A Remark on the Restricted Isometry Property in Orthogonal Matching Pursuit

This paper demonstrates that if the restricted isometry constant δK+1 of the measurement matrix A satisfies [δK+1 <; 1 √K+1] then a greedy algorithm called Orthogonal Matching Pursuit (OMP) can recover every K-sparse signal x in K iterations from Ax. By contrast, a matrix is also constructed with the restricted isometry constant [δK+1 = 1 √K] such that OMP can not recover some K-sparse signal x in K iterations. This result positively verifies the conjecture given by Dai and Milenkovic in 2009.