Can we allow linear dependencies in the dictionary in the sparse synthesis framework?

Raja Giryes, Michael Elad

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Signal recovery from a given set of linear measurements using a sparsity prior has been a major subject of research in recent years. In this model, the signal is assumed to have a sparse representation under a given dictionary. Most of the work dealing with this subject has focused on the reconstruction of the signal's representation as the means for recovering the signal itself. This approach forced the dictionary to be of low coherence and with no linear dependencies between its columns. Recently, a series of contributions that focus on signal recovery using the analysis model find that linear dependencies in the analysis dictionary are in fact permitted and beneficial. In this paper we show theoretically that the same holds also for signal recovery in the synthesis case for the ℓ0-synthesis minimization problem. In addition, we demonstrate empirically the relevance of our conclusions for recovering the signal using an ℓ1-relaxation.

Original languageEnglish
Title of host publication2013 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2013 - Proceedings
Pages5459-5463
Number of pages5
DOIs
StatePublished - 18 Oct 2013
Externally publishedYes
Event2013 38th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2013 - Vancouver, BC, Canada
Duration: 26 May 201331 May 2013

Publication series

NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
ISSN (Print)1520-6149

Conference

Conference2013 38th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2013
Country/TerritoryCanada
CityVancouver, BC
Period26/05/1331/05/13

Keywords

  • Sparse representations
  • analysis versus synthesis
  • compressed sensing
  • inverse problems

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