Addressing the Noise Variance Problem in Sparse Bayesian Learning

Tharun Adithya Srikrishnan, Bhaskar D. Rao

Abstract: The Sparse Bayesian Learning (SBL) / Relevance Vector Machine (RVM) algorithm and their variations show exceptional performance for compressed sensing and sparse signal recovery applications. The Bayesian framework allows for naturally incorporating multiple measurement vectors, structure, temporal correlations, etc. A drawback of this algorithm is the failure of recovering the noise variance / regularization in low SNR scenarios despite there being a closed-form EM update rule. There is potential for suboptimal performance due to difficulty in setting the noise variance. We attempt to alleviate this problem by using a Jeffreys prior as an alternate to a uniform prior on the hyper-parameters in the original SBL formulation. We suggest an approach for setting the optimal noise variance such that the Jeffreys prior is imitated and provide some preliminary theoretical justification. The resulting method has the benefit of avoiding premature pruning as well as better noise variance characteristics. The hypothesis is validated with an experimental study. We further provide extensions of this approach for the case of Multiple Measurement Vectors (MMV), perturbed sensing matrices and complex-domain settings.

External IDs:dblp:conf/acssc/SrikrishnanR18