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Exact and inexact proximal algorithms for convex and non-convex optimization, with applications in image processing

par Loris, Ignace
Référence Second Workshop on Optimization for Image and Signal Processing (7-9/12/2015: Paris, France)
Publication Non publié, 2015-12-08

Communication à un colloque

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Résumé :

Inverse problems in imaging are sometimes cast in the form of a non-smooth optimization problem involving an objective function that is the combination of a data misfit term and regularizing penalty or constraint. In this talk I will discuss iterative algorithms for the numerical solution of such problems. The algorithms are based on the availability of the proximal operator of the non-smooth part of the objective function. In particular, I will discuss convergence when the proximal operator can only be calculated inexactly. Verifiable criteria for such an inexact computation are also given in some cases of practical interest. I will also discuss convergence results in the case of convex and non-convex optimization problems. Finally, some applications in imaging are presented.This presentation is based on joint work with S. Bonettini, F. Porta, M. Prato and S. Rebegoldi.