Robust multi-frequency sparse Bayesian learning: Theory and simulations

Abstract

Compressive sensing based techniques have recently been applied successfully to underwater acoustics problems such as beamforming and matched field processing. Sparse Bayesian Learning (SBL) is one of the fast compressive sensing methods and is formulated using Bayesian statistics. In the SBL framework, source amplitudes are modeled as complex Gaussian random variables with unknown variance. Evidence maximization is performed to estimate the unknown source amplitude variance and source position. A major advantage of SBL over more commonly used methods such as basis pursuit is that it is computationally faster. In this work, we develop a robust sparse Bayesian learning algorithm that can account for model mismatch leading to errors in the replica vector dictionary. Specifically, the likelihood function is modified so that it takes into account the covariance matrix of error in replica vectors. We also extend the SBL algorithm to process observations from multiple frequencies. The derived update rule combines observations from all the frequencies in a holistic manner. We demonstrate the robust SBL algorithm with simulations. A comparison is done with other compressed sensing methods including basis pursuit and orthogonal matching pursuit.