Variational Bayesian and Generalized Approximate Message Passing-Based Sparse Bayesian Learning Model for Image Reconstruction

In this paper, we present a novel sparse Bayesian learning (SBL) framework for large-scale image recovery. We formulate variational Bayesian (VB) and generalized approximate message passing (GAMP) into the SBL model (called VGAMP-SBL) to speed up image reconstruction. GAMP can be argued a scalar estimation function described by a set of simple state evolution (SE) equations. From the SE equations, one can accurately predict the values of SBL Params, while it can obtain better reconstruction results without matrix inversion. Moreover, the interaction between data fluctuations and parameter fluctuations is negligible in VB structure, so the maximum marginal likelihood function can be easily obtained, This improves the computation efficiency of our algorithm greatly. Experimental results corroborate these claims.