A Framework for Compressive Sensing of Asymmetric Signals Using Normal and Skew-Normal Mixture Prior

In this work, we are interested in the compressive sensing of sparse signals whose significant coefficients are distributed asymmetrically with respect to zero. To properly address this problem, we develop a framework utilizing a two-state normal and skew normal mixture density as the prior distribution of the signal. The significant and insignificant coefficients of the signal are represented by skew normal and normal distributions, respectively. A novel approximate message passing-based algorithm is developed to estimate the signal from its compressed measurements. A fast gradient-based estimator is designed to infer the density of each state. Experiment results on simulated data and two real-world tests, i.e., multi-input multi-output (MIMO) communication system and weather sensor network, confirm that our proposed technique is powerful in exploiting asymmetrical feature, and outperforms many sophisticated methods.