A Local MM Subspace Method for Solving Constrained Variational Problems in Image Recovery

Abstract

This article introduces a new penalized majorization–minimization subspace algorithm (P-MMS) for solving smooth, constrained optimization problems. In short, our approach consists of embedding a subspace algorithm in an inexact exterior penalty procedure. The subspace strategy, combined with a majoration–minimization step-size search, takes great advantage of the smoothness of the penalized cost function, while the penalty method allows to handle a wide range of constraints. The main drawback of exterior penalty approaches, namely ill-conditioning for large values of the penalty parameter, is overcome by using a trust-region-like technique. The convergence of the resulting algorithm is analyzed. Numerical experiments carried out on two large-scale image recovery applications demonstrate that, compared with state-of-the-art algorithms, the proposed method performs well in terms of computational time.