is implemented with simulated and real data for emission and transmission tomography. The results demonstrate that the convergence speed of the proposed method is comparable to that of the ordered subsets method.