Sparse Bayesian learning with multiple dictionaries.

Highlights • A multi-dictionary sparse Bayesian learning (SBL) algorithm is proposed that can simultaneous process observations generated from different underlying dictionaries. • Multi-dictionary SBL is successfully able to suppress aliasing while processing multifrequency data for direction-of-arrival estimation. • Multi-dictionary SBL is able to significantly improve direction-of-arrival estimation in presence of heteroscedastic noise in low SNR region. Abstract 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. [ABSTRACT FROM AUTHOR]