The solution of many problems in imaging sciences involves the minimization of a cost function in a feasible convex domain. The latter constraints can be efficiently tackled by adding a logarithmic barrier to the cost function multiplied by a weight tending progressively to zero. We propose a novel interior point method for minimizing a non-smooth convex function under general convex constraints. Its practical efficiency is illustrated through numerical experiments on large scale image recovery applications.

This presentation is part of Minisymposium “MS59 - Approaches for fast optimisation in imaging and inverse problems (3 parts)”
organized by: Jingwei Liang (University of Cambridge) , Carola-Bibiane Schönlieb (University of Cambridge) , Mila Nikolova (CMLA - CNRS ENS Cachan, University Paris-Saclay) .

Authors:

Emilie Chouzenoux (Université Paris-Est Marne-la-Vallée)

Marie-Caroline Corbineau (CentraleSupélec, Université Paris Saclay, Gif-sur-Yvette)

Jean-Christophe Pesquet (Université Paris-Saclay)

Keywords:

hyperspectral imaging, image enhancement, interior point methods, inverse problems, nonlinear optimization, proximal minimization