A Variational Bayesian approach to Block-Sparse Reconstruction based on Intra-Cluster Relevance

In many practical scenarios, block-sparse structure occurs in sparse signals with nonzero coefficients in some clusters. However, the prior knowledge about the block partition is not available in practice. In this paper, a block-sparse recovery method without need to prior knowledge of cluster patterns and based on intra-cluster relevances between the neighboring coefficients of the sparse signal is proposed. This method utilizes a two layer hierarchical Gaussian-Gamma prior distribution to modeling the intra-cluster relevances between the neighboring coefficients. The prior distribution not only involves it's own hyperparameter, but also its other neighboring hyperparameters. Also, to reduction of reconstruction error and increasing the convergence rate, a variational Bayesian (VB) inference has been designed and developed to learn the hyperparameters. The simulation results show the superiority of the proposed method compared with other methods in terms of the normalized mean square error (NMSE), perfect recovery percentage, correlation and Peak signal-to-noise ratio (PSNR).