An approach to direct reconstruction of a solenoidal part in vector and tensor tomography problems
An approach to direct reconstruction of a solenoidal part in vector and tensor tomography problems
复制标题
矢量和张量断层扫描问题中螺线管部分直接重建的方法
DOI：
10.1515/156939405775199587
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发表时间：
2005
影响因子：
0.3
通讯作者：
E. Derevtsov
中科院分区：
文献类型：
--
作者：
E. Derevtsov
本文讨论了折射媒质中矢量场和2-张量场的重建问题。提出了一种直接重构螺线管零件的方法。利用最小二乘法重建的螺线管部分的原始矢量和2张量场通过使用某些螺线管基地的多项式型为此目的而构建。通过考虑多项式向量和2-张量场的多项式分解，从理论上证明了这种方法的合理性。解决了原场螺线管部分逼近的存在性、唯一性和收敛性问题。给出了数值模拟的结果并进行了讨论。
The problem of reconstruction of vector and 2-tensor fields, given in refracting medium, is considered. The approach of direct reconstruction of a solenoidal part is presented. Least squares method is exploited for a reconstruction of solenoidal parts of original vector and 2-tensor fields by usage of certain solenoidal bases of polynomial type constructed for this purpose. The approach is justified theoretically by consideration of polynomial decompositions of polynomial vector and 2-tensor fields. The problems of existence, uniqueness and convergence of obtained approximation to the solenoidal part of original field are solved. The results of numerical simulation are presented and discussed.