A Sharp RIP Condition for Orthogonal Matching Pursuit

Abstract EN

A restricted isometry property (RIP) condition δK+KθK,1<1 is known to be sufficient for orthogonal matching pursuit (OMP) to exactly recover every K-sparse signal x from measurements y=Φx.

This paper is devoted to demonstrate that this condition is sharp.

We construct a specific matrix with δK+KθK,1=1 such that OMP cannot exactly recover some K-sparse signals.