A comparison of Maximum List-Mode-Likelihood Estimation and Maximum-Likelihood Clustering algorithms for depth calibration in continuous-crystal PET detectors

Parallax error in close-proximity applications of thick gamma-ray detectors, such as preclinical or organ-specific Positron Emission Tomography, motivates the need to accurately resolve interaction depth. In our lab, we routinely use a collimated gamma-ray source and apply an iterative maximum-likelihood clustering (MLC) algorithm to calibrate detector response statistics as a function of 3D interaction position. These detector response functions calibrate a signal-probability model that we use to determine the interaction position of events by maximum likelihood estimation. In this work, we compare the accuracy of this clustering algorithm to a more computationally intensive method (MLMLE) that maximizes the list-mode likelihood of a parametric model of the detector response function. Accuracy of the calibrated mean and variance of detector response versus depth are experimentally determined for a slat-shaped detector using a collimated gamma-rays normally incident to the side of the slat. We also verify our experimental findings by Monte-Carlo simulation, where ground truth is known. Our results suggest that MLMLE is more accurate than MLC for estimating the variance of detector response, but these algorithms fair similarly for accurately estimating the mean detector response. However, for the reduced dimensional case considered, the MLC algorithm required nearly 1 minute to execute, while the MLMLE algorithm took just over 10 hours to complete.