A hierarchical Bayesian-MAP approach to inverse problems in imaging

作     者：Raj, Raghu G. 

作者机构：US Naval Res Lab Washington DC 20375 USA 

出 版 物：《INVERSE PROBLEMS》 (逆问题)

年 卷 期：2016年第32卷第7期

页      面：075003-075003页

核心收录：

学科分类：07[理学] 0701[理学-数学] 0702[理学-物理学] 

基　　金：Office of Naval Research through the US Naval Research Laboratory Base Program 

主　　题：inverse problems imaging compressive sensing Bayesian probabilistic graphical models hierarchical Bayes sparse reconstruction 

摘      要：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 object of interest is viewed from multiple directions by independent sensors. Given the measurements recorded by these sensors, the problem is to reconstruct the image (of the object) with a high degree of fidelity. We employ a probabilistic graphical modeling extension of the compound Gaussian distribution as a global image prior into a hierarchical Bayesian inference procedure. Since the prior employed by our HB-MAP algorithm is general enough to subsume a wide class of priors including those typically employed in compressive sensing (CS) algorithms, HB-MAP algorithm offers a vehicle to extend the capabilities of current CS algorithms to include truly global priors. After rigorously deriving the regression algorithm for solving our inverse problem from first principles, we demonstrate the performance of the HB-MAP algorithm on Monte Carlo trials and on real empirical data (natural scenes). In all cases we find that our algorithm outperforms previous approaches in the literature including filtered back-projection and a variety of state-of-the-art CS algorithms. We conclude with directions of future research emanating from this work.