Weighted Block Sparse Bayesian Learning for Basis Selection

Block Sparse Bayesian Learning (BSBL) methods estimate a block sparse vector by maximizing the posterior distribution and using sparsity-inducing priors. In BSBL works, all hyperparameters priors are assumed to follow the same distribution with the same parameters. In this paper, we propose to assign different parameters to each hyperparameter, giving more importance to some hyperparameters over others. The importance weights are obtained by leveraging a low resolution estimate of the underlying sparse vector, for example, an estimate obtained via a method that does not encourage sparsity. We refer to the proposed approach as Weighted Block Sparse Bayesian Learning (WBSBL). Simulation results show that, as compared to BSBL, WBSBL achieves substantial improvement in terms of probability of detection and probability of false alarm in the low signal to noise ratio regime. Also, WBSBL's performance degrades slower than that of BSBL as the number of active blocks increases.