Structured Bayesian compressive sensing exploiting spatial location dependence

Abstract

In this paper, we propose a novel structured compressive sensing algorithm based on non-parametric Bayesian framework for the reconstruction of sparse entries with a continuous structure. A paired spike-and-slab prior is first employed to impose signal sparsity. A logistic Gaussian kernel model, which involves the logistic model and location-dependent Gaussian kernel, is then proposed to encourage the underlying structure of a sparse signal. A closed-form and analytical posterior inference is carried out in a Gibbs sampling scheme. Simulation results demonstrate that the proposed algorithm outperforms existing state-of-the-art sparse Bayesian learning algorithms.