Non-convex priors in Bayesian compressed sensing

We propose a novel Bayesian formulation for the reconstruction from compressed measurements. We demonstrate that high-sparsity enforcing priors based on l
p
-norms, with 0 < p ≤ 1, can be used within a Bayesian framework by majorization-minimization methods. By employing a fully Bayesian analysis of the compressed sensing system and a variational Bayesian analysis for inference, the proposed framework provides model parameter estimates along with the unknown signal, as well as the uncertainties of these estimates. We also show that some existing methods can be derived as special cases of the proposed framework. Experimental results demonstrate the high performance of the proposed algorithm in comparison with commonly used methods for compressed sensing recovery.