Effect of geometric models on convergence rate in iterative PET image reconstructions

Iterative PET image reconstructions can improve quantitation accuracy by explicitly modeling photon-limited nature and physical effects of coincident photons. Geometric model in iterative reconstructions defines the mapping between image and sinogram domains based on scanner's geometry, which affects the accuracy of image results and the convergence rate of reconstruction algorithms. This paper examines the convergence rates of a reconstruction algorithm with three PET geometric models: interpolative, area-based, and solid-angle. The iterative algorithm used in this study is the maximum likelihood expectation-maximization (MLEM) algorithm. Experimental data are generated by the GATE package which simulates the Inveon microPET system. The comparison of convergence rate is based on the plot of log-likelihood value versus iteration number. From the plots of log-likelihood curves, the results from solid-angle model consistently reach the highest values at early iterations. It means that the MLEM algorithm with the solid-angle model will converge faster than the other two models. The experimental results indicate that the solid-angle model is a favorable geometric model for faster iterative PET image reconstruction.