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dc.contributor.authorDenoyelle, Quentin
dc.contributor.authorDuval, Vincent
dc.contributor.authorPeyré, Gabriel
dc.date.accessioned2017-11-22T12:06:11Z
dc.date.available2017-11-22T12:06:11Z
dc.date.issued2016
dc.identifier.issn1069-5869
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/17014
dc.language.isoenen
dc.subjectRadon measure
dc.subjectSparse Signal Processing
dc.subjectSuper-resolution
dc.subjectSparsity
dc.subjectDeconvolution
dc.subjectConvex optimization
dc.subjectLASSO
dc.subjectBLASSO
dc.subject.ddc621.3en
dc.titleSupport Recovery for Sparse Super-Resolution of Positive Measures
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe study sparse spikes super-resolution over the space of Radon measures on \(\mathbb {R}\) or \(\mathbb {T}\) when the input measure is a finite sum of positive Dirac masses using the BLASSO convex program. We focus on the recovery properties of the support and the amplitudes of the initial measure in the presence of noise as a function of the minimum separation t of the input measure (the minimum distance between two spikes). We show that when \({w}/\lambda \), \({w}/t^{2N-1}\) and \(\lambda /t^{2N-1}\) are small enough (where \(\lambda \) is the regularization parameter, w the noise and N the number of spikes), which corresponds roughly to a sufficient signal-to-noise ratio and a noise level small enough with respect to the minimum separation, there exists a unique solution to the BLASSO program with exactly the same number of spikes as the original measure. We show that the amplitudes and positions of the spikes of the solution both converge toward those of the input measure when the noise and the regularization parameter drops to zero faster than \(t^{2N-1}\).
dc.relation.isversionofjnlnameJournal of Fourier Analysis and Applications
dc.relation.isversionofjnlvol23
dc.relation.isversionofjnlissue5
dc.relation.isversionofjnldate2016
dc.relation.isversionofjnlpages1153–1194
dc.relation.isversionofdoi10.1007/s00041-016-9502-x
dc.subject.ddclabelTraitement du signalen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen
dc.description.ssrncandidatenon
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dc.description.readershiprecherche
dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2017-12-19T09:54:16Z
hal.person.labIds60
hal.person.labIds60
hal.person.labIds60


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