Fully Bayesian estimation of Gibbs hyperparameters for emission computed tomography data
Abstract
In recent years, many investigators have proposed Gibbs prior models to regularize images reconstructed from emission computed tomography data. Unfortunately, hyperparameters used to specify Gibbs priors can greatly influence the degree of regularity imposed by such priors and, as a result, numerous procedures have been proposed to estimate hyperparameter values from observed image data. Many of these procedures attempt to maximize the joint posterior distribution on the image scene. To implement these methods, approximations to the joint posterior densities are required, because the dependence of the Gibbs partition function on the hyperparameter values is unknown. In this paper, the authors use recent results in Markov chain Monte Carlo (MCMC) sampling to estimate the relative values of Gibbs partition functions and using these values, sample from joint posterior distributions on image scenes. This allows for a fully Bayesian procedure which does not fix the hyperparameters at some estimated or specified value, but enables uncertainty about these values to be propagated through to the estimated intensities. The authors utilize realizations from the posterior distribution for determining credible regions for the intensity of the emission source. They consider two different Markov random field (MRF) models  the power model and a linesite model.more »
 Authors:

 Duke Univ., Durham, NC (United States). Inst. of Statistics and Decision Sciences
 Duke Univ. Medical Center, Durham, NC (United States). Dept. of Radiology
 Publication Date:
 Sponsoring Org.:
 National Science Foundation, Washington, DC (United States); Whitaker Foundation (United States); Public Health Service, Washington, DC (United States); USDOE, Washington, DC (United States)
 OSTI Identifier:
 580448
 DOE Contract Number:
 FG0589ER60894
 Resource Type:
 Journal Article
 Journal Name:
 IEEE Transactions on Medical Imaging
 Additional Journal Information:
 Journal Volume: 16; Journal Issue: 5; Other Information: PBD: Oct 1997
 Country of Publication:
 United States
 Language:
 English
 Subject:
 55 BIOLOGY AND MEDICINE, BASIC STUDIES; IMAGE PROCESSING; SINGLE PHOTON EMISSION COMPUTED TOMOGRAPHY; MATHEMATICAL MODELS; MONTE CARLO METHOD; COMPUTERIZED SIMULATION
Citation Formats
Higdon, D M, Johnson, V E, Bowsher, J E, Turkington, T G, Gilland, D R, and Jaszczak, R J. Fully Bayesian estimation of Gibbs hyperparameters for emission computed tomography data. United States: N. p., 1997.
Web. doi:10.1109/42.640741.
Higdon, D M, Johnson, V E, Bowsher, J E, Turkington, T G, Gilland, D R, & Jaszczak, R J. Fully Bayesian estimation of Gibbs hyperparameters for emission computed tomography data. United States. doi:10.1109/42.640741.
Higdon, D M, Johnson, V E, Bowsher, J E, Turkington, T G, Gilland, D R, and Jaszczak, R J. Wed .
"Fully Bayesian estimation of Gibbs hyperparameters for emission computed tomography data". United States. doi:10.1109/42.640741.
@article{osti_580448,
title = {Fully Bayesian estimation of Gibbs hyperparameters for emission computed tomography data},
author = {Higdon, D M and Johnson, V E and Bowsher, J E and Turkington, T G and Gilland, D R and Jaszczak, R J},
abstractNote = {In recent years, many investigators have proposed Gibbs prior models to regularize images reconstructed from emission computed tomography data. Unfortunately, hyperparameters used to specify Gibbs priors can greatly influence the degree of regularity imposed by such priors and, as a result, numerous procedures have been proposed to estimate hyperparameter values from observed image data. Many of these procedures attempt to maximize the joint posterior distribution on the image scene. To implement these methods, approximations to the joint posterior densities are required, because the dependence of the Gibbs partition function on the hyperparameter values is unknown. In this paper, the authors use recent results in Markov chain Monte Carlo (MCMC) sampling to estimate the relative values of Gibbs partition functions and using these values, sample from joint posterior distributions on image scenes. This allows for a fully Bayesian procedure which does not fix the hyperparameters at some estimated or specified value, but enables uncertainty about these values to be propagated through to the estimated intensities. The authors utilize realizations from the posterior distribution for determining credible regions for the intensity of the emission source. They consider two different Markov random field (MRF) models  the power model and a linesite model. As applications they estimate the posterior distribution of source intensities from computer simulated data as well as data collected from a physical single photon emission computed tomography (SPECT) phantom.},
doi = {10.1109/42.640741},
journal = {IEEE Transactions on Medical Imaging},
number = 5,
volume = 16,
place = {United States},
year = {1997},
month = {10}
}