Biomedical Imaging GroupSTI
English only   BIG > Publications > Exact Relaxations

 Home Page
 News & Events
 Tutorials and Reviews
 Download Algorithms

 PDF not available
 PS not available
 All BibTeX References

Exact Continuous Relaxations for the ℓ0-Regularized Least-Squares Criteria

E. Soubies

SIAM Conference on Imaging Science (SIS'18), Bologna, Italian Republic, June 5-8, 2018, session MS37-2.

Several continuous non-convex relaxations of the ℓ0 pseudo-norm have been proposed over the past. In this talk, considering the ℓ0-regularized least-squares minimization problem (ℓ2-ℓ0), I will present theoretical results which allow to compare such relaxations from the perspective of their fidelity to the initial ℓ2-ℓ0 problem. I will exhibit necessary and sufficient conditions on separable penalties approximating the ℓ0 pseudo-norm which ensure that the associated regularized least-squares functional preserves the global minimizers of the initial one and do not add new local minimizers. From these conditions, we get a class of penalties said to be exact regarding to their properties concerning the relaxed functional.

AUTHOR="Soubies, E.",
TITLE="Exact Continuous Relaxations for the $\ell_{0}$-Regularized
        Least-Squares Criteria",
BOOKTITLE="{SIAM} Conference on Imaging Science ({SIS'18})",
address="Bologna, Italian Republic",
month="June 5-8,",
note="session MS37-2")

© 2018 SIAM. 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 SIAM.
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.