Numerical inversion of the sperical Radon transform: estimation of the directional distribution of fibres of stationary anisotropic cylinder processes

这是一个申请援助的一个跨学科的研究项目的科学小组的萨尔兰大学（逆问题）和乌尔姆大学（随机几何）。联合研究的主题是球形Radon变换的数值反演及其应用于估计静态各向异性圆柱过程模拟的多孔随机介质的典型纤维的方向分布。将研究近似反演公式的总误差以及估计量的统计优度特性。这些估计将测试模拟数据，然后在聚合物电解质膜（PEM）燃料电池中的气体扩散层的真实的显微图像数据的统计分析中使用。

This is an application for assistance for an interdisciplinary research project of the scientific groups of the Saarland University (inverse problems) and the Ulm University (stochastic geometry). The topic of the joint research is the numerical inversion of the spherical Radon transform and its application to the estimation of the directional distribution of typical fibres of porous random media modelled by stationary anisotropic cylinder processes. The total error of the approximative inversion formula together with statistical goodness properties of developed estimators will be studied. These estimators will be tested on simulated data and then used in the statistical analysis of real microscopic image data of gas diffusion layers in polymer electrolyte membrane (PEM) fuel cells.