A hybrid algorithm for randoms variance reduction

We describe a new algorithm for randoms variance reduction in positron emission tomography (PET) that makes use of both delayed coincidence data and separately measured, coarsely sampled, detector singles event rates. The algorithm has been tested on 2D data for several phantom studies. We find that it gives randoms estimates nearly as precise as a fan-sum algorithm, but with low bias. The amount of bias depends on how accurately the singles data represents the actual structure of the singles. With 12 samples per detector ring on a clinical PET scanner, maximum local bias for a clinically realistic phantom is ±2%, but can be twice this much for highly asymmetric objects.