Approximate maximum likelihood estimators for position and energy in scintillation cameras

It is often assumed that the photon arrival process incident on the photodetector array in a scintillation camera is Poisson. Conditioned on the location and energy of the incident gamma-ray. A simple experiment, in which the covariance between the sensor outputs is empirically determined demonstrates that the observations are not independent conditioned merely on location and energy. We assume that this lack of independence arises from random parameters influencing the Poisson intensity or photodetector responses. Because, these responses can be difficult to either model or measure as a function of the nuisance parameters, we develop two simple approximations to the ideal maximum likelihood estimator for location and energy.