| dc.contributor.author | Denoyelle, Quentin | * |
| dc.contributor.author | Duval, Vincent | * |
| dc.contributor.author | Peyré, Gabriel | * |
| dc.contributor.author | Soubies, Emmanuel | * |
| dc.date.accessioned | 2019-02-18T16:09:41Z | |
| dc.date.available | 2019-02-18T16:09:41Z | |
| dc.date.issued | 2018 | |
| dc.identifier.uri | https://basepub.dauphine.fr/handle/123456789/18449 | |
| dc.language.iso | en | en |
| dc.subject | Frank-Wolfe Algorithm | |
| dc.subject | Super-Resolution Microscopy | |
| dc.subject.ddc | 515 | en |
| dc.title | The Sliding Frank-Wolfe Algorithm and its Application to Super-Resolution Microscopy | |
| dc.type | Document de travail / Working paper | |
| dc.description.abstracten | This 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.citationpages | 42 | |
| dc.relation.ispartofseriestitle | Cahier de recherche CEREMADE, Université Paris-Dauphine | |
| dc.identifier.urlsite | https://hal.archives-ouvertes.fr/hal-01921604 | |
| dc.subject.ddclabel | Analyse | en |
| dc.description.ssrncandidate | non | |
| dc.description.halcandidate | non | |
| dc.description.readership | recherche | |
| dc.description.audience | International | |
| dc.date.updated | 2019-09-20T13:10:02Z | |
| hal.person.labIds | | * |
| hal.person.labIds | 60 | * |
| hal.person.labIds | 60 | * |
| hal.person.labIds | | * |
