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

Emilie Chouzenoux(emilie.chouzenouxcentralesupelec.fr)
Ségolène Martin(segolene.martincentralesupelec.fr)
Jean-Christophe Pesquet(jean-christophe.pesquetcentralesupelec.fr)

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.

Keywords: constrained optimization ; smooth optimization ; subspace acceleration ; exterior penalty method ; Majorization-Minimization ; wavelet restoration ; PET reconstruction

Category 1: Nonlinear Optimization (Constrained Nonlinear Optimization )

Category 2: Convex and Nonsmooth Optimization (Convex Optimization )

Category 3: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

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Entry Submitted: 09/22/2021
Entry Accepted: 09/22/2021
Entry Last Modified: 09/22/2021

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