Sparse Recovery With Orthogonal Matching Pursuit Under RIP - Zhang, Tong (IEEE transactions on information theory, 2011)
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 (k̅), then OMP can stably recover a k̅ -sparse signal in 2-norm under measurement noise. For compressed sensing applications, this result implies that in order to uniformly recover a k̅ -sparse signal in R d , only O ( k̅ 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( k̅ 2 ln d ) or Ω( k̅ 1.6 ln d ) random projections.