Quasi-Monte Carlo method for calculating X-ray scatter in CT.

In this paper we transform the trajectories of X-ray as it interacts with a phantom into a high-dimensional integration problem and give the integral formula for the probability of photons emitted from the X-ray source through the phantom to reach the detector. We propose a superior algorithm called gQMCFRD, which combines GPU-based quasi-Monte Carlo (gQMC) method with forced random detection (FRD) technique to simulate this integral. QMC simulation is deterministic versions of Monte Carlo (MC) simulation, which uses deterministic low discrepancy points (such as Sobol' points) instead of the random points. By using the QMC and FRD technique, the gQMCFRD greatly increases the simulation convergence rate and efficiency. We benchmark gQMCFRD, GPU based MC tool (gMCDRR), which performs conventional simulations, a GPU-based Metropolis MC tool (gMMC), which uses the Metropolis-Hasting algorithm to sample the entire photon path from the X-ray source to the detector and gMCFRD, that uses random points for sampling against PENELOPE subroutines: MC-GPU. The results are in excellent agreement and the Efficiency Improvement Factor range 27 ∼ 37 (or 1.09 ∼ 1.16, or 0.12 ∼ 0.15, or 3.62 ∼ 3.70) by gQMCFRD (or gMCDRR, or gMMC, or gMCFRD) with comparison to MC-GPU in all cases. It shows that gQMCFRD is more effective in these cases.