Maximum Likelihood Reconstruction in PET and TOFPET

The expectation-maximization (EM) algorithm for maximum likelihood estimation can be applied to image reconstruction in positron emission tomography (PET) and time-of-flight assisted PET (TOFPET). To implement this algorithm, one can employ either the projection data acquired at various angles or the rotationally integrated image. In the case of TOFPET, the latter approach can reduce the required computation time substantially. Three approaches -- the conventional, direct and statistical methods -- that incorporate the effect of photon attenuation in the EM algorithm have been investigated. Preliminary results from computer simulation studies indicate that the direct method can provide a good compromise between image quality and computation time. Three acceleration approaches -- the geometric, additive and multiplicative methods -- that increase the rate of convergence of these EM reconstruction methods have been studied also.