Modeling Stochastic Processes in Gamma-Ray Imaging Detectors and Evaluation of a Multi-Anode PMT Scintillation Camera for Use with Maximum-Likelihood Estimation Methods

Abstract

Maximum-likelihood estimation or other probabilistic estimation methods are underused in many areas of applied gamma-ray imaging, particularly in biomedicine. In this work, we show how to use our understanding of stochastic processes in a scintillation camera and their effect on signal formation to better estimate gamma-ray interaction parameters such as interaction position or energy.To apply statistical estimation methods, we need an accurate description of the signal statistics as a function of the parameters to be estimated. First, we develop a probability model of the signals conditioned on the parameters to be estimated by carefully examining the signal generation process. Subsequently, the likelihood model is calibrated by measuring signal statistics for an ensemble of events as a function of the estimate parameters.In this work, we investigate the application of ML-estimation methods for three topics. First, we design, build, and evaluate a scintillation camera based on a multi-anode PMT readout for use with ML-estimation techniques. Next, we develop methods for calibrating the response statistics of a thick-detector gamma camera as a function of interaction depth. Finally, we demonstrate the use of ML estimation with a modified clinical Anger camera.