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Journal Articles Journal of Mathematical Imaging and Vision Year : 2022

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

Emilie Chouzenoux
Ségolène Martin

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-regionlike 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.
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Dates and versions

hal-03740823 , version 1 (30-07-2022)

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Emilie Chouzenoux, Ségolène Martin, Jean-Christophe Pesquet. A Local MM Subspace Method for Solving Constrained Variational Problems in Image Recovery. Journal of Mathematical Imaging and Vision, In press, ⟨10.1007/s10851-022-01112-z⟩. ⟨hal-03740823⟩
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