In this paper, a restricted transverse ray transform acting on vector and symmetric m-tensor fields is studied. We developed inversion algorithms using restricted transverse ray transform data to recover symmetric m-tensor fields in R3 and vector fields in Rn . We restrict the transverse ray transform to all lines going through a fixed curve γ that satisfies the Kirillov–Tuy condition. We show that the known restricted data can be used to reconstruct a specific weighted Radon transform of the unknown vector/tensor field’s components, which we then use to explicitly recover the unknown field.

中文翻译：

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曲线上源的受限横向射线变换的反演

本文提出了作用于矢量和对称的受限横向射线变换米-研究张量场。我们开发了使用受限横向射线变换数据的反演算法来恢复对称米-张量场 右3 和向量场 右n 。我们将横向射线变换限制为穿过固定曲线的所有线γ满足基里洛夫-图伊条件。我们表明，已知的受限数据可用于重建未知向量/张量场分量的特定加权 Radon 变换，然后我们使用该变换来显式恢复未知场。