Partly Smooth Regularization of Inverse Problems

Samuel Vaiter 1 Gabriel Peyré 1 Jalal M. Fadili 2
2 Equipe Image - Laboratoire GREYC - UMR6072
GREYC - Groupe de Recherche en Informatique, Image, Automatique et Instrumentation de Caen
Abstract : This article studies the regularization of inverse problems with a con- vex prior promoting some notion of low-complexity. This low-complexity is obtained by using regularizers that are partly smooth functions. Such functions force the solution of variational problems to live in a low-dimension manifold which is stable under small perturbations of the functional. This property is crucial to make the underlying low-complexity model robust to small noise. We show that a simple criterion implies the stability of the active manifold to small noise perturbations of the observation when the regularization parameter is tuned proportionally to the noise level. This unifies and generalizes several previous works, where this theorem is known to hold for sparse, group sparse, total variation and low-rank regularizations.
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-00987293
Contributeur : Gabriel Peyré <>
Soumis le : lundi 5 mai 2014 - 21:01:07
Dernière modification le : jeudi 11 janvier 2018 - 06:27:17
Document(s) archivé(s) le : mardi 5 août 2014 - 13:16:02

Fichiers

PartlySmoothSensitivity.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-00987293, version 1
  • ARXIV : 1405.1004

Citation

Samuel Vaiter, Gabriel Peyré, Jalal M. Fadili. Partly Smooth Regularization of Inverse Problems. 2014. 〈hal-00987293v1〉

Partager

Métriques

Consultations de la notice

135

Téléchargements de fichiers

90