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

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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.