On the recovery limit of sparse signals using orthogonal matching pursuit

Jian Wang, Byonghyo Shim

Research output: Contribution to journalArticlepeer-review

106 Citations (Scopus)

Abstract

Orthogonal matching pursuit (OMP) is a greedy search algorithm popularly being used for the recovery of compressive sensed sparse signals. In this correspondence, we show that if the isometry constant δ K+1 of the sensing matrix Φ satisfies δi <1 K+1 then the OMP algorithm can perfectly recover K-sparse signals from the compressed measurements y= Φx. Our bound offers a substantial improvement over the recent result of Davenport and Wakin and also closes gap between the recovery bound and fundamental limit over which the perfect recovery of the OMP cannot be guaranteed.

Original languageEnglish
Article number6213142
Pages (from-to)4973-4976
Number of pages4
JournalIEEE Transactions on Signal Processing
Volume60
Issue number9
DOIs
Publication statusPublished - 2012

Keywords

  • Compressed sensing (CS)
  • orthogonal matching pursuit (OMP)
  • restricted isometry property (RIP)
  • sparse signal

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering

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