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dc.contributor.authorVaiter, Samuel
HAL ID: 1995
ORCID: 0000-0002-4077-708X
dc.contributor.authorPeyré, Gabriel
HAL ID: 1211
dc.contributor.authorFadili, Jalal
HAL ID: 15510
dc.date.accessioned2013-04-23T12:23:18Z
dc.date.available2013-04-23T12:23:18Z
dc.date.issued2013
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/11240
dc.language.isoenen
dc.subjectinverse problem
dc.subjectpolyhedral regularization
dc.subjectnoise robustness
dc.subject.ddc621.3en
dc.titleRobust Polyhedral Regularization
dc.typeCommunication / Conférence
dc.contributor.editoruniversityotherGroupe 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.abstractenIn 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.cityParisen
dc.identifier.urlsitehttps://hal.archives-ouvertes.fr/hal-00816377
dc.subject.ddclabelTraitement du signalen
dc.relation.conftitleInternational Conference on Sampling Theory and Applications (SampTA), 2013
dc.relation.confcityBremen
dc.relation.confcountryGERMANY
dc.description.submittednonen
dc.description.ssrncandidatenon
dc.description.halcandidateoui
dc.description.readershiprecherche
dc.description.audienceInternational
dc.date.updated2016-10-13T09:25:39Z


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