DELEDALLE, Charles; VAITER, Samuel; PEYRÉ, Gabriel; FADILI, Jalal M.; DOSSAL, Charles

doi:10.1088/1742-6596/386/1/012003

Métadonnées

Afficher la notice complète

Licence d’utilisation du document

DELEDALLE, Charles
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]

VAITER, Samuel
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]

PEYRÉ, Gabriel
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]

Langue

Communication dans un congrès

Ce document a été publié dans

Journal of Physics: Conference Series, Proc. 2nd Int. Workshop on New Computational Methods for Inverse Problems (NCMIP 2012), Proc. 2nd Int. Workshop on New Computational Methods for Inverse Problems (NCMIP 2012), NCMIP'12, 2012-04. 2012-04, vol. 386, p. 012003

IOP Science

Résumé en anglais

This paper develops a novel framework to compute a projected Generalized Stein Unbiased Risk Estimator (GSURE) for a wide class of sparsely regularized solutions of inverse problems. This class includes arbitrary convex data fidelities with both analysis and synthesis mixed L1-L2 norms. The GSURE necessitates to compute the (weak) derivative of a solution w.r.t.~the observations. However, as the solution is not available in analytical form but rather through iterative schemes such as proximal splitting, we propose to iteratively compute the GSURE by differentiating the sequence of iterates. This provides us with a sequence of differential mappings, which, hopefully, converge to the desired derivative and allows to compute the GSURE. We illustrate this approach on total variation regularization with Gaussian noise and to sparse regularization with poisson noise, to automatically select the regularization parameter.< Réduire

Mots clés en italien

Sparsity

regularization

inverse problems

risk estimator

GSURE

automatic differentiation

URI

https://oskar-bordeaux.fr/handle/20.500.12278/189886

DOI

http://dx.doi.org/10.1088/1742-6596/386/1/012003

Projet Européen

ERC SIGMA-Vision

Project ANR

Adaptivité pour la représentation des images naturelles et des textures - ANR-08-EMER-0009

Origine

Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251