Stable recovery of low-dimensional cones in Hilbert spaces: One RIP to rule them all

Yann Traonmilin 1 Rémi Gribonval 1
1 PANAMA - Parcimonie et Nouveaux Algorithmes pour le Signal et la Modélisation Audio
Inria Rennes – Bretagne Atlantique , IRISA-D5 - SIGNAUX ET IMAGES NUMÉRIQUES, ROBOTIQUE
Abstract : Many inverse problems in signal processing deal with the robust estimation of unknown data from underdetermined linear observations. Low dimensional models, when combined with appropriate regularizers, have been shown to be efficient at performing this task. Sparse models with the 1-norm or low rank models with the nuclear norm are examples of such successful combinations. Stable recovery guarantees in these settings have been established using a common tool adapted to each case: the notion of restricted isometry property (RIP). In this paper, we establish generic RIP-based guarantees for the stable recovery of cones (positively homogeneous model sets) with arbitrary regularizers. These guarantees are illustrated on selected examples. For block structured sparsity in the infinite dimensional setting, we use the guarantees for a family of regularizers which efficiency in terms of RIP constant can be controlled, leading to stronger and sharper guarantees than the state of the art.
Type de document :
Article dans une revue
Applied and Computational Harmonic Analysis, Elsevier, 2016, 〈10.1016/j.acha.2016.08.004〉
Liste complète des métadonnées

https://hal.inria.fr/hal-01207987
Contributeur : Yann Traonmilin <>
Soumis le : lundi 5 décembre 2016 - 11:35:18
Dernière modification le : mercredi 2 août 2017 - 10:11:05
Document(s) archivé(s) le : mardi 21 mars 2017 - 12:44:37

Fichiers

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

Identifiants

Citation

Yann Traonmilin, Rémi Gribonval. Stable recovery of low-dimensional cones in Hilbert spaces: One RIP to rule them all. Applied and Computational Harmonic Analysis, Elsevier, 2016, 〈10.1016/j.acha.2016.08.004〉. 〈hal-01207987v5〉

Partager

Métriques

Consultations de la notice

516

Téléchargements de fichiers

60