Improved Bayesian learning Algorithms for recovering Block Sparse Signals With Known and Unknown Borders

This paper presents two novel Bayesian learning recovery algorithms for block sparse signals. Two cases are considered. In the first case, the signals within each block are correlated and the block borders are known. In the second case, the block borders are unknown and the signal elements are uncorrelated. Unlike their existing counterparts, the proposed algorithms obtain the optimal block covariances from the data estimated in the previous iterations. Furthermore, the decision to declare a block as zero is based on hypothesis testing. For the second case, we introduce a new prior model which is characterized by elastic dependencies among neighbouring signal elements. Using this model, we develop a novel Bayesian learning algorithm which iterates between estimating the dependencies among the signal elements and updating the Gaussian prior model. Numerical simulations illustrate the effectiveness of the proposed algorithms.