具有吸收和折射介质的发射和矢量二维层析成像问题的b样条数值解

2008 IEEE Region 8 International Conference on Computational Technologies in Electrical and Electronics Engineering Pub Date : 2008-07-21 DOI:10.1109/SIBIRCON.2008.4602618

E. Derevtsov, I. Svetov, Yu. S. Volkov, T. Schuster

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引用次数: 9

摘要

提出了一种具有折射和吸收介质的层析成像问题的数值求解方法。即，通过沿黎曼度量的测地线计算的标量场或矢量场的射线变换，重构标量场或矢量场。利用最小二乘法确定了解的近似值。作为基，我们使用由二维b样条构造的标量场和向量场的局部基。对所需场的平滑度、指标的曲率和吸收系数的变化特征、数据的数字化程度、b样条基的阶数和数量、局部基的各种构造方式等因素对重建精度的影响进行了数值研究。

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Numerical B-spline solution of emission and vector 2D-tomography problems for media with absorption and refraction

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.

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来源期刊

2008 IEEE Region 8 International Conference on Computational Technologies in Electrical and Electronics Engineering

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