Compressed sensing and best approximation from unions of subspaces: Beyond dictionaries

Tomer Peleg, Remi Gribonval, Mike E. Davies

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

1 Scopus citations

Abstract

We propose a theoretical study of the conditions guaranteeing that a decoder will obtain an optimal signal recovery from an underdetermined set of linear measurements. This special type of performance guarantee is termed instance optimality and is typically related with certain properties of the dimensionality-reducing matrix M. Our work extends traditional results in sparse recovery, where instance optimality is expressed with respect to the set of sparse vectors, by replacing this set with an arbitrary finite union of subspaces. We show that the suggested instance optimality is equivalent to a generalized null space property of M and discuss possible relations with generalized restricted isometry properties.

Original languageEnglish
Title of host publication2013 Proceedings of the 21st European Signal Processing Conference, EUSIPCO 2013
PublisherEuropean Signal Processing Conference, EUSIPCO
ISBN (Print)9780992862602
StatePublished - 1 Jan 2013
Externally publishedYes
Event2013 21st European Signal Processing Conference, EUSIPCO 2013 - Marrakech, Morocco
Duration: 9 Sep 201313 Sep 2013

Publication series

NameEuropean Signal Processing Conference
ISSN (Print)2219-5491

Conference

Conference2013 21st European Signal Processing Conference, EUSIPCO 2013
Country/TerritoryMorocco
CityMarrakech
Period9/09/1313/09/13

Keywords

  • Instance optimality
  • null space property
  • restricted isometry property
  • union-of-subspaces

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering

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