Joint-MAP Bayesian tomographic reconstruction with a gamma-mixture prior

被引:31
作者
Hsiao, IT
Rangarajan, A
Gindi, G
机构
[1] SUNY Stony Brook, Dept Elect & Comp Engn, Stony Brook, NY 11784 USA
[2] SUNY Stony Brook, Dept Radiol, Stony Brook, NY 11784 USA
[3] Univ Florida, Dept Comp & Informat Sci & Engn, Gainesville, FL 32611 USA
关键词
gamma mixture; joint-MAP estimation; mixture decomposition; tomographic reconstruction;
D O I
10.1109/TIP.2002.806254
中图分类号
TP18 [人工智能理论];
学科分类号
081104 ; 0812 ; 0835 ; 1405 ;
摘要
We address the problem of Bayesian image reconstruction with a prior that captures the notion of a clustered intensity histogram. The problem is formulated in the framework of a joint-MAP (maximum a posteriori) estimation with the prior pdf modeled as a mixture-of-gammas density. This prior pdf has appealing properties, including positivity enforcement. The joint MAP optimization is carried out as an iterative alternating descent wherein a regularized likelihood estimate is followed by a mixture decomposition of the histogram of the current tomographic image estimate. The mixture decomposition step estimates the hyperparameters of the prior pdf. The objective functions associated with the joint MAP estimation are complicated and difficult to optimize, but we show how they may be transformed to allow for much easier optimization while preserving the fixed point of the iterations. We demonstrate the method in the context of medical emission and transmission tomography.
引用
收藏
页码:1466 / 1477
页数:12
相关论文
共 28 条
[1]   Transmission scanning in emission tomography [J].
Bailey, DL .
EUROPEAN JOURNAL OF NUCLEAR MEDICINE, 1998, 25 (07) :774-787
[2]  
BARRETT HH, 1981, RAD IMAGING THEORY I, V1
[3]  
BARRETT HH, 1981, RAD IMAGING THEORY I, V2
[4]   MAXIMUM LIKELIHOOD FROM INCOMPLETE DATA VIA EM ALGORITHM [J].
DEMPSTER, AP ;
LAIRD, NM ;
RUBIN, DB .
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-METHODOLOGICAL, 1977, 39 (01) :1-38
[5]   A reversible jump algorithm for analysis of Gamma mixtures [J].
Djuric, PM .
BAYESIAN INFERENCE FOR INVERSE PROBLEMS, 1998, 3459 :262-270
[6]  
GOPAL S, 1996, THESIS U HOUSTON HOU
[7]   ANOTHER INTERPRETATION OF THE EM ALGORITHM FOR MIXTURE DISTRIBUTIONS [J].
HATHAWAY, RJ .
STATISTICS & PROBABILITY LETTERS, 1986, 4 (02) :53-56
[8]   Bayesian image reconstruction for transmission tomography using mixture model priors and deterministic annealing algorithms [J].
Hsiao, IT ;
Rangarajan, A ;
Gindi, G .
MEDICAL IMAGING: 2001: IMAGE PROCESSING, PTS 1-3, 2001, 4322 :899-908
[9]  
HSIAO IT, 2000, THESIS STATE U NEW Y
[10]   TOMOGRAPHIC RADIOPHARMACEUTICAL IMAGING [J].
JASZCZAK, RJ .
PROCEEDINGS OF THE IEEE, 1988, 76 (09) :1079-1094