Broken ray transform: inversion and a range condition
Broken ray transform: inversion and a range condition
复制标题
断线变换：反演和范围条件
DOI：
10.1088/0266-5611/29/7/075008
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发表时间：
2013
期刊：
影响因子：
2.1
通讯作者：
Roman Krylov
中科院分区：
文献类型：
--
作者：
Alexander Katsevich;Roman Krylov
在本文中，我们研究了一类破碎射线变换（BRT），它可以实现与平面和/或弯曲的检测器。在两个检测器的情况下，我们得到一个反演公式，其中涉及的数据和积分的二阶导数沿沿着特征。在三个检测器的情况下，我们得到一个反演公式，这是纯粹的本地和只涉及一阶导数的数据。因此，该公式解决了内部问题。无论是物体还是源和探测器都不需要旋转以获得完整的数据集。我们还证明了一个定理，它描述了在三个检测器的情况下的BRT的范围。最后给出了数值实验结果。
In this paper we study a class of broken ray transforms (BRT), which can be implemented with flat and/or curved detectors. In the case of two detectors we obtain an inversion formula, which involves a second-order derivative of the data and integration along characteristics. In the case of three detectors, we obtain an inversion formula, which is purely local and involves only the first-order derivatives of the data. Hence the formula solves the interior problem. Neither the object nor the source and detectors require to be rotated in order to obtain a complete data set. We also prove a theorem, which describes the range of the BRT in the case of three detectors. Finally, the results of numerical experiments are presented.