Recovery of sparse signals via generalized orthogonal matching pursuit: A new analysis

Jian Wang, Suhyuk Kwon, Ping Li, Byonghyo Shim

Research output: Contribution to journalArticle

57 Citations (Scopus)

Abstract

As an extension of orthogonal matching pursuit (OMP) for improving the recovery performance of sparse signals, generalized OMP (gOMP) has recently been studied in the literature. In this paper, we present a new analysis of the gOMP algorithm using the restricted isometry property (RIP). We show that if a measurement matrix Φ ∈ Rm×n satisfies the RIP with isometry constant δmax{9,S+1}K ≤ 1/8, then gOMP performs stable reconstruction of all K-sparse signals x ∈ Rn from the noisy measurements y=Φ x+ v, within {K,⌊8K/S⌋ iterations, where v is the noise vector and S is the number of indices chosen in each iteration of the gOMP algorithm. For Gaussian random measurements, our result indicates that the number of required measurements is essentially m= O(K log n/K), which is a significant improvement over the existing result m= O(K2 log n/K), especially for large K.

Original languageEnglish
Article number7321045
Pages (from-to)1076-1089
Number of pages14
JournalIEEE Transactions on Signal Processing
Volume64
Issue number4
DOIs
Publication statusPublished - 2016 Feb 15
Externally publishedYes

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Keywords

  • Compressed Sensing (CS)
  • Generalized Orthogonal Matching Pursuit (gOMP)
  • Mean Square Error (MSE)
  • Restricted Isometry Property (RIP)
  • sparse recovery
  • stability

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Signal Processing

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