Skip to Main content Skip to Navigation
Journal articles

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

Yann Traonmilin 1, * Rémi Gribonval 1
* Corresponding author
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.
Complete list of metadata

https://hal.inria.fr/hal-01207987
Contributor : Yann Traonmilin <>
Submitted on : Monday, December 5, 2016 - 11:35:18 AM
Last modification on : Monday, February 22, 2021 - 2:25:01 PM
Long-term archiving on: : Tuesday, March 21, 2017 - 12:44:37 PM

Files

article_RIP.pdf
Files produced by the author(s)

Identifiers

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, 2018, 45 (1), pp.170--205. ⟨10.1016/j.acha.2016.08.004⟩. ⟨hal-01207987v5⟩

Share

Metrics

Record views

1678

Files downloads

550