Bayesian Compressive Sensing for clustered 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. Besides sparse prior, cluster prior is introduced in this paper in order to investigate a class of structural sparse signals, called clustered sparse signals. A hierarchical statistical model is employed via Bayesian approach to model both the sparse prior and cluster prior and Markov Chain Monte Carlo (MCMC) sampling is implemented for the inference. Unlike the state-of-the-art algorithms based on the cluster prior, the proposed algorithm solves the inverse problem without any prior knowledge of the cluster parameters, even without the knowledge of the sparsity. The experimental results show that the proposed algorithm outperforms many state-of-the-art algorithms.