Novel Recovery Algorithms for Block Sparse Signals With Known and Unknown Borders

Abstract

This paper presents two novel Bayesian learning recovery algorithms for block sparse signals corresponding to two distinct cases. In the first case, the signals within each block are correlated and the block borders are known, whereas in the second case, the block borders are unknown and the signal elements are uncorrelated. For the first case, the proposed recovery algorithm differs from existing ones in two aspects. First, in each iteration, the optimal block covariances are obtained based on the data estimated in previous iterations. Hence, it does not rely on prior assumptions nor does it restrict the covariance matrices to have a particular structure. Second, the decision to declare a block as zero or non-zero is based on hypothesis testing, which ensures that the probability of erroneous detection is minimized. 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.