Show simple item record

hal.structure.identifierBiomedical Imaging Group [Lausanne]
dc.contributor.authorDenoyelle, Quentin
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorDuval, Vincent
HAL ID: 7243
ORCID: 0000-0002-7709-256X
hal.structure.identifierDépartement de Mathématiques et Applications - ENS Paris [DMA]
dc.contributor.authorPeyré, Gabriel
HAL ID: 1211
hal.structure.identifierInstitut de recherche en informatique de Toulouse [IRIT]
hal.structure.identifierBiomedical Imaging Group [Lausanne]
dc.contributor.authorSoubies, Emmanuel
HAL ID: 225
ORCID: 0000-0003-0571-6983
dc.date.accessioned2021-10-27T09:39:57Z
dc.date.available2021-10-27T09:39:57Z
dc.date.issued2019
dc.identifier.urihttps://basepub.dauphine.psl.eu/handle/123456789/22110
dc.language.isoenen
dc.subjectTraitement du signal et de l'imageen
dc.subject.ddc621.3en
dc.titleThe Sliding Frank-Wolfe Algorithm for the BLASSOen
dc.typeCommunication / Conférence
dc.description.abstractenThis paper showcases the theoretical and numerical performance of the Sliding Frank-Wolfe, which is a novel optimization algorithm to solve the BLASSO sparse spikes super-resolution problem. The BLASSO is a continuous (i.e. off-the-grid or grid-less) counterpart to the well-known 1 sparse regularisation method (also known as LASSO or Basis Pursuit). Our algorithm is a variation on the classical Frank-Wolfe (also known as conditional gradient) which follows a recent trend of interleaving convex optimization updates (corresponding to adding new spikes) with non-convex optimization steps (corresponding to moving the spikes). Our main theoretical result is that this algorithm terminates in a finite number of steps under a mild non-degeneracy hypothesis. We then target applications of this method to several instances of single molecule fluorescence imaging modalities, among which certain approaches rely heavily on the inversion of a Laplace transform. Our second theoretical contribution is the proof of the exact support recovery property of the BLASSO to invert the 1-D Laplace transform in the case of positive spikes. On the numerical side, we conclude this paper with an extensive study of the practical performance of the Sliding Frank-Wolfe on different instantiations of single molecule fluorescence imaging, including convolutive and non-convolutive (Laplace-like) operators. This shows the versatility and superiority of this method with respect to alternative sparse recovery technics.en
dc.identifier.citationpages2en
dc.relation.ispartoftitleWorkshop on Signal Processing with Adaptative Sparse Structured Representations - SPARS 2019en
dc.relation.ispartofpublnameProceedings of the Workshop on Signal Processing with Adaptative Sparse Structured Representations -en
dc.relation.ispartofdate2019
dc.identifier.urlsitehttps://hal.archives-ouvertes.fr/hal-03012568en
dc.subject.ddclabelTraitement du signalen
dc.relation.conftitleSPARS 2019en
dc.relation.confdate2019
dc.relation.confcityToulouseen
dc.relation.confcountryFranceen
dc.relation.forthcomingnonen
dc.description.ssrncandidatenon
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.relation.Isversionofjnlpeerreviewednonen
dc.date.updated2021-10-27T09:35:09Z
hal.author.functionaut
hal.author.functionaut
hal.author.functionaut
hal.author.functionaut


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record