Sparse recovery with orthogonal matching pursuit under RIP

Abstract

This paper presents a new analysis for the orthogonal matching pursuit (OMP) algorithm. It is shown that if the restricted isometry property (RIP) is satisfied at sparsity level O(k), then OMP can stably recover a k-sparse signal in 2-norm under measurement noise. For compressed sensing applications, this result implies that in order to uniformly recover a k-sparse signal in ℝd, only O(k ln d) random projections are needed. This analysis improves some earlier results on OMP depending on stronger conditions that can only be satisfied with Ω(k2 ln d) or Ω(k1.6 ln d) random projections. © 2011 IEEE.