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Blockwise SVD with error in the operator and application to blind deconvolution

dc.contributor.authorVareschi, Thomas
dc.contributor.authorPicard, Dominique
dc.contributor.authorHoffmann, Marc
dc.contributor.authorDelattre, Sylvain
dc.date.accessioned2013-01-31T08:23:02Z
dc.date.available2013-01-31T08:23:02Z
dc.date.issued2012
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/10924
dc.language.isoenen
dc.subjecterror in the operatoren
dc.subjectlinear in- verse problemsen
dc.subjectnonparametric adaptive estimationen
dc.subjectcircular and spherical deconvolutionen
dc.subjectblockwise SVDen
dc.subjectBlind deconvolutionen
dc.subject.ddc519en
dc.titleBlockwise SVD with error in the operator and application to blind deconvolutionen
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherLaboratoire de Probabilités et Modèles Aléatoires (LPMA) http://www.proba.jussieu.fr/ CNRS : UMR7599 – Université Paris VI - Pierre et Marie Curie – Université Paris VII - Paris Diderot;France
dc.description.abstractenWe consider linear inverse problems in a nonparametric statistical framework. Both the signal and the operator are unknown and subject to error measurements. We establish minimax rates of convergence under squared error loss when the operator admits a blockwise singular value decomposition (blockwise SVD) and the smoothness of the signal is measured in a Sobolev sense. We construct a nonlinear procedure adapting simultaneously to the unknown smoothness of both the signal and the operator and achieving the optimal rate of convergence to within logarithmic terms. When the noise level in the operator is dominant, by taking full advantage of the blockwise SVD property, we demonstrate that the block SVD procedure outperforms classical methods based on Galerkin projection or nonlinear wavelet thresholding. We subsequently apply our abstract framework to the specific case of blind deconvolution on the torus and on the sphere.en
dc.relation.isversionofjnlnameElectronic Journal of Statistics
dc.relation.isversionofjnlvol6en
dc.relation.isversionofjnldate2012
dc.relation.isversionofjnlpages2274-2308en
dc.relation.isversionofdoihttp://dx.doi.org/10.1214/12-EJS745en
dc.relation.isversionofjnlpublisherInstitute of Mathematical Statisticsen
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen


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