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dc.contributor.authorDossal, Charles
dc.contributor.authorFadili, Jalal
HAL ID: 15510
dc.contributor.authorPeyré, Gabriel
HAL ID: 1211
dc.contributor.authorVaiter, Samuel
HAL ID: 1995
ORCID: 0000-0002-4077-708X
dc.contributor.authorDeledalle, Charles-Alban
dc.date.accessioned2012-02-07T13:05:53Z
dc.date.available2012-02-07T13:05:53Z
dc.date.issued2012
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/8055
dc.language.isoenen
dc.subjectGSUREen
dc.subjectrisk estimatoren
dc.subjectinverse problemsen
dc.subjectanalysis regularizationen
dc.subjectSparsityen
dc.subject.ddc621.3en
dc.titleUnbiased Risk Estimation for Sparse Analysis Regularizationen
dc.typeCommunication / Conférence
dc.contributor.editoruniversityotherInstitut de Mathématiques de Bordeaux (IMB) http://www.math.u-bordeaux.fr/IMB/ CNRS : UMR5251 – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II;France
dc.contributor.editoruniversityotherGroupe de Recherche en Informatique, Image, Automatique et Instrumentation de Caen (GREYC) http://www.greyc.unicaen.fr/ CNRS : UMR6072 – Université de Caen – Ecole Nationale Supérieure d'Ingénieurs de Caen;France
dc.description.abstractenIn this paper, we propose a rigorous derivation of the expression of the projected Generalized Stein Unbiased Risk Estimator ($\GSURE$) for the estimation of the (projected) risk associated to regularized ill-posed linear inverse problems using sparsity-promoting L1 penalty. The projected GSURE is an unbiased estimator of the recovery risk on the vector projected on the orthogonal of the degradation operator kernel. Our framework can handle many well-known regularizations including sparse synthesis- (e.g. wavelet) and analysis-type priors (e.g. total variation). A distinctive novelty of this work is that, unlike previously proposed L1 risk estimators, we have a closed-form expression that can be implemented efficiently once the solution of the inverse problem is computed. To support our claims, numerical examples on ill-posed inverse problems with analysis and synthesis regularizations are reported where our GSURE estimates are used to tune the regularization parameter.en
dc.identifier.citationpages3053-3056en
dc.relation.ispartoftitle19th IEEE International Conference on Image Processing (ICIP), 2012 - proceedings
dc.relation.ispartofpublnameIEEE
dc.relation.ispartofdate2012
dc.relation.isversionofdoihttp://dx.doi.org/10.1109/ICIP.2012.6467544
dc.identifier.urlsitehttp://hal.archives-ouvertes.fr/hal-00662718en
dc.description.sponsorshipprivateouien
dc.subject.ddclabelTraitement du signalen
dc.relation.ispartofisbn978-1-4673-2534-9
dc.relation.conftitle2012 IEEE International Conference on Image Processing (ICIP)
dc.relation.confdate2012-10
dc.relation.confcityOrlando
dc.relation.confcountryEtats-Unis


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