# Robust Polyhedral Regularization

2 Equipe Image - Laboratoire GREYC - UMR6072
GREYC - Groupe de Recherche en Informatique, Image, Automatique et Instrumentation de Caen
Abstract : In this paper, we establish robustness to noise perturbations of polyhedral regularization of linear inverse problems. We provide a sufficient condition that ensures that the polyhedral face associated to the true vector is equal to that of the recovered one. This criterion also implies that the $\ell^2$ recovery error is proportional to the noise level for a range of parameter. Our criterion is expressed in terms of the hyperplanes supporting the faces of the unit polyhedral ball of the regularization. This generalizes to an arbitrary polyhedral regularization results that are known to hold for sparse synthesis and analysis $\ell^1$ regularization which are encompassed in this framework. As a byproduct, we obtain recovery guarantees for $\ell^\infty$ and $\ell^1-\ell^\infty$ regularization.
Keywords :
Type de document :
Communication dans un congrès
International Conference on Sampling Theory and Applications (SampTA), 2013, Bremen, Germany
Domaine :

Littérature citée [10 références]

https://hal.archives-ouvertes.fr/hal-00816377
Contributeur : Samuel Vaiter <>
Soumis le : lundi 22 avril 2013 - 11:19:04
Dernière modification le : mercredi 18 juillet 2018 - 12:42:01
Document(s) archivé(s) le : mardi 23 juillet 2013 - 04:12:13

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• HAL Id : hal-00816377, version 1
• ARXIV : 1304.6033

### Citation

Samuel Vaiter, Gabriel Peyré, Jalal M. Fadili. Robust Polyhedral Regularization. International Conference on Sampling Theory and Applications (SampTA), 2013, Bremen, Germany. 〈hal-00816377〉

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