Reconstruction of 2-tensor fields, given in a unit circle, by their ray transforms based on LSM with B-splines
Reconstruction of 2-tensor fields, given in a unit circle, by their ray transforms based on LSM with B-splines
复制标题
通过基于带有 B 样条的 LSM 的射线变换来重建单位圆中给出的 2 张量场
DOI：
10.1134/s1995423910020047
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发表时间：
2010
影响因子：
0.3
通讯作者：
A. Polyakova
中科院分区：
文献类型：
--
作者：
I. E. Svetov;A. Polyakova
提出了一种求解单位圆内对称2-张量场重建张量层析成像问题的数值方法。从沿着穿过场的支撑的直线计算的横向和（或）纵向射线变换中找到在边界上具有固定性质的所需场的势和（或）螺线管部分。该解决方案是寻求通过最小二乘法与使用，作为一个近似序列，构建的基础上的B-样条的本地基地。
A numerical method for solving a tensor tomography problem of reconstructing a symmetric 2-tensor field, given in a unit circle, is proposed. The potential and (or) solenoidal part of the desired field with fixed properties on the boundary are found from transverse and (or) longitudinal ray transforms calculated along the straight lines crossing the support of the field. The solution is sought by means of the least-squares method with the use, as an approximating sequence, of local bases constructed on the basis of B-splines.