SAVE - SPACE ALTERNATING VARIATIONAL ESTIMATION FOR SPARSE BAYESIAN LEARNING

摘要

In this paper, we address the fundamental problem of sparse signal recovery in a Bayesian framework. The computational complexity associated with Sparse Bayesian Learning (SBL) renders it infeasible even for moderately large problem sizes. To address this issue, we propose a fast version of SBL using Variational Bayesian (VB) inference. VB allows one to obtain analytical approximations to the posterior distributions of interest even when exact inference of these distributions is intractable. We propose a novel fast algorithm called space alternating variational estimation (SAVE), which is a version of VB(-SBL) pushed to the scalar level. Similarly as for SAGE (space-alternating generalized expectation maximization) compared to EM, the component-wise approach of SAVE compared to SBL renders it less likely to get stuck in bad local optima and its inherent damping (more cautious progression) also leads to typically faster convergence of the non-convex optimization process. Simulation results show that the proposed algorithm has a faster convergence rate and achieves lower MSE than other state of the art fast SBL methods.