Sparse Signal Recovery Using MPDR Estimation

Abstract

Utilizing the array processing minimum power distortionless response (MPDR) beamformer framework, we present a new perspective on the sparse Bayesian learning (SBL) algorithm used in sparse signal recovery. In addition to providing more insight into the SBL algorithm, this new perspective allows us to extend the algorithm to more general non-Gaussian priors. Finally, we use the connection between the MPDR and the LMMSE estimator to lower the complexity of the algorithm using a generalized approximate message passing (GAMP) based LMMSE estimator. The result is a GAMP based algorithm with improved convergence properties.