Sparse Bayesian learning with multiple dictionaries

Sparse Bayesian learning (SBL) has emerged as a fast and competitive method to perform sparse processing. The SBL algorithm, which is developed using a Bayesian framework, iteratively solves a non-convex optimization problem using fixed point updates. It provides comparable performance and is significantly faster than convex optimization techniques used in sparse processing. We propose a multi-dictionary SBL algorithm that simultaneously can process observations generated by different underlying dictionaries sharing the same sparsity profile. Two algorithms are proposed and corresponding fixed point update equations are derived. Noise variances are estimated using stochastic maximum likelihood. The multi dictionary SBL has many practical applications. We demonstrate this using direction-of-arrival (DOA) estimation. The first example uses the proposed multi-dictionary SBL to process multi-frequency observations. We show how spatial aliasing can be avoided while processing multi-frequency observations using SBL. SWellEx-96 experimental data demonstrates qualitatively these advantages. In the second example we show how data corrupted with heteroscedastic noise can be processed using multi-dictionary SBL with data pre-whitening. (C) 2019 Elsevier B.V. All rights reserved.