Abstract
This paper describes a statistical model for reconstruction of emission computed tomography (ECT) images. A distinguishing feature of this model is that it is parameterized in terms of quantities of direct physiological significance, rather than only in terms of grey-level voxel values. Specifically, parameters representing regions, region means, and region volumes are included in the model formulation and are estimated directly from projection data. The model is specified hierarchically within the Bayesian paradigm. At the lowest level of the hierarchy, a Gibbs distribution is employed to specify a probability distribution on the space of all possible partitions of the discretized image scene. A novel feature of this distribution is that the number of partitioning elements, or image regions, is not assumed known a priori. In contrast, any other segmentation models (e.g., Liang et al., 1991, Amit et al., 1991) require that the number of regions be specified prior to image reconstruction. Since the number of regions in a source distribution is seldom known a priori, allowing the number of regions to vary within the model framework is an important practical feature of this model. In the second level of the model hierarchy, random variables representing emission intensity are associated with each partitioning element or region. Individual voxel intensities are assumed to be drawn from a gamma distribution with mean equal to the region mean in the third stage, and in the final stage of the hierarchy projection data are assumed to be generated from Poisson distributions with means equal to weighted sums of voxel intensities.
