Exploiting the tree-structured compressive sensing of wavelet coefficients via block sparse Bayesian learning

In this Letter, the authors propose a novel framework based on block sparse Bayesian learning (bSBL) for exploiting the tree structure on wavelet coefficients in the process of recovering signals. A Boolean matrix is designed to transfer the tree structure of wavelet coefficients to a non-overlapped block structure. In this block-structured sparse model, the bSBL-based algorithm is used to learn the intra-block correlations and to derive the updating rule of model parameters. Experimental results show that for both 1D and 2D signals their proposed algorithm has superior performances compared with other model-based compressive sensing algorithms.