Double‐level binary tree Bayesian compressed sensing for block structured sparse signals

Abstract

Sparsity is one of the key points in the compressed sensing (CS) theory, which provides a sub‐Nyquist sampling paradigm. Nevertheless, apart from sparsity, structures on the sparse patterns such as block structures and tree structures can also be exploited to improve the reconstruction performance and further reduce the sampling rate in CS framework. Based on the fact that the block structure is also sparse for a widely studied block sparse signal, in this study, a double‐level binary tree (DBT) hierarchical Bayesian model is proposed under the Bayesian CS (BCS) framework. The authors exploit a recovery algorithm with the proposed DBT structured model, and the block clustering in the proposed algorithm can be achieved fastly and correctly using the Markov Chain Monte Carlo method. The experimental results demonstrate that, compared with most existing CS algorithms for block sparse signals, our proposed DBT‐based BCS algorithm can obtain good recovery results with less time consuming.