Bayesian compressive sensing for cluster structured sparse signals

In traditional framework of compressive sensing (CS), only sparse prior on the property of signals in time or frequency domain is adopted to guarantee the exact inverse recovery. Other than sparse prior, structures on the sparse pattern of the signal have also been used as an additional prior, called model-based compressive sensing, such as clustered structure and tree structure on wavelet coefficients. In this paper, the cluster structured sparse signals are investigated. Under the framework of Bayesian compressive sensing, a hierarchical Bayesian model is employed to model both the sparse prior and cluster prior, then Markov Chain Monte Carlo (MCMC) sampling is implemented for the inference. Unlike the state-of-the-art algorithms which are also taking into account the cluster prior, the proposed algorithm solves the inverse problem automatically—prior information on the number of clusters and the size of each cluster is unknown. The experimental results show that the proposed algorithm outperforms many state-of-the-art algorithms.

► Compressive sensing is new theoretical sampling framework. ► Implicit structures can be exploited to improve the CS reconstruction performance. ► We investigate into the cluster structures via a hierarchical Bayesian model. ► An MCMC sampling is implemented to carry out the Bayesian inference.