A new convex edge-preserving median prior with applications to tomography

作     者：Hsiao, IT Rangarajan, A Gindi, G 

作者机构：SUNY Stony Brook Dept Radiol Stony Brook NY 11784 USA SUNY Stony Brook Dept Elect & Comp Engn Stony Brook NY 11784 USA Univ Florida Dept Comp & Informat Sci & Engn Gainesville FL 32611 USA 

出 版 物：《IEEE TRANSACTIONS ON MEDICAL IMAGING》 (IEEE Trans. Med. Imaging)

年 卷 期：2003年第22卷第5期

页      面：580-585页

核心收录：

学科分类：0831[工学-生物医学工程（可授工学、理学、医学学位）] 0808[工学-电气工程] 1002[医学-临床医学] 08[工学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 1009[医学-特种医学] 

基　　金：NINDS NIH HHS [R01-NS32879] Funding Source: Medline 

主　　题：Bayesian tomographic reconstruction edge-preserving prior emission tomography iterative algorithm median 

摘      要：In a Bayesian tomographic maximum a posteriori (MAP) reconstruction, an estimate of the object f is computed by iteratively minimizing an objective function that typically comprises the sum of a log-likelihood (data consistency) term and prior (or penalty) term. The prior can be used to stabilize the solution and to also impose spatial properties on the solution. One such property, preservation of edges and locally monotonic regions, is captured by the well-known median root prior (MRP) [1], [2], an empirical method that has been applied to emission and transmission tomography. We propose an entirely new class of convex priors that depends on f and also on m, an auxiliary field in register with f. We specialize this class to our median prior (MP). The approximate action of the median prior is to draw, at each iteration, an object voxel toward its own local median. This action is similar to that of MRP and results in solutions that impose the same sorts of object properties as does MRP. Our MAP method is not empirical, since the problem is stated completely as the minimization of a joint (on f and m) objective. We propose an alternating algorithm to compute the joint MAP solution and apply this to emission tomography, showing that the reconstructions are qualitatively similar to those obtained using MRP.