Optimal and sub-optimal post-detection timing estimators for PET

In this paper the authors derive linear and non-linear approximations to the post-detection likelihood function for scintillator interaction time in nuclear particle detection systems. The likelihood function is the optimal statistic for performing detection and estimation of scintillator events and event times. The authors derive the likelihood function approximations from a statistical model for the post-detection waveform which is common in the optical communications literature and takes account of finite detector bandwidth, random gains, and thermal noise. They then present preliminary simulation results for the associated approximate maximum likelihood timing estimators which indicate that significant MSE improvements may be achieved for low post-detection signal-to-noise ratio