A sharp RIP condition for orthogonal matching pursuit

Abstract

A restricted isometry property (RIP) condition δK + √K θK, 1 < 1 is known to be sufficient for orthogonal matching pursuit (OMP) to exactly recover every K-sparse signal x from measurements y = Φ x. This paper is devoted to demonstrate that this condition is sharp. We construct a specific matrix with δK + √K θK, 1 = 1 such that OMP cannot exactly recover some K-sparse signals. © 2013 Wei Dan.