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

The authors derive linear and nonlinear approximations to the postdetection 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 postdetection waveform which is common in the optical communications literature and takes account of finite detector bandwidth, random gains, and thermal noise. They present preliminary simulation results for the associated approximate maximum likelihood timing estimators which indicate that significant MSE (mean square error) improvements can be achieved for low postdetection signal-to-noise ratio