Time estimation with multichannel digital silicon photomultipliers

Accuracy in timemark estimation is crucial for time-of-flight positron emission tomography, in order to ensure high quality images after reconstruction. Since the introduction of multichannel digital silicon photomultipliers, it is possible to acquire several photoelectron timestamps for each individual gamma event. We study several timemark estimators based on multiple photoelectron timestamps by means of a comprehensive statistical model. In addition, we calculate the MSE of the estimators in comparison to the Cramér-Rao lower bound as a function of the system design parameters. We investigate the effect of skipping some of the photoelectron timestamps, which is a direct consequence of the limited number of time-to-digital converters and we propose a technique to compensate for this effect. In addition, we carry out an extensive analysis to evaluate the influence of dark counts on the detector timing performance. Moreover, we investigate the improvement of the timing performance that can be obtained with dark count filtering and we propose an appropriate filtering method based on measuring the time difference between sorted timestamps. Finally, we perform a full Monte Carlo simulation to compare different timemark estimators by exploring several system design parameters. It is demonstrated that a simple weighted-average estimator can achieve a comparable performance as the more complex maximum likelihood estimator.