Effect of random and scatter fractions in variance reduction using time-of-flight information

The ability of differential time-of-flight (TOF) information to reduce the statistical noise variance in PET reconstructions has been known since the 1980's. Since then, the technology and applications of PET have evolved, warranting a reconsideration of the estimated improvements of TOF with respect to modern PET. For example, whereas 2D cardiology or neurology studies were once the only options, 3D clinical whole-body oncology imaging is becoming more common. The augmented sensitivity, change in object size and shape, as well as the accompanying changes in isotope and dose, result in different relative amounts of scattered, random, and true coincidences than were seen in the past. Thus in an analysis of the TOF gain for modern PET, it is useful to consider the separate effects of varying these fractions. We present a simulation study investigating the relative amount of TOF contrast-to-noise gain for a range of levels of scattered and random coincidences. We demonstrate that both increased scatter and increased randoms noticeably enhance the TOF gain, but that the higher randoms fraction introduces the most drastic improvement. These results are encouraging for modern PET, where there is a greater random/scatter fraction than in the PET of the 1980's.