An efficient mollifier method for three-dimensional vector tomography: convergence analysis and implementation
An efficient mollifier method for three-dimensional vector tomography: convergence analysis and implementation
复制标题
三维矢量断层扫描的高效软化方法：收敛性分析与实现
DOI：
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发表时间：
2001
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：
T. Schuster
我们考虑三维矢量层析成像的问题，这意味着重建的矢量场和他们的旋度从线积分的某些组成部分的领域。众所周知，从这些数据中只能恢复电磁场的螺线管部分。本文对矢量场近似逆方法进行了改进，并将其应用于该问题，得到了一种有效的滤波反投影型求解器。当数据个数趋于无穷大时，证明了重构解的收敛性，说明该方法是精确的。最后给出了圆柱绕流的数值计算结果。
We consider the problem of three-dimensional vector tomography, that means the reconstruction of vector fields and their curl from line integrals over certain components of the field. It is well known that only the solenoidal part of the field can be recovered from these data. In this paper the method of approximate inverse is modified for vector fields and applied to this problem, leading to an efficient solver of filtered backprojection type. We prove convergence of the reconstructed solution, if the number of data tends to infinity, which means the method is exact. Finally, numerical results are presented for a straight flow through a cylinder.