A Framework for Clustered and Skewed Sparse Signal Recovery

A novel framework, clustered-skew normal mixture-belief propagation, is developed to solve the reconstruction of undersampled clustered signals, where the magnitudes of signal coefficients in each cluster are distributed asymmetrically w.r.t the cluster mean. To address the skewness feature, a finite skew-normal density mixture is utilized to model the prior distribution, where the marginal posterior of the signal is inferred by an efficient approximate message-passing-based algorithm. An expectation-maximization-based algorithm is developed to estimate the mixture density. The clustered property is then modeled by the Potts model, and a loopy belief propagation algorithm is designed to promote the spatial feature. Experimental results show that our technique is highly effective and efficient in exploiting both the clustered feature and asymmetrical feature of the signals and outperforms many sophisticated techniques.