Maximum-Likelihood Estimation of Scintillation Pulse Timing

Including time-of-flight information in positron emission tomography reconstruction increases the signal-to-noise ratio if the timing information is sufficiently accurate. We estimate timing information by analyzing sampled waveforms, where the sampling frequency and number of samples acquired affect the accuracy of timing estimation. An efficient data-acquisition system acquires the minimum number of samples that contains the most timing information for a desired resolution. We describe a maximum-likelihood (ML) estimation algorithm to assign a time stamp to digital pulses. The method is based on a contracting-grid search algorithm that can be implemented in a field-programmable gate array and in graphics processing units. The Fisher-information (FI) matrix quantifies the amount of timing information that can be extracted from the waveforms. FI analyses on different segments of the waveform allow us to determine the smallest amount of data that we need to acquire in order to obtain a desired timing resolution. We describe the model and the procedure used to simulate waveforms for ML estimation and FI analysis, the ML-estimation algorithm and the timing resolution obtained from experimental data using a LaBr₃:Ce crystal and two photomultiplier tubes. The results show that for lengthening segments of the pulse, timing resolution approaches a limit. We explored the method as a function of sampling frequency and compared the results to other digital time pickoff methods. This information will be used to build an efficient data-acquisition system with reduced complexity and cost that nonetheless preserves full timing performance.