Compressive Sensing for Cluster Structured Sparse Signals: Variational Bayes Approach

Compressive Sensing (CS) provides a new paradigm of sub-Nyquist sampling which can be considered as an alternative to Nyquist sampling theorem. In particular, providing that signals are with sparse representations in some known space (or domain), information can be perfectly preserved even with small amount of measurements captured by random projections. Besides sparsity prior of signals, the inherent structure property underline some specific signals is often exploited to enhance the reconstruction accuracy and promote the ability of recovery. In this paper, we are aiming to take into account the cluster structure property of sparse signals, of which the nonzero coefficients appear in clustered blocks. By modeling simultaneously both sparsity and cluster prior within a hierarchical statistical Bayesian framework, a nonparametric algorithm can be obtained through variational Bayes approach to recover original sparse signals. The proposed algorithm could be slightly considered as a generalization of Bayesian CS, but with a consideration on cluster property. Consequently, the performance of the proposed algorithm is at least as good as Bayesian CS, which is verified by the experimental results. Index Terms Compressive Sensing, Cluster Structure, Variational Bayes.