Structured Bayesian compressive sensing with spatial location dependence via variational Bayesian inference

In this paper, a novel non-parametric Bayesian compressive sensing algorithm is proposed to enhance reconstruction performance of sparse entries with a continuous structure by exploiting the location dependence of entries. An approach is proposed which involves the logistic model and location-dependent Gaussian kernel. The variational Bayesian inference scheme is used to perform the posterior distributions and acquire an approximately analytical solution. Compared to the conventional clustered based methods, which only exploit the information of neighboring pixels, the proposed approach takes the relationship between the pixels of the entire image into account to enable the utilization of the underlying sparse signal structure. It significantly reduces the required number of observations for sparse reconstruction. Both real-valued signal applications, including one-dimension signal and two-dimension image, and complex-valued signal applications, including single-snapshot direction-of-arrival (DOA) estimation of distributed sources and inverse synthetic aperture radar (ISAR) imaging with a limited number of pluses, demonstrate the superiority of the proposed algorithm.