Stable recovery of low-dimensional cones in Hilbert spaces: One RIP to rule them all - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Article Dans Une Revue Applied and Computational Harmonic Analysis Année : 2018

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

Résumé

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.
Fichier principal
Vignette du fichier
article_RIP.pdf (351.23 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-01207987 , version 1 (01-10-2015)
hal-01207987 , version 2 (02-10-2015)
hal-01207987 , version 3 (28-10-2015)
hal-01207987 , version 4 (07-03-2016)
hal-01207987 , version 5 (05-12-2016)

Identifiants

Citer

Yann Traonmilin, Rémi Gribonval. Stable recovery of low-dimensional cones in Hilbert spaces: One RIP to rule them all. Applied and Computational Harmonic Analysis, 2018, 45 (1), pp.170--205. ⟨10.1016/j.acha.2016.08.004⟩. ⟨hal-01207987v5⟩
500 Consultations
475 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More