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 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 behind some specific signals is often exploited to enhance the reconstruction accuracy. In this study, the authors are aiming to take into account the cluster structure property of sparse signals, of which the non-zero coefficients appear in clustered blocks. By modelling simultaneously both sparsity and cluster prior within a hierarchical statistical Bayesian framework, a non-parametric algorithm can be obtained through variational Bayes approach to recover original sparse signals. The proposed algorithm could be slightly considered as a generalisation of Bayesian CS (BCS), but with a consideration on cluster property. Consequently, the performance of the proposed algorithm is at least as good as BCS, which is verified by the experimental results.