Partitioned Separable Paraboloidal Surrogate Coordinate Ascent Algorithm for Image Restoration

Abstract

We introduce a new fast converging parallelizable algorithm for image restoration. This algorithm is based on paraboloidal surrogate functions to simplify the optimization problem and a concavity technique developed by De Pierro (1995) to simultaneously update a set of pixels. To obtain large step sizes which affect the convergence rate, we choose the paraboloidal surrogate functions that have small curvatures. The concavity technique is applied to separate pixels into partitioned sets so that parallel processors can be assigned to each set. The partitioned separable paraboloidal surrogates are maximized by using coordinate ascent (CA) algorithms. Unlike other existing algorithms such EM and CA algorithms, the proposed algorithm not only requires less time per iteration to converge, but is guaranteed to monotonically increase the objective function and intrinsically accommodates nonnegativity constraints as well.