Analytic modeling of software coincidence detection in PET

PET imaging is based on the detection in coincidence of two back-to-back annihilation photons. Implementation of coincidence detection in PET data acquisition systems usually involve energy discrimination and time discrimination. Depending on which is performed at first, the coincidence detection can be divided into two ways: energy discrimination before time discrimination (ETD) and time discrimination before energy discrimination (TED). The major difference of them is that, certain double coincidences from multiples which will be discarded by TED may be recovered by ETD. Since the extra double coincidences retrieved by ETD contain not only true coincidences but also scatter coincidences and random coincidences, it is hard to tell whether they can improve the final image quality. In this work, an primary analytic model of coincidence detection in PET is proposed, and the noise equivalent count (NEC) of TED and ETD are deduced from the model to estimate the image quality. The validity of the model is evaluated by GATE simulation. The model and simulation results suggested that the ETD has a better sensitivity while suffers from the random coincidences sorted from multiple coincidences. The NEC of TED is superior when the dose is relatively low and/or a narrow coincidence time window is used, while this turns to inverse while dose getting higher and/or a broader coincidence time window is used. This implies that compromises should be made while choosing the coincidence detection method and the choice is rather application dependent.