Empirical Bayesian energy estimation for multi-voltage threshold digitizer in PET

Multi-voltage threshold (MVT) digitization is a cost-effective low-power sampling solution for fast scintillation pulse signal sampling, which has been proven to be practical in our preclinical scanner - Trans-PET BioCaliBurn. However, MVT digitization does not provide the amplitude information directly, while regular-time sampling (RTS) provides energy information as an integral form. This work focuses on event energy estimation for MVT digitizer, which is a crucial task for scintillation detection systems. Generally, critical scintillation pulses characteristics related with MVT can be summarized as: a. fixed pulse shape; b. fast leading edge; c. relatively slow decay; d. filtered Poisson noise. Based on these knowledge, we propose an empirical method, referred to as the empirical Bayesian energy estimation (EBEE), to obtain the pulse energy for MVT samples. In EBEE method, event energy information is the assumed pulse height which maximizes a posteriori probability of the given MVT samples. To evaluate the method, we set up a library of scintillation pulses. Scintillation pulses in this digital library are obtained at a high sampling rate of 50 Giga-samples per second so that their waveforms are recorded with high accuracy. Evaluation results are implemented between EBEE and pulse fitting(PF). With eight voltage thresholds, 4.335 keV Root Mean Square Error (RMSE) is obtained by EBEE, while 18.464 keV RMSE by PF. The evaluation shows that MVT of eight thresholds can produce nearly the same estimated energys as 50 GSps RTS when the MVT digitizer works with EBEE. The results have therefore demonstrated the potential advantage of EBEE in energy measurement for the MVT digitizer.