Bayesian Cram\'{e}r-Rao Bound for Noisy Non-Blind and Blind Compressed Sensing

Abstract

In this paper, we address the theoretical limitations in reconstructing sparse signals (in a known complete basis) using compressed sensing framework. We also divide the CS to non-blind and blind cases. Then, we compute the Bayesian Cramer-Rao bound for estimating the sparse coefficients while the measurement matrix elements are independent zero mean random variables. Simulation results show a large gap between the lower bound and the performance of the practical algorithms when the number of measurements are low.