dc.contributor.author Denoyelle, Quentin dc.contributor.author Duval, Vincent dc.contributor.author Peyré, Gabriel dc.date.accessioned 2017-11-22T12:06:11Z dc.date.available 2017-11-22T12:06:11Z dc.date.issued 2016 dc.identifier.issn 1069-5869 dc.identifier.uri https://basepub.dauphine.fr/handle/123456789/17014 dc.language.iso en en dc.subject Radon measure dc.subject Sparse Signal Processing dc.subject Super-resolution dc.subject Sparsity dc.subject Deconvolution dc.subject Convex optimization dc.subject LASSO dc.subject BLASSO dc.subject.ddc 621.3 en dc.title Support Recovery for Sparse Super-Resolution of Positive Measures dc.type Article accepté pour publication ou publié dc.description.abstracten We 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.isversionofjnlname Journal of Fourier Analysis and Applications dc.relation.isversionofjnlvol 23 dc.relation.isversionofjnlissue 5 dc.relation.isversionofjnldate 2016 dc.relation.isversionofjnlpages 1153–1194 dc.relation.isversionofdoi 10.1007/s00041-016-9502-x dc.subject.ddclabel Traitement du signal en dc.relation.forthcoming non en dc.relation.forthcomingprint non en dc.description.ssrncandidate non dc.description.halcandidate non dc.description.readership recherche dc.description.audience International dc.relation.Isversionofjnlpeerreviewed oui dc.date.updated 2017-12-19T09:54:16Z hal.person.labIds 60 hal.person.labIds 60 hal.person.labIds 60
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