Randoms Estimation for Long Axial Field-of-View PET

The high sensitivity of long axial field-of-view (AFOV) PET scanners has enabled studies over a wide range of count rates and count densities. However, these systems have a large axial acceptance angle that necessitates a wide coincidence window to capture the oblique true coincidences. In addition, the measured delays sinogram is sparse and noisy. We studied four methods of randoms estimation on a long AFOV system to assess their impact on accuracy and image noise: measured delays using a delayed coincidence window (RD), 2D Casey averaging of measured delays (RD-smooth), 2D average of measured delays (RD-ave - the current default method on the PennPET Explorer), and estimation of randoms from singles (RS). We looked at cases with varying count densities, randoms fractions, and non-pure positron emitters. A positive bias observed at low randoms counts for the RD and RD-smooth methods was not seen with the RD-ave or RS methods. For all cases, quantitative results with RS agreed to within 2.5% of the RD-ave method, while RD and RD-smooth estimates showed differences of 5-49%, with larger differences in areas of low uptake. The RS method is a practical technique for list-mode data and list-mode reconstruction by reducing the size of stored list events. It also avoids small approximations in the RD-ave method. For long AFOV systems, estimating randoms from singles is a practical and accurate method.