Simultaneous update iterative algorithm for variance reduction on random coincidences in PET

The use of the ordinary Poisson iterative reconstruction algorithm in PET requires the estimation of expected random coincidences. In a clinical environment, random coincidences are often acquired with a delayed coincidence technique, and expected randoms are estimated through variance reduction (VR) of measured delayed coincidences. While numerous analytical methods exist for reducing the variance of measured random coincidences, iterative methods have the advantage of being easily adapted to any acquisition geometry and of allowing the estimation of the singles rate at the crystal level, when the number of crystals is relatively small. In this paper we present a VR algorithm with a simultaneous update, which is derived by using surrogate functions. A monotonic algorithm is designed for data in line-of- response projection or list mode formats. The updated equation requires the knowledge of a fan sum of random data; therefore, the algorithm is extremely fast. The algorithm derivation provides a theoretical basis for a more heuristic simultaneous update algorithm, which was used in our previous work with list mode data. Measured data from a Siemens TruePoint clinical scanner were used to validate the algorithm.