Numerical B-spline solution of emission and vector 2D-tomography problems for media with absorption and refraction
Numerical B-spline solution of emission and vector 2D-tomography problems for media with absorption and refraction
复制标题
具有吸收和折射介质的发射和矢量二维断层扫描问题的数值 B 样条解
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
T. Schuster
中科院分区：
文献类型：
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作者：
E. Derevtsov;I. E. Svetov;Yu. S. Volkov;T. Schuster
本文提出了一种数值求解折射和吸收介质中层析成像问题的方法。即，通过沿黎曼度量的测地线沿着计算的射线变换，重建标量场或矢量场。利用最小二乘法确定了解的近似值。作为基地，我们使用的标量和矢量场的局部基地，通过二维B样条构造。影响（重建精度）的因素，如所需的领域，曲率的度量和吸收系数的变化，数据的数字化程度，B样条的顺序和数量的基础，各种方式的建设的地方基地的光滑度进行了数值研究。
A method of numerical solution for the tomography problems setting in a with medium with refraction and absorption is suggested. Namely, scalar or vector field by its ray transform calculated along geodesics of a Riemannian metric is reconstructed. The approximation of the solution is determined with usage of the least squares method. As bases we use the local bases of scalar and vector fields constructed by means of two-dimensional B-splines. Influence (on accuracy of reconstruction) such factors as smoothness of the required fields, curvature of the metrics and character of change of absorption coefficient, degree of digitization of data, an order and quantity of bases B-splines, various ways of construction of the local bases was numerically investigated.