DROPS

Document

Arbitrary Shrinkage Rules for Approximation Schemes with Sparsity Constraints

Authors: Martin Ehler and Simone Geisel

Published in: Dagstuhl Seminar Proceedings, Volume 8492, Structured Decompositions and Efficient Algorithms (2009)

Abstract

Finding a sparse representation of a possibly noisy signal is a common problem in signal representation and processing. It can be modeled as a variational minimization with $ell_ au$-sparsity constraints for $ au<1$. Applications whose computation time is crucial require fast algorithms for this minimization. However, there are no fast methods for finding the exact minimizer, and to circumvent this limitation, we consider minimization up to a constant factor. We verify that arbitrary shrinkage rules provide closed formulas for such minimizers, and we introduce a new shrinkage strategy, which is adapted to $ au<1$.

Cite as

Martin Ehler and Simone Geisel. Arbitrary Shrinkage Rules for Approximation Schemes with Sparsity Constraints. In Structured Decompositions and Efficient Algorithms. Dagstuhl Seminar Proceedings, Volume 8492, pp. 1-12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

Copy BibTex To Clipboard

@InProceedings{ehler_et_al:DagSemProc.08492.5,
  author =	{Ehler, Martin and Geisel, Simone},
  title =	{{Arbitrary Shrinkage Rules for Approximation Schemes with Sparsity Constraints}},
  booktitle =	{Structured Decompositions and Efficient Algorithms},
  pages =	{1--12},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2009},
  volume =	{8492},
  editor =	{Stephan Dahlke and Ingrid Daubechies and Michal Elad and Gitta Kutyniok and Gerd Teschke},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.08492.5},
  URN =		{urn:nbn:de:0030-drops-18816},
  doi =		{10.4230/DagSemProc.08492.5},
  annote =	{Keywords: Frames, shrinkage, variational problems, sparse approximation}
}

Search Results

Documents authored by Geisel, Simone

Arbitrary Shrinkage Rules for Approximation Schemes with Sparsity Constraints

Abstract

Cite as

Thanks for your feedback!

Could not send message