Exact Recovery of Sparse Signals Using Orthogonal Matching Pursuit: How Many Iterations Do We Need?

Jian Wang, Byonghyo Shim

Research output: Contribution to journalArticlepeer-review

38 Citations (Scopus)

Abstract

Orthogonal matching pursuit (OMP) is a greedy algorithm widely used for the recovery of sparse signals from compressed measurements. In this paper, we analyze the number of iterations required for the OMP algorithm to perform exact recovery of sparse signals. Our analysis shows that OMP can accurately recover all K-sparse signals within lceil 2.8 \; K \rceil iterations when the measurement matrix satisfies a restricted isometry property (RIP). Our result improves upon the recent result of Zhang and also bridges the gap between Zhang's result and the fundamental limit of OMP at which exact recovery of K-sparse signals cannot be uniformly guaranteed.

Original languageEnglish
Article number7469405
Pages (from-to)4194-4202
Number of pages9
JournalIEEE Transactions on Signal Processing
Volume64
Issue number16
DOIs
Publication statusPublished - 2016 Aug 15

Keywords

  • Sparse signal recovery
  • orthogonal matching pursuit (OMP)
  • restricted isometry property (RIP)

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering

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