One-step adaptive markov random field for structured compressive sensing

Recently, Markov random fields (MRFs) have gained much success in sparse signal recovery. One of the challenges is to adaptively estimate the MRF parameters from a few compressed measurements in compressive sensing (CS). To address this problem, a recently developed method proposes to estimate the MRF parameters based on the point estimation of sparse signals. However, the point estimation cannot depict the statistical uncertainty of the latent sparse signal, which can result in inaccurate parameters estimation; thus, limiting the ultimate performance. In this study, we propose a one-step MRF based CS that estimates the MRF parameters from the given measurements through solving a maximum marginal likelihood (MML) problem. Since the marginal likelihood is obtained from averaging over the latent sparse signal population, it offers better generalization over all the latent sparse signals than the point estimation. To solve the MML problem effectively, we approximate the MRF distribution by the product of two simpler distributions, which enables to produce closed-form solutions for all unknown variables with low computational cost. Extensive experiments on a synthetic and three real-world datasets demonstrate the effectiveness of the proposed method in recovery accuracy, noise tolerance, and runtime.