The Barankin Bound for Time Estimation in TOF-PET

Data quality in TOF-PET depends on the accuracy of the detector time resolution (DTR). Given a model of the time distribution of the optical photons emission and of the photon transport and detection, the best achievable DTR can be obtained from a lower bound on the variance of any unbiased estimator of the interaction time of the incident annihilation photon. With current detectors hundreds of optical photons are typically detected and the Cramer-Rao bound (CRB) can be used because of its asymptotic tightness property. With some novel fast detectors involving e.g. Cerenkov photons the emission rate is low and the CRB yields an over-optimistic value of the DTR. We revisit the Barankin bound [1] (BB) originally proposed by Gorman and Hero [2] in this context. Using simulated data for a bi-exponential model of the emission we show that the BB is close to tight even when less than 10 photons are detected.