dc.contributor.author Vaiter, Samuel HAL ID: 1995 ORCID: 0000-0002-4077-708X dc.contributor.author Peyré, Gabriel HAL ID: 1211 dc.contributor.author Fadili, Jalal HAL ID: 15510 dc.date.accessioned 2013-04-23T12:23:18Z dc.date.available 2013-04-23T12:23:18Z dc.date.issued 2013 dc.identifier.uri https://basepub.dauphine.fr/handle/123456789/11240 dc.language.iso en en dc.subject inverse problem dc.subject polyhedral regularization dc.subject noise robustness dc.subject.ddc 621.3 en dc.title Robust Polyhedral Regularization dc.type Communication / Conférence dc.contributor.editoruniversityother Groupe de Recherche en Informatique, Image, Automatique et Instrumentation de Caen (GREYC) http://www.greyc.fr CNRS : UMR6072 – Université de Caen Basse-Normandie – Ecole Nationale Supérieure d'Ingénieurs de Caen;France dc.description.abstracten 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. dc.publisher.city Paris en dc.identifier.urlsite https://hal.archives-ouvertes.fr/hal-00816377 dc.subject.ddclabel Traitement du signal en dc.relation.conftitle International Conference on Sampling Theory and Applications (SampTA), 2013 dc.relation.confcity Bremen dc.relation.confcountry GERMANY dc.description.submitted non en dc.description.ssrncandidate non dc.description.halcandidate oui dc.description.readership recherche dc.description.audience International dc.date.updated 2016-10-13T09:25:39Z
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