Robustness of orthogonal matching pursuit under restricted isometry property

Orthogonal matching pursuit (OMP) algorithm is an efficient method for the recovery of a sparse signal in compressed sensing, due to its ease implementation and low complexity. In this paper, the robustness of the OMP algorithm under the restricted isometry property (RIP) is presented. It is shown that $\delta _K + \sqrt K \theta _{K,1} < 1$ is sufficient for the OMP algorithm to recover exactly the support of arbitrary K-sparse signal if its nonzero components are large enough for both l ₂ bounded and l _∞ bounded noises.