An RIP-Based Performance Guarantee of Covariance-Assisted Matching Pursuit

An OMP-like covariance-assisted matching pursuit (CAMP) method has recently been proposed. Given a prior knowledge of the covariance and mean of the sparse coefficients, CAMP balances the least squares estimator and the prior knowledge by leveraging the Gauss–Markov theorem. In this letter, we study the performance of CAMP in the framework of restricted isometry property (RIP). It is shown that under some conditions on RIP and the minimum magnitude of the nonzero elements of the sparse signal, CAMP with sparse level <inline-formula> <tex-math notation="LaTeX">$K$</tex-math></inline-formula> can recover the exact support of the sparse signal from noisy measurements. <inline-formula><tex-math notation="LaTeX">$l_2$</tex-math></inline-formula> bounded noise and Gaussian noise are considered in our analysis. We also discuss the extreme conditions of noise (e.g., the noise power is infinite) to simply show the stability of CAMP.