An RIP Condition for Exact Support Recovery With Covariance-Assisted Matching Pursuit

Abstract

The covariance-assisted matching pursuit (CAMP) algorithm has recently been proposed for recovering sparse signals f from noisy linear measurements based on a priori knowledge of the covariance and mean of the nonzero coefficients of f. It utilizes the a priori knowledge by incorporating the Gauss-Markov theorem into the orthogonal matching pursuit (OMP) algorithm and has a significantly better reconstruction performance than OMP. This letter develops sufficient conditions of exact support recovery of any k-sparse signals f via CAMP ink iterations, under the 12-bounded and Gaussian noises. These sufficient conditions are based on the restricted isometry constant of the sensing matrix and minimum magnitude of the nonzero elements of f, and are much better than the existing ones.