Inexact Bregman iteration with an application toudPoisson data reconstruction

摘要

This work deals with the solution of image restoration problems by anuditerative regularization method based on the Bregman iteration. Any iteration of thisudscheme requires to exactly compute the minimizer of a function. However, in someudimage reconstruction applications, it is either impossible or extremely expensive toudobtain exact solutions of these subproblems. In this paper, we propose an inexactudversion of the iterative procedure, where the inexactness in the inner subproblemudsolution is controlled by a criterion that preserves the convergence of the Bregmanuditeration and its features in image restoration problems. In particular, the methodudallows to obtain accurate reconstructions also when only an overestimation of theudregularization parameter is known. The introduction of the inexactness in the iterativeudscheme allows to address image reconstruction problems from data corrupted byudPoisson noise, exploiting the recent advances about specialized algorithms for theudnumerical minimization of the generalized Kullback–Leibler divergence combined withuda regularization term. The results of several numerical experiments enable to evaluate