Pattern-Coupled Sparse Bayesian Learning for Recovery of Block-Sparse Signals

Abstract—In this paper, we develop a new sparse Bayesian learning method for recovery of block-sparse signals with un-known cluster patterns. A pattern-coupled hierarchical Gaussian prior model is introduced to characterize the statistical depen-dencies among coefficients, where a set of hyperparameters are employed to control the sparsity of signal coefficients. Unlike the conventional sparse Bayesian learning framework in which each individual hyperparameter is associated independently with each coefficient, in this paper, the prior for each coefficient not only involves its own hyperparameter, but also the hyperparameters of its immediate neighbors. In doing this way, the sparsity patterns of neighboring coefficients are related to each other and the hierarchical model has the potential to encourage structured-sparse solutions. The hyperparameters, along with the sparse signal, are learned by maximizing their posterior probability via an expectation-maximization (EM) algorithm. Index Terms—Sparse Bayesian learning, pattern-coupled hi-erarchical model, block-sparse signal recovery. I