A lower bound on PET timing estimation with pulse pileup

Pulse pileup is an important limiting factor on coincidence detection and timing estimation performance in conventional and time-of-flight (TOF) positron emission tomography (PET). The authors derive a Cramer-Rao (CR) lower bound on timing estimator mean-square error (MSE) when there are multiple overlapping single photon response (SPR) pulses within the photodetector coincidence window. This bound is used to study the loss in achievable timing resolution due to varying amounts of pulse overlap. The case of a biexponential BGO/Burle 8850 SPR is considered. It is shown that in this case timing resolution need not degrade significantly even when pulse overlap is quite severe; up to approximately 20% overlap of the leading edges of the overlapping pulses can be tolerated with less than a 25% degradation in achievable timing resolution. This suggests that multiple event separation and improved coincidence resolving time can be attained well beyond the photon saturation limit of current scintillation detectors