EPFL
 Biomedical Imaging GroupSTI
EPFL
  Publications
English only   BIG > Publications > Frank-Wolfe Algorithm


 CONTENTS
 Home Page
 News & Events
 People
 Publications
 Tutorials and Reviews
 Research
 Demos
 Download Algorithms

 DOWNLOAD
 PDF
 Postscript
 All BibTeX References

The Sliding Frank-Wolfe Algorithm for the BLASSO

Q. Denoyelle, V. Duval, G. Peyré, E. Soubies

Proceedings of the Workshop on Signal Processing with Adaptive Sparse Structured Representations (SPARS'19), Toulouse, French Republic, July 1-4, 2019, paper no. 172.



This paper showcases the Sliding Frank-Wolfe (SFW), which is a novel optimization algorithm to solve the BLASSO sparse spikes super-resolution problem. The BLASSO is the continuous (i.e. off-thegrid or grid-less) counterpart of the well-known ℓ1 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). We prove theoretically that this algorithm terminates in a finite number of steps under a mild non-degeneracy hypothesis.


@INPROCEEDINGS(http://bigwww.epfl.ch/publications/denoyelle1901.html,
AUTHOR="Denoyelle, Q. and Duval, V. and Peyr{\'{e}}, G. and Soubies,
        E.",
TITLE="The Sliding {F}rank-{W}olfe Algorithm for the {BLASSO}",
BOOKTITLE="Proceedings of the Workshop on Signal Processing with
        Adaptive Sparse Structured Representations ({SPARS'19})",
YEAR="2019",
editor="",
volume="",
series="",
pages="",
address="Toulouse, French Republic",
month="July 1-4,",
organization="",
publisher="",
note="paper no.\ 172")

© 2019 INP. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from INP.
This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.