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

Abstract

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 determinedfor 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.

Gamma-photon equivalent UV excitation of LYSO:Ce scintillator material

“…In a simplified case of this solution the γ-beam is parallel to the sensor surface (α = 0 • ), i.e. all scintillation occur in the same depth but at different lateral positions [13]. Some of the characterizations use refined statistical methods to categorize measurement results with known entry point and α [14,15,17].…”

“…Such radiation beams have approximately constant diameter due to their low divergence. Thus, if we direct the γ-beam perpendicularly to the sensor, the lateral coordinates of the POI can be controlled by positioning the source into the required location, but on the other hand the depth of the POIs inside the scintillator is very hard to determine [10][11][12][13][14][15][16], it is often not considered at all [8,17].…”