  In this paper, a sparse signal recovery algorithm using Bayesian linear
regression with Cauchy prior (BLRC) is proposed. Utilizing an approximate
expectation maximization(AEM) scheme, a systematic hyper-parameter updating
strategy is developed to make BLRC practical in highly dynamic scenarios.
Remarkably, with a more compact latent space, BLRC not only possesses essential
features of the well-known sparse Bayesian learning (SBL) and iterative
reweighted l2 (IR-l2) algorithms but also outperforms them. Using sparse array
(SPA) and coprime array (CPA), numerical analyses are first performed to show
the superior performance of BLRC under various noise levels, array sizes, and
sparsity levels. Applications of BLRC to sparse multiple-input and
multiple-output (MIMO) radar array signal processing are then carried out to
show that the proposed BLRC can efficiently produce high-resolution images of
the targets.
