School of Physical Sciences, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China.
Biomedical Imaging Center, Center for Biotechnology & Interdisciplinary Studies, Department of Biomedical Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180, United States of America.
Phys Med Biol. 2022 Mar 25;67(7). doi: 10.1088/1361-6560/ac5b21.
The phase function is a key element of a light propagation model for Monte Carlo (MC) simulation, which is usually fitted with an analytic function with associated parameters. In recent years, machine learning methods were reported to estimate the parameters of the phase function of a particular form such as the Henyey-Greenstein phase function but, to our knowledge, no studies have been performed to determine the form of the phase function.Here we design a convolutional neural network (CNN) to estimate the phase function from a diffuse optical image without any explicit assumption on the form of the phase function. Specifically, we use a Gaussian mixture model (GMM) as an example to represent the phase function generally and learn the model parameters accurately. The GMM is selected because it provides the analytic expression of phase function to facilitate deflection angle sampling in MC simulation, and does not significantly increase the number of free parameters.Our proposed method is validated on MC-simulated reflectance images of typical biological tissues using the Henyey-Greenstein phase function with different anisotropy factors. The mean squared error of the phase function is 0.01 and the relative error of the anisotropy factor is 3.28%.We propose the first data-driven CNN-based inverse MC model to estimate the form of scattering phase function. The effects of field of view and spatial resolution are analyzed and the findings provide guidelines for optimizing the experimental protocol in practical applications.
相位函数是蒙特卡罗 (MC) 模拟中光传播模型的关键要素，通常用具有相关参数的解析函数来拟合。近年来，有报道称机器学习方法可用于估计特定形式（如 Henyey-Greenstein 相位函数）的相位函数参数，但据我们所知，尚无研究确定相位函数的形式。在这里，我们设计了一个卷积神经网络 (CNN)，无需对相位函数的形式做出任何明确假设，即可从漫射光图像中估计相位函数。具体来说，我们使用高斯混合模型 (GMM) 作为示例来表示一般的相位函数，并准确学习模型参数。选择 GMM 是因为它提供了相位函数的解析表达式，便于在 MC 模拟中进行偏转角采样，并且不会显著增加自由参数的数量。我们的方法使用不同各向异性因子的 Henyey-Greenstein 相位函数对典型生物组织的 MC 模拟反射率图像进行了验证。相位函数的均方误差为 0.01，各向异性因子的相对误差为 3.28%。我们提出了第一个基于数据驱动的 CNN 反向 MC 模型来估计散射相位函数的形式。分析了视场和空间分辨率的影响，研究结果为优化实际应用中的实验方案提供了指导。
