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

这是萨尔大学（反问题）和乌尔姆大学（随机几何）科学小组的一个跨学科研究项目的援助申请。联合研究的课题是球面Radon变换的数值反演及其在静态各向异性圆柱过程模拟多孔随机介质中典型纤维方向分布估计中的应用。研究了近似反演公式的总误差以及所开发的估计器的统计优良性。这些估计器将在模拟数据上进行测试，然后用于聚合物电解质膜（PEM）燃料电池中气体扩散层的真实显微图像数据的统计分析。

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.