Sparse Bayesian learning with multiple dictionaries

Sparse Bayesian learning (SBL) employs Gaussian priors with unknown parameters to solve an underdetermined system of linear equation. It provides comparable performance and is significantly faster than convex optimization techniques used in sparse processing. In this paper we extend SBL to process observations from multiple dictionaries when the sparse solutions have common support across dictionaries. Two solutions are presented, a multiple covariance formulation and a common covariance formulation. As an example, the multi-dictionary approach is used to estimate the direction-of-arrivals in presence of aliasing. Simulations and data from the SwellEx-96 experiment are used to demonstrate qualitatively the advantages of multi-dictionary SBL.