Sparse Bayesian learning using correlated hyperparameters for recovery of block sparse signals

Abstract Traditional sparse Bayesian learning applies independent hyperparameters to control the sparsity of each coefficient in the sparse signal. For recovery of block-sparse signals with unknown block partitioning structure, pattern coupled sparse Bayesian learning (PCSBL) method considers the sparsity patterns of the neighboring coefficients to be related to each other and uses a predefined parameter to control the relevance between the hyperparameters. However, for most real signals with block sparsity, the degree of relevance between neighboring coefficients is inhomogeneous, and should be data-dependent. This motivates us to modify PCSBL by replacing the single predefined parameter with a set of data-dependent coupling parameters (DDCP) to capture the relevance. In this paper, by performing a linear transformation to the independent hyperparameters, a set of correlated hyperparameters is generated to build the hierarchical Gaussian prior model for recovery of block sparse signals. The coupling parameters which compose the transformation matrix are estimated by the expectation maximization (EM) principle. The relevance between the hyperparameters is data dependent so the sparsity patterns of neighboring coefficients are related in an adaptive way. Compared with existing block sparse recovery methods, our approach is able to encourage the block sparse structure in a more flexible and more reliable way.