On the recovery limit of sparse signals using orthogonal matching pursuit

Jian Wang; Byonghyo Shim

doi:10.1109/TSP.2012.2203124

On the recovery limit of sparse signals using orthogonal matching pursuit

Jian Wang, Byonghyo Shim

Department of Computer Science and Engineering

Research output: Contribution to journal › Article › peer-review

134 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 language	English
Article number	6213142
Pages (from-to)	4973-4976
Number of pages	4
Journal	IEEE Transactions on Signal Processing
Volume	60
Issue number	9
DOIs	https://doi.org/10.1109/TSP.2012.2203124
Publication status	Published - 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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10.1109/TSP.2012.2203124

Cite this

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title = "On the recovery limit of sparse signals using orthogonal matching pursuit",

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.",

keywords = "Compressed sensing (CS), orthogonal matching pursuit (OMP), restricted isometry property (RIP), sparse signal",

author = "Jian Wang and Byonghyo Shim",

note = "Funding Information: Manuscript received August 18, 2011; revised February 23, 2012; accepted May 24, 2012. Date of publication June 06, 2012; date of current version August 07, 2012. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Trac D. Tran. This research was supported by the KCC (Korea Communications Commission) under the R&D program supervised by the KCA (Korea Communications Agency) (KCA-2012-911-01-110).",

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N2 - 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.

AB - 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.

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On the recovery limit of sparse signals using orthogonal matching pursuit

Abstract

Keywords

ASJC Scopus subject areas

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