Iterative algorithms for variance reduction on compressed sinogram 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. In this paper we present iterative VR algorithms for random compressed sinograms, when previously known methods are not applicable. Iterative methods have the advantage of easy adaptation to any acquisition geometry and of allowing the estimation of singles rates at the crystal level when the number of crystals is relatively small. Two types of sinogram compression are considered: axial (span) rebinning and transaxial mashing. A monotonic sequential coordinate descent algorithm, which optimizes the Least Squares objective function, is investigated. A simultaneous update algorithm, which possesses the advantage of easy parallelization, is also derived for both cases of the Least Squares and Poisson Likelihood objective function. Measured data from a Siemens TruePoint clinical scanner are used to validate the algorithm performance.