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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 482357, 3 pages
http://dx.doi.org/10.1155/2013/482357
Research Article

A Sharp RIP Condition for Orthogonal Matching Pursuit

School of Mathematics and Statistics, Guangdong University of Finance & Economics, Guangzhou 510320, China

Received 3 July 2013; Revised 14 September 2013; Accepted 5 October 2013

Academic Editor: Sergei V. Pereverzyev

Copyright © 2013 Wei Dan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A restricted isometry property (RIP) condition is known to be sufficient for orthogonal matching pursuit (OMP) to exactly recover every K-sparse signal x from measurements . This paper is devoted to demonstrate that this condition is sharp. We construct a specific matrix with such that OMP cannot exactly recover some K-sparse signals.