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dc.contributor.authorDenoyelle, Quentin
dc.contributor.authorDuval, Vincent
dc.contributor.authorPeyré, Gabriel
dc.contributor.authorSoubies, Emmanuel
dc.date.accessioned2019-09-20T13:14:12Z
dc.date.available2019-09-20T13:14:12Z
dc.date.issued2019
dc.identifier.issn0266-5611
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/19866
dc.language.isoenen
dc.subjectFrank-Wolfe Algorithmen
dc.subjectSuper-Resolution Microscopyen
dc.subject.ddc515en
dc.titleThe Sliding Frank-Wolfe Algorithm and its Application to Super-Resolution Microscopyen
dc.typeArticle accepté pour publication ou publié
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.relation.isversionofjnlnameInverse Problems
dc.relation.isversionofjnldate2019-06
dc.relation.isversionofjnlpages42en
dc.relation.isversionofdoi10.1088/1361-6420/ab2a29en
dc.relation.isversionofjnlpublisherIOP Scienceen
dc.subject.ddclabelAnalyseen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen
dc.description.ssrncandidatenonen
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.relation.Isversionofjnlpeerreviewedouien
dc.relation.Isversionofjnlpeerreviewedouien
dc.date.updated2019-09-20T13:09:43Z
hal.person.labIds60
hal.person.labIds60$$$34587
hal.person.labIds66
hal.person.labIds241828


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