A hierarchical Bayesian-map approach to computational imaging

We present a novel approach to inverse problems in imaging based on a Hierarchical Bayesian-MAP (HB-MAP) formulation. In this paper we specifically focus on the difficult and basic inverse problem of multi-sensor (tomographic) imaging wherein the source image of interest is viewed from multiple directions by independent sensors. We employ a Probabilistic Graphical Modeling extension of the Compound Gaussian (CG) distribution as a global image prior into a Hierarchical Bayesian inference procedure. We first demonstrate the performance of the algorithm on Monte-Carlo trials followed by empirical data involving natural (optical) images. We demonstrate how our algorithm outperforms many of the previous approaches in the literature including Filtered Back-projection (FBP) and a variety of state-of-the-art compressive sensing (CS) algorithms.