Generalized covariance-assisted matching pursuit

Abstract

Sparse recovery aims to accurately recover the support of sparse vector from a very limited number of noisy linear measurements. By utilizing the covariance and mean of the sparse coefficients, we propose a new algorithm: generalized covariance-assisted matching pursuit (GCAMP). It preserves the elegance and practicality of generalized orthogonal matching pursuit (gOMP) and provides better performance than the CAMP algorithm. In the framework of restricted isometry property (RIP), we present some sufficient conditions on RIP and the minimum magnitude of the nonzero elements of the sparse coefficients, which can guarantee that GCAMP identifies at least one index in the support of any K-sparse signal in each iteration in the noisy case. Numerical experiments are also presented to verify the effectiveness of GCAMP.