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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, we 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. We utilize realizations from the posterior distribution for determining credible regions for the intensity of the emission source. We consider two different Markov random field (MRF) models-the power model and a line-site model. As applications we 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.

The primary goal of this work has been to develop a processing method for gated cardiac emission computed tomography (ECT) that simultaneously reconstructs the pixel intensities of the gated images and estimates the motion of the cardiac wall. The simultaneous reconstruction and motion estimation is achieved using conjugate gradient optimization with an objective function that is dependent on the gated reconstructed images at two time frames and the estimated motion of the object between the two frames. The method was evaluated on simulated phantom data both with and without Poisson noise. With noise-free data, the accuracy of the motion estimate and the quality of the reconstructed images were found to be dependent on the hyperparameter selection. With noisy data, the simultaneous method produced reconstructed images with smaller squared error compared with images reconstructed without motion estimation. In a patient gated myocardial perfusion study, the estimated motion between two frames agreed with subjective assessment of wall motion.

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