Ordered subsets acceleration of iterative algorithm for variance reduction on compressed sinogram random coincidences

As an input to Poisson model based image reconstruction, expected randoms are estimated through the variance reduction (VR) of measured delayed coincidences. In the past we have developed iterative VR algorithms that estimate singles rates from random compressed sinograms. The simultaneous update type algorithm has the advantages of easy implementation and computing parallelization. The disadvantage is slow convergence of high frequency components in the singles estimation. In addition to this, the algorithm iteration is computationally expensive, since the compressed mean value sinogram must be constructed and compared against the measured one. In this paper we consider a subset acceleration algorithm, based on the consideration of a certain group of crystals in the transaxial direction in the update of the solution. Each group of crystals produces a distinguished data subset in the sinogram. The number of LOR is significantly larger than the number of crystals; therefore singles estimations can be obtained from a subset of measured data. This fact likely explains the observed monotonicity of the proposed ordered subset algorithm. Measured data from a Siemens mCT clinical scanner were used to validate the algorithm performance.