Abstract

Under consideration is the problem of improving the contrast of the image obtained by processing tomographic projections with phase distortion. The study is based on the well-known intensity transfer equation. Unlike other works, this equation is solved in a bounded region of variation of the tomographic parameters. In a domain, a boundary value problem is posed for the intensity transfer equation which is then specialized for a three-dimensional parallel tomographic scheme. The case of two-dimensional tomography is also considered, together with the corresponding boundary value problem for the intensity transfer equation. We propose numerical methods for solving the boundary value problems of phase correction. The results are given of the numerical experiments on correction of tomographic projections and reconstruction of the structure of the objects under study (in particular, a slice of a geological sample) by using piecewise uniform regularization.

中文翻译：

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层析成像研究中的相位校正

摘要

考虑中的问题是改善通过处理具有相位失真的断层摄影投影而获得的图像的对比度的问题。该研究基于众所周知的强度传递方程。与其他工作不同，该方程在断层扫描参数变化的有界区域内求解。在一个领域中，强度传递方程提出了一个边值问题，然后该方程专门用于三维平行层析成像方案。还考虑了二维层析成像的情况，以及强度传递方程的相应边界值问题。我们提出了数值方法来解决相位校正的边值问题。