Abstract
Positron Emission Tomography (PET) is one of the most important techniques formedical diagnosis. The statistical methods are needed in image reconstruction forPET. In this dissertation we develop a new approach to the reconstruction of theimage. We use hierarchical Bayesian model to describe how the observations areobtained and apply a modied EM-type approach, the one-step-late algorithm, tocalculate the maximum likelihood estimate for the emission intensity at each pixel.This method take care of both smoothness and edge eects of the image simulta-neously. Finally the performance of this method is demonstrated and comparedwith other methods by computer simulations.