An improved RIP-based performance guarantee for sparse signal reconstruction via subspace pursuit

Ling Hua Chang, Jwo-Yuh Wu

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

5 Scopus citations

Abstract

Subspace pursuit (SP) is a well-known greedy algorithm capable of reconstructing a sparse signal vector from a set of incomplete measurements. In this paper, by exploiting an approximate orthogonality condition characterized in terms of the achievable angles between two compressed orthogonal sparse vectors, we show that perfect signal recovery in the noiseless case, as well as stable signal recovery in the noisy case, is guaranteed if the sensing matrix satisfies RIP of order 3K with RIC δ3K ≤ 0.2412. Our work improves the best-known existing results, namely, δ3K < 0.165 for the noiseless case [3] and δ3K < 0.139 when noise is present [4]. In addition, for the noisy case we derive a reconstruction error upper bound, which is shown to be smaller as compared to the bound reported in [4].

Original languageEnglish
Title of host publication2014 IEEE 8th Sensor Array and Multichannel Signal Processing Workshop, SAM 2014
PublisherIEEE Computer Society
Pages405-408
Number of pages4
ISBN (Print)9781479914814
DOIs
StatePublished - 1 Jan 2014
Event2014 IEEE 8th Sensor Array and Multichannel Signal Processing Workshop, SAM 2014 - A Coruna, Spain
Duration: 22 Jun 201425 Jun 2014

Publication series

NameProceedings of the IEEE Sensor Array and Multichannel Signal Processing Workshop
ISSN (Electronic)2151-870X

Conference

Conference2014 IEEE 8th Sensor Array and Multichannel Signal Processing Workshop, SAM 2014
CountrySpain
CityA Coruna
Period22/06/1425/06/14

Keywords

  • Compressive sensing
  • restricted isometry constant (RIC)
  • restricted isometry property (RIP)
  • subspace pursuit

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