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

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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

Proc. ICIP'12, Proc. ICIP'12, Proc. ICIP'12, 2012-09, Orlando. 2012-09p. 3053-3056

Résumé en anglais

In this paper, we propose a rigorous derivation of the expression of the projected Generalized Stein Unbiased Risk Estimator ($\GSURE$) for the estimation of the (projected) risk associated to regularized ill-posed linear inverse problems using sparsity-promoting L1 penalty. The projected GSURE is an unbiased estimator of the recovery risk on the vector projected on the orthogonal of the degradation operator kernel. Our framework can handle many well-known regularizations including sparse synthesis- (e.g. wavelet) and analysis-type priors (e.g. total variation). A distinctive novelty of this work is that, unlike previously proposed L1 risk estimators, we have a closed-form expression that can be implemented efficiently once the solution of the inverse problem is computed. To support our claims, numerical examples on ill-posed inverse problems with analysis and synthesis regularizations are reported where our GSURE estimates are used to tune the regularization parameter.< Réduire

Mots clés en anglais

Sparsity

analysis regularization

inverse problems

risk estimator

GSURE

URI

https://oskar-bordeaux.fr/handle/20.500.12278/189891

Projet Européen

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