License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
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DOI: 10.4230/DagSemProc.08492.5
URN: urn:nbn:de:0030-drops-18816
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2009/1881/
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Ehler, Martin ; Geisel, Simone

Arbitrary Shrinkage Rules for Approximation Schemes with Sparsity Constraints

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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$.

BibTeX - Entry

@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/opus/volltexte/2009/1881},
  URN =		{urn:nbn:de:0030-drops-18816},
  doi =		{10.4230/DagSemProc.08492.5},
  annote =	{Keywords: Frames, shrinkage, variational problems, sparse approximation}
}

Keywords: Frames, shrinkage, variational problems, sparse approximation
Collection: 08492 - Structured Decompositions and Efficient Algorithms
Issue Date: 2009
Date of publication: 24.02.2009

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