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首页> 外文会议>International Conference "Functional Analysis in Interdisciplinary Applications" >On a Problem of Reconstruction of Discontinuities of a Function by its Attenuated Ray Transform along Geodesics
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On a Problem of Reconstruction of Discontinuities of a Function by its Attenuated Ray Transform along Geodesics

机译：沿着大地测量射线变换的函数重建问题的重构问题

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摘要

A problem of reconstruction of the first kind discontinuities of a given in a unit disk B discontinuous function by its attenuated ray transform is considered. A mathematical model of an inhomogeneous medium includes known Riemannian metric and two positive functions. One of them describes a known absorption factor e of the medium, and the other has the physical meaning of a distribution f of internal sources to be determined. The attenuated ray transform is the integrals of f with the weight depending on e, which are evaluated along all geodesics in B, and are the initial data for the problem. The algorithm of approximate determination of lines of discontinuities of the function/ having the discontinuities of the first kind is suggested and realized. The algorithm is investigated numerically. The results of simulation are satisfactory and allow to hope for the further development of the approach.
机译：考虑了通过其减毒射线变换来重建在单位盘B不连续功能中给出的第一种不连续性的问题。 非均匀介质的数学模型包括已知的Riemannian度量和两个正函数。 其中一个描述了培养基的已知吸收因子E，另一个具有要确定的内部来源的分布F的物理含义。 衰减的射线变换是F的重量的F的积分，这取决于e沿着B中的所有测地测器评估，并且是问题的初始数据。 建议和实现了函数的近似确定的近距离确定的算法，并实现了第一种的不连续性。 该算法在数值上进行了研究。 仿真结果令人满意，并希望能够进一步发展这种方法。

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