Biomedical Imaging Group
Logo EPFL
    • Splines Tutorials
    • Splines Art Gallery
    • Wavelets Tutorials
    • Image denoising
    • ERC project: FUN-SP
    • Sparse Processes - Book Preview
    • ERC project: GlobalBioIm
    • The colored revolution of bioimaging
    • Deconvolution
    • SMLM
    • One-World Seminars: Representer theorems
    • A Unifying Representer Theorem
Follow us on Twitter.
Join our Github.
Masquer le formulaire de recherche
Menu
BIOMEDICAL IMAGING GROUP (BIG)
Laboratoire d'imagerie biomédicale (LIB)
  1. School of Engineering STI
  2. Institute IEM
  3.  LIB
  4.  Continuous Relaxations
  • Laboratory
    • Laboratory
    • Laboratory
    • People
    • Jobs and Trainees
    • News
    • Events
    • Seminars
    • Resources (intranet)
    • Twitter
  • Research
    • Research
    • Researchs
    • Research Topics
    • Talks, Tutorials, and Reviews
  • Publications
    • Publications
    • Publications
    • Database of Publications
    • Talks, Tutorials, and Reviews
    • EPFL Infoscience
  • Code
    • Code
    • Code
    • Demos
    • Download Algorithms
    • Github
  • Teaching
    • Teaching
    • Teaching
    • Courses
    • Student projects
  • Splines
    • Teaching
    • Teaching
    • Splines Tutorials
    • Splines Art Gallery
    • Wavelets Tutorials
    • Image denoising
  • Sparsity
    • Teaching
    • Teaching
    • ERC project: FUN-SP
    • Sparse Processes - Book Preview
  • Imaging
    • Teaching
    • Teaching
    • ERC project: GlobalBioIm
    • The colored revolution of bioimaging
    • Deconvolution
    • SMLM
  • Machine Learning
    • Teaching
    • Teaching
    • One-World Seminars: Representer theorems
    • A Unifying Representer Theorem

Quelles relaxations continues pour le critère ℓ2-ℓ0 ?

E. Soubies, L. Blanc-Féraud, G. Aubert

Proceedings of the Twenty-Sixth GRETSI Symposium on Signal and Image Processing (GRETSI'17), Juan-les-Pins, French Republic, September 5-8, 2017, paper no. ID252.


For more than two decades, several continuous (and generally separable) penalties approximating (relaxing) the ℓ0-pseudo norm have been proposed. Although some "good" properties for such penalties have been highlighted, the choice of one relaxation rather than another one remains unclear. One approach to compare them is to investigate their fidelity to the initial problem. In other words, do they preserve global minimizers of the initial criteria without adding new local ones? Within the context of the ℓ0 penalized least squares, we have recently studied this question resulting in a class of penalties said exact. In this communication, we present these results and complete them with a study concerning the local minimizers eliminated by such relaxations. In particular, we show that the CEL0 penalty is the one removing the largest number of local minimizers.

@INPROCEEDINGS(http://bigwww.epfl.ch/publications/soubies1702.html,
AUTHOR="Soubies, E. and Blanc-F{\'{e}}raud, L. and Aubert, G.",
TITLE="Quelles relaxations continues pour le crit{\`{e}}re
	$\ell_{2}$-$\ell_{0}$?",
BOOKTITLE="Proceedings of the Twenty-Sixth GRETSI Symposium on Signal
	and Image Processing ({GRETSI'17})",
YEAR="2017",
editor="",
volume="",
series="",
pages="",
address="Juan-les-Pins, French Republic",
month="September 5-8,",
organization="",
publisher="",
note="paper no.\ ID252")
© 2017 GRETSI. 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 GRETSI. 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.
  • Laboratory
  • Research
  • Publications
    • Database of Publications
    • Talks, Tutorials, and Reviews
    • EPFL Infoscience
  • Code
  • Teaching
Logo EPFL, Ecole polytechnique fédérale de Lausanne
Emergencies: +41 21 693 3000 Services and resources Contact Map Webmaster email

Follow EPFL on social media

Follow us on Facebook. Follow us on Twitter. Follow us on Instagram. Follow us on Youtube. Follow us on LinkedIn.
Accessibility Disclaimer Privacy policy

© 2023 EPFL, all rights reserved