Statistical examination of FBP and ML for estimating mixture models from dynamic PET data

We have been developing the use of mixture models for quantitative analysis of dynamic PET data (O'Sullivan, IEEE, TMI, 1993). In the approach pixel-wise time activity curve (TAC) data are represented as a mixture of a set of underlying sub-TACs corresponding to distinct tissue types represented in the data. This work attempts to quantify the potential improvements of using maximum likelihood based approaches to estimating these models. Maximum likelihood makes use of the assumed Poissoness of raw sinogram counts and because of this might be expected to have some theoretical statistical advantage. An iterative expectation-maximization (EM) algorithm was developed to determine parameters in the mixture model. The EM approach was compared to a simpler non-iterative filtered backprojection (FBP) based approach as well a modified form of the EM algorithm called EMS. A set of 1-d numerical simulations were carried out to compare these. The results show that there is little indication that the EM algorithm for estimating mixture models in PET would yield appreciable improvements in statistical accuracy over FBP. EMS, however does show some improvement over FBP.