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Block based refitting in $\ell_{12}$ sparse regularisation

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
hal.structure.identifierDepartment of Electrical and Computer Engineering [Univ California San Diego] [ECE - UC San Diego]
dc.contributor.authorDELEDALLE, Charles-Alban
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorPAPADAKIS, Nicolas
hal.structure.identifierInstitut Montpelliérain Alexander Grothendieck [IMAG]
dc.contributor.authorSALMON, Joseph
hal.structure.identifierCentre National de la Recherche Scientifique [CNRS]
hal.structure.identifierInstitut de Mathématiques de Bourgogne [Dijon] [IMB]
dc.contributor.authorVAITER, Samuel
dc.date.accessioned2024-04-04T02:59:26Z
dc.date.available2024-04-04T02:59:26Z
dc.date.issued2021
dc.date.conference2019-06-30
dc.identifier.issn0924-9907
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/192742
dc.description.abstractEnIn many linear regression problems, including ill-posed inverse problems in image restoration, the data exhibit some sparse structures that can be used to regularize the inversion. To this end, a classical path is to usel l(12) block-based regularization. While efficient at retrieving the inherent sparsity patterns of the data-the support-the estimated solutions are known to suffer from a systematical bias. We propose a general framework for removing this artifact by refitting the solution toward the data while preserving key features of its structure such as the support. This is done through the use of refitting block penalties that only act on the support of the estimated solution. Based on an analysis of related works in the literature, we introduce a new penalty that is well suited for refitting purposes. We also present a new algorithm to obtain the refitted solution along with the original (biased) solution for any convex refitting block penalty. Experiments illustrate the good behavior of the proposed block penalty for refitting solutions of total variation and total generalized variation models.
dc.description.sponsorshipGeneralized Optimal Transport Models for Image processing - ANR-16-CE33-0010
dc.language.isoen
dc.publisherSpringer Verlag
dc.subject.enBlock sparsity
dc.subject.enTotal variation
dc.subject.enBias correction
dc.subject.enRefitting
dc.title.enBlock based refitting in $\ell_{12}$ sparse regularisation
dc.typeArticle de revue
dc.identifier.doi10.1007/s10851-020-00993-2
dc.subject.halMathématiques [math]
dc.subject.halInformatique [cs]/Intelligence artificielle [cs.AI]
dc.description.sponsorshipEuropeNonlocal Methods for Arbitrary Data Sources
bordeaux.journalJournal of Mathematical Imaging and Vision
bordeaux.page216–236
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue63
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.conference.title7th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2019
bordeaux.countryDE
bordeaux.conference.cityHofgeismar
bordeaux.peerReviewedoui
hal.identifierhal-02330441
hal.version1
hal.invitednon
hal.proceedingsnon
hal.conference.end2019-07-04
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-02330441v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Journal%20of%20Mathematical%20Imaging%20and%20Vision&rft.date=2021&rft.issue=63&rft.spage=216%E2%80%93236&rft.epage=216%E2%80%93236&rft.eissn=0924-9907&rft.issn=0924-9907&rft.au=DELEDALLE,%20Charles-Alban&PAPADAKIS,%20Nicolas&SALMON,%20Joseph&VAITER,%20Samuel&rft.genre=article


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