Recursive calculation of the two-dimensional maximum likelihood position estimate for a scintillation camera

Abstract

Maximum likelihood position estimation of a scintillation event in a gamma-ray imaging detector has been described using two independent one-dimensional estimates in x and y. This approximation is only valid when the sampled light-spread function is separable, and spatial distortion is observed when this constraint is violated. Recursive calculation of the 2-D position estimate using a sequence of one-dimensional estimates was investigated. Mean phototube response functions were computed from Monte Carlo simulations of the light-spread function, and position was estimated for scintillation events using recursive estimation. After three steps the maximum errors were mod delta x mod =0.04 mm and mod delta y mod =0.06 mm for the case of noise-free data and when mean response functions were known at each estimated location. Using response functions interpolated over 6-mm intervals gave increased distortion with average x and y errors of 0.097 and 0.082 mm, respectively.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>