Quadratic programming time pickoff method for multi-voltage threshold digitizer in PET

Multi-voltage threshold (MVT) digitization is a low-power sampling solution with reasonable cost for fast scintillation pulse, which has been implemented in our preclinical scanner - Trans-PET^® BioCaliBurn^™. This digitizing scheme employs a few comparators with programmable reference voltage for determining the time points when the scintillation pulse crosses some of the user-defined voltage thresholds. And the use of various sophisticated statistics-based or nonlinear algorithms to improve the accuracy of timing information becomes possible. In the previous implementation of MVT digitizers, we have employed the linear fitting (LF) algorithm to pickoff the arrival time of a scintillation pulse. About 300ps Coincidence Timing Resolution (CTR) has been achieved. In such implementations, no optimization targeted for the combination of MVT samples has been performed, and only samples on the leading edge involved. It is not unreasonable to expect achieving a better timing resolution in MVT PET detectors by the combination optimization of MVT samples both on leading and tail edges. In this work, a new method, referred to as quadratic programming (QP) method is proposed. In this method, the arrival time is directly depicted as a parametric combination of the MVT samples. Quadratic programming is then used to optimize the parameters of the combination using the variation of time differences as a minimization criteria. The experimental results show timing resolution of 197.31 ps, 183.08 ps, 162.40 ps by use of digital constant fraction discrimination (DCFD), LF/MVT and QP/MVT time pickoff methods, respectively, and therefore preliminarily demonstrate the potential advantage of QP/MVT in timing determination for PET imaging.