Hierarchical Bayesian Image Reconstruction for Emission Tomography Using Dependent Likelihood

Abstract

Emission computed tomography is a non-invasive functional imaging technique that is nowadays widely applied in medical diagnostic imaging, especially to determine physiological function. The available set of measurements is, however, often incomplete and corrupted, and the quality of image reconstruction is enhanced by the computation of a statistically optimal estimate. Most statistical reconstruction methods for emission tomography use the conditionally independent Poisson model to measure fidelity to data. Although the conditionally independent Poisson model is appropriate for a conceptual view of PET imaging, once the reconstruction problem is to estimate the number of emissions in each pixel, the stochastic nature of the emission process is no longer Poisson and the measurement data are no longer independent. Correlations are introduced into the measurement model, which result in dependent random variables. In this dissertation, we propose a hierarchical Bayesian model which combines a dependent likelihood function and the quadratic pairwise difference prior with locally varying weighting hyerparameters to reconstruct image in terms of emission counts in pixels. This dissertation addresses the second concern, seeking to simplify the reconstruction of correlated data and provide a more precise image estimate than the conventional independent methods. We apply and test the proposed hierarchical Bayesian model with two PET data sets. The reconstructed images reveal that the proposed hierarchical Bayesian model produces reconstruction with superior visual quality to MLEM in terms of contrast and noise artifact suppression.