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Optimality of 1-norm regularization among weighted 1-norms for sparse recovery: a case study on how to find optimal regularizations

hal.structure.identifierCentre National de la Recherche Scientifique [CNRS]
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorTRAONMILIN, Yann
hal.structure.identifierCentre National de la Recherche Scientifique [CNRS]
hal.structure.identifierInstitut de Mathématiques de Bourgogne [Dijon] [IMB]
dc.contributor.authorVAITER, Samuel
dc.date.accessioned2024-04-04T03:05:58Z
dc.date.available2024-04-04T03:05:58Z
dc.date.issued2018
dc.date.conference2018-05-25
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/193300
dc.description.abstractEnThe 1-norm was proven to be a good convex regularizer for the recovery of sparse vectors from under-determined linear measurements. It has been shown that with an appropriate measurement operator, a number of measurements of the order of the sparsity of the signal (up to log factors) is sufficient for stable and robust recovery. More recently, it has been shown that such recovery results can be generalized to more general low-dimensional model sets and (convex) regularizers. These results lead to the following question: to recover a given low-dimensional model set from linear measurements, what is the "best" convex regularizer? To approach this problem, we propose a general framework to define several notions of "best regularizer" with respect to a low-dimensional model. We show in the minimal case of sparse recovery in dimension 3 that the 1-norm is optimal for these notions. However, generalization of such results to the n-dimensional case seems out of reach. To tackle this problem, we propose looser notions of best regularizer and show that the 1-norm is optimal among weighted 1-norms for sparse recovery within this framework.
dc.language.isoen
dc.publisherIOP Science
dc.source.titleJournal of Physics: Conference Series
dc.title.enOptimality of 1-norm regularization among weighted 1-norms for sparse recovery: a case study on how to find optimal regularizations
dc.typeCommunication dans un congrès
dc.identifier.doi10.1088/1742-6596/1131/1/012009
dc.subject.halInformatique [cs]/Théorie de l'information [cs.IT]
dc.subject.halInformatique [cs]/Traitement du signal et de l'image
dc.identifier.arxiv1803.00773
bordeaux.pageconference 1
bordeaux.volume1131
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.conference.title8th International Conference on New Computational Methods for Inverse Problems
bordeaux.countryFR
bordeaux.title.proceedingJournal of Physics: Conference Series
bordeaux.conference.cityParis
bordeaux.peerReviewedoui
hal.identifierhal-01720871
hal.version1
hal.invitednon
hal.proceedingsnon
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01720871v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.btitle=Journal%20of%20Physics:%20Conference%20Series&rft.date=2018&rft.volume=1131&rft.spage=conference%201&rft.epage=conference%201&rft.au=TRAONMILIN,%20Yann&VAITER,%20Samuel&rft.genre=unknown


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