Generalized orthogonal matching pursuit

Jian Wang, Seokbeop Kwon, Byonghyo Shim

Research output: Contribution to journalArticle

306 Citations (Scopus)

Abstract

As a greedy algorithm to recover sparse signals from compressed measurements, orthogonal matching pursuit (OMP) algorithm has received much attention in recent years. In this paper, we introduce an extension of the OMP for pursuing efficiency in reconstructing sparse signals. Our approach, henceforth referred to as generalized OMP (gOMP), is literally a generalization of the OMP in the sense that multiple N indices are identified per iteration. Owing to the selection of multiple correct indices, the gOMP algorithm is finished with much smaller number of iterations when compared to the OMP. We show that the gOMP can perfectly reconstruct any K-sparse signals (K ≥ 1) , provided that the sensing matrix satisfies the RIP with δNK< √ N/√K+3√N. We also demonstrate by empirical simulations that the gOMP has excellent recovery performance comparable to L1- minimization technique with fast processing speed and competitive computational complexity.

Original languageEnglish
Article number6302206
Pages (from-to)6202-6216
Number of pages15
JournalIEEE Transactions on Signal Processing
Volume60
Issue number12
DOIs
Publication statusPublished - 2012 Dec 10

Fingerprint

Computational complexity
Recovery
Processing

Keywords

  • Compressive sensing (CS)
  • orthogonal matching pursuit
  • restricted isometry property (RIP)
  • sparse recovery

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Signal Processing

Cite this

Generalized orthogonal matching pursuit. / Wang, Jian; Kwon, Seokbeop; Shim, Byonghyo.

In: IEEE Transactions on Signal Processing, Vol. 60, No. 12, 6302206, 10.12.2012, p. 6202-6216.

Research output: Contribution to journalArticle

Wang, Jian ; Kwon, Seokbeop ; Shim, Byonghyo. / Generalized orthogonal matching pursuit. In: IEEE Transactions on Signal Processing. 2012 ; Vol. 60, No. 12. pp. 6202-6216.
@article{3a46adc4aacc4f0583ca0e9a7d4a262f,
title = "Generalized orthogonal matching pursuit",
abstract = "As a greedy algorithm to recover sparse signals from compressed measurements, orthogonal matching pursuit (OMP) algorithm has received much attention in recent years. In this paper, we introduce an extension of the OMP for pursuing efficiency in reconstructing sparse signals. Our approach, henceforth referred to as generalized OMP (gOMP), is literally a generalization of the OMP in the sense that multiple N indices are identified per iteration. Owing to the selection of multiple correct indices, the gOMP algorithm is finished with much smaller number of iterations when compared to the OMP. We show that the gOMP can perfectly reconstruct any K-sparse signals (K ≥ 1) , provided that the sensing matrix satisfies the RIP with δNK< √ N/√K+3√N. We also demonstrate by empirical simulations that the gOMP has excellent recovery performance comparable to L1- minimization technique with fast processing speed and competitive computational complexity.",
keywords = "Compressive sensing (CS), orthogonal matching pursuit, restricted isometry property (RIP), sparse recovery",
author = "Jian Wang and Seokbeop Kwon and Byonghyo Shim",
year = "2012",
month = "12",
day = "10",
doi = "10.1109/TSP.2012.2218810",
language = "English",
volume = "60",
pages = "6202--6216",
journal = "IEEE Transactions on Signal Processing",
issn = "1053-587X",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
number = "12",

}

TY - JOUR

T1 - Generalized orthogonal matching pursuit

AU - Wang, Jian

AU - Kwon, Seokbeop

AU - Shim, Byonghyo

PY - 2012/12/10

Y1 - 2012/12/10

N2 - As a greedy algorithm to recover sparse signals from compressed measurements, orthogonal matching pursuit (OMP) algorithm has received much attention in recent years. In this paper, we introduce an extension of the OMP for pursuing efficiency in reconstructing sparse signals. Our approach, henceforth referred to as generalized OMP (gOMP), is literally a generalization of the OMP in the sense that multiple N indices are identified per iteration. Owing to the selection of multiple correct indices, the gOMP algorithm is finished with much smaller number of iterations when compared to the OMP. We show that the gOMP can perfectly reconstruct any K-sparse signals (K ≥ 1) , provided that the sensing matrix satisfies the RIP with δNK< √ N/√K+3√N. We also demonstrate by empirical simulations that the gOMP has excellent recovery performance comparable to L1- minimization technique with fast processing speed and competitive computational complexity.

AB - As a greedy algorithm to recover sparse signals from compressed measurements, orthogonal matching pursuit (OMP) algorithm has received much attention in recent years. In this paper, we introduce an extension of the OMP for pursuing efficiency in reconstructing sparse signals. Our approach, henceforth referred to as generalized OMP (gOMP), is literally a generalization of the OMP in the sense that multiple N indices are identified per iteration. Owing to the selection of multiple correct indices, the gOMP algorithm is finished with much smaller number of iterations when compared to the OMP. We show that the gOMP can perfectly reconstruct any K-sparse signals (K ≥ 1) , provided that the sensing matrix satisfies the RIP with δNK< √ N/√K+3√N. We also demonstrate by empirical simulations that the gOMP has excellent recovery performance comparable to L1- minimization technique with fast processing speed and competitive computational complexity.

KW - Compressive sensing (CS)

KW - orthogonal matching pursuit

KW - restricted isometry property (RIP)

KW - sparse recovery

UR - http://www.scopus.com/inward/record.url?scp=84870506486&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84870506486&partnerID=8YFLogxK

U2 - 10.1109/TSP.2012.2218810

DO - 10.1109/TSP.2012.2218810

M3 - Article

AN - SCOPUS:84870506486

VL - 60

SP - 6202

EP - 6216

JO - IEEE Transactions on Signal Processing

JF - IEEE Transactions on Signal Processing

SN - 1053-587X

IS - 12

M1 - 6302206

ER -