A method to reject random coincidences and extract true from multiple coincidences in PET using 3-D detectors

In this work, we develop a new method to reject random coincidences and identify true coincidences from multiple photon coincidences using 3-D photon positioning PET detectors. We are developing scintillation and cadmium zinc telluride (CZT) detectors with the ability to position the 3-D coordinates of every detector interaction with 1 mm intrinsic spatial and ≪2.5% FWHM energy resolution at 511 keV. For multiple interactions, the position of the first two interactions and the energy of the first interaction are used to electronically collimate single photons by the kinematics of Compton scatter. We use a “direction window” to determine coincident lines of response. Using a hypothesis testing framework, we derive a direction window threshold that maximizes the noise equivalent counts (NEC) of the system. This new method is compared against conventional coincidence processing for a dual-panel breast CZT PET system under development in our laboratory. For a simplified approximation of our maximum NEC derivation, we show that the addition of a direction window reduced random coincidences by 55–60%. At high activities, the ability to recover trues from multiple coincidences increased the true coincidence rate of the system by as much as 11%.