Calibration Method for ML Estimation of 3D Interaction Position in a Thick Gamma-Ray Detector

High-energy (> 100 keV) photon detectors are often made thick relative to their lateral resolution in order to improve their photon-detection efficiency. To avoid issues of parallax and increased signal variance that result from random interaction depth, we must determine the 3D interaction position in the imaging detector. With this goal in mind, we examine a method of calibrating response statistics of a thick-detector gamma camera to produce a maximum-likelihood estimate of 3D interaction position. We parameterize the mean detector response as a function of 3D position, and we estimate these parameters by maximizing their likelihood given prior knowledge of the pathlength distribution and a complete list of camera signals for an ensemble of gamma-ray interactions. Furthermore, we describe an iterative method for removing multiple-interaction events from our calibration data and for refining our calibration of the mean detector response to single interactions. We demonstrate this calibration method with simulated gamma-camera data. We then show that the resulting calibration is accurate and can be used to produce unbiased estimates of 3D interaction position.

I. Introduction

Detectors used for high-energy photon detection are often made thick in order to improve their photon-detection efficiency. Use of a thick detector, in turn, motivates depth of interaction (DOI) estimation for each gamma ray. If we estimate only the two-dimensional (2D) position of interaction in a gamma camera, ambiguity in DOI may result in a loss of detector and/or image resolution [1]. Random DOI can cause increased signal variance, which in turn can degrade the 2D resolution of a gamma camera. Additionally, DOI ambiguity for obliquely incident gamma rays causes parallax, which can subsequently limit image resolution. Random DOI can also degrade coincidence-timing resolution for a time-of-flight PET system [2]. For many clinical gamma cameras with moderately thick scintillators (< 10 mm), signal-variance and parallax issues are mitigated by choice of camera geometry and optical properties. However, to avoid these issues in general for a thicker gamma-ray detector, we must estimate the three-dimensional (3D) coordinates of interaction.