Division of Imaging, Diagnostics, and Software Reliability, OSEL/CDRH, U.S. Food and Drug Administration, Silver Spring, MD, USA.
Institute of Energy Technologies, Polytechnic University of Catalonia, Barcelona, Spain.
Med Phys. 2018 Feb;45(2):629-634. doi: 10.1002/mp.12638. Epub 2017 Nov 19.
Monte Carlo simulations require large number of histories to obtain reliable estimates of the quantity of interest and its associated statistical uncertainty. Numerous variance reduction techniques (VRTs) have been employed to increase computational efficiency by reducing the statistical uncertainty. We investigate the effect of two VRTs for optical transport methods on accuracy and computing time for the estimation of variance (noise) in x-ray imaging detectors.
We describe two VRTs. In the first, we preferentially alter the direction of the optical photons to increase detection probability. In the second, we follow only a fraction of the total optical photons generated. In both techniques, the statistical weight of photons is altered to maintain the signal mean. We use fastdetect2, an open-source, freely available optical transport routine from the hybridmantis package. We simulate VRTs for a variety of detector models and energy sources. The imaging data from the VRT simulations are then compared to the analog case (no VRT) using pulse height spectra, Swank factor, and the variance of the Swank estimate.
We analyze the effect of VRTs on the statistical uncertainty associated with Swank factors. VRTs increased the relative efficiency by as much as a factor of 9. We demonstrate that we can achieve the same variance of the Swank factor with less computing time. With this approach, the simulations can be stopped when the variance of the variance estimates reaches the desired level of uncertainty.
We implemented analytic estimates of the variance of Swank factor and demonstrated the effect of VRTs on image quality calculations. Our findings indicate that the Swank factor is dominated by the x-ray interaction profile as compared to the additional uncertainty introduced in the optical transport by the use of VRTs. For simulation experiments that aim at reducing the uncertainty in the Swank factor estimate, any of the proposed VRT can be used for increasing the relative efficiency.
蒙特卡罗模拟需要大量的历史记录来获得感兴趣数量及其相关统计不确定性的可靠估计。已经采用了许多方差减少技术 (VRT) 通过减少统计不确定性来提高计算效率。我们研究了两种光学传输方法的 VRT 对 X 射线成像探测器中方差（噪声）估计的准确性和计算时间的影响。
我们描述了两种 VRT。在第一种方法中，我们优先改变光的方向以增加检测概率。在第二种方法中，我们只跟随生成的总光的一部分。在这两种技术中，改变光子的统计权重以保持信号平均值。我们使用 fastdetect2，这是来自 hybridmantis 包的开源、免费提供的光学传输例程。我们模拟了各种探测器模型和能量源的 VRT。然后，使用脉冲高度谱、Swank 因子和 Swank 估计的方差将 VRT 模拟的成像数据与模拟情况（无 VRT）进行比较。
我们分析了 VRT 对与 Swank 因子相关的统计不确定性的影响。VRT 将相对效率提高了多达 9 倍。我们证明，我们可以用更少的计算时间获得相同的 Swank 因子方差。通过这种方法，可以在方差估计的方差达到所需的不确定性水平时停止模拟。
我们实现了 Swank 因子方差的解析估计，并演示了 VRT 对图像质量计算的影响。我们的发现表明，与使用 VRT 在光学传输中引入的额外不确定性相比，Swank 因子主要由 X 射线相互作用分布决定。对于旨在降低 Swank 因子估计不确定性的模拟实验，可以使用任何建议的 VRT 来提高相对效率。
