Optimal Calibration of PET Crystal Position Maps Using Gaussian Mixture Models

A method is developed for estimating optimal PET gamma-ray detector crystal position maps, for arbitrary crystal configurations, based on a binomial distribution model for scintillation photon arrival. The approach is based on maximum likelihood estimation of Gaussian mixture model parameters using crystal position histogram data, with determination of the position map taken from the posterior probability boundaries between mixtures. This leads to minimum probability of error crystal identification under the assumed model.