Estimation of Crystal Timing Properties and Efficiencies for the Improvement of (Joint) Maximum-Likelihood Reconstructions in TOF-PET

With increasing improvements in the time of flight (TOF) resolution of positron emission tomography (PET) scanners, an accurate model of the TOF measurements is becoming increasingly important. This work considers two parameters of the TOF kernel; the relative positioning of the timing data-bins and the timing resolution along each line of response (LOR). Similar to an existing data-driven method, we assume that any shifts of data-bins along lines of response can be modelled as differences between crystal timing offsets. Inspired by this, timing resolutions of all LORs are modelled as the hypotenuse of timing resolutions of the crystal-pairs in coincidence. Furthermore, in order to mitigate the influence of potential inaccuracies of detector-pair sensitivities on crystal timing resolutions, relative LOR sensitivities are modelled as the product of efficiency factors for the two crystals in coincidence. We validate estimating maps of crystal timing offsets, timing resolutions and efficiencies from the emission data using noisy simulations of a brain phantom. Results are shown for phantom and patient data scanned on clinically available TOF-PET scanners. We find that the estimation of crystal timing resolutions is more sensitive to the data statistics than the estimation of crystal timing offsets. As a result, estimation of crystal timing properties could either be limited to high count emission data, or be obtained utilizing additional regularizations on the estimates. Using a more accurate model of the TOF acquisition, improvements are observed in standard activity reconstructions as well as joint reconstructions of activity and attenuation.