Show simple item record

dc.contributor.authorDenoyelle, Quentin*
dc.contributor.authorDuval, Vincent*
dc.contributor.authorPeyré, Gabriel*
dc.contributor.authorSoubies, Emmanuel*
dc.date.accessioned2019-02-18T16:09:41Z
dc.date.available2019-02-18T16:09:41Z
dc.date.issued2018
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/18449
dc.language.isoenen
dc.subjectFrank-Wolfe Algorithm
dc.subjectSuper-Resolution Microscopy
dc.subject.ddc515en
dc.titleThe Sliding Frank-Wolfe Algorithm and its Application to Super-Resolution Microscopy
dc.typeDocument de travail / Working paper
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.
dc.identifier.citationpages42
dc.relation.ispartofseriestitleCahier de recherche CEREMADE, Université Paris-Dauphine
dc.identifier.urlsitehttps://hal.archives-ouvertes.fr/hal-01921604
dc.subject.ddclabelAnalyseen
dc.description.ssrncandidatenon
dc.description.halcandidatenon
dc.description.readershiprecherche
dc.description.audienceInternational
dc.date.updated2019-09-20T13:10:02Z
hal.person.labIds*
hal.person.labIds60*
hal.person.labIds60*
hal.person.labIds*


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record