$\u211d^2$中张量场的高斯束Radon变换
Gaussian beam Radon transform for tensor fields in $\mathbb{R}^2$
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中文总结 AI 辅助
该研究将标量函数的高斯束Radon变换（GbRt）拓展至$\u211d^2$中的张量场，定义了纵向、横向、混合GbRt及其积分矩，通过其组合实现了向量场与对称2阶张量场的重构，推广了经典的张量场广义Radon变换。
中文摘要 AI 辅助
本文引入并研究了一类作用于$\u211d^2$中张量场的广义高斯束Radon变换（GbRt）。所考虑的算子包括纵向、横向、混合GbRt及其积分矩，这些算子推广了经典的张量场广义Radon变换的相应概念。我们通过所定义变换的适当组合，建立了向量场和对称2阶张量场的重构结果。本工作将近期从标量函数的GbRt恢复标量函数的研究，拓展至通过类似定义的广义GbRt恢复向量场与张量场。
英文摘要
In this article, we introduce and study a set of generalized Gaussian beam Radon transforms (GbRt) acting on tensor fields in $\mathbb{R}^2$. The operators considered include longitudinal, transverse, mixed GbRts, along with their integral moments. These operators extend the corresponding notions of the classical generalized Radon transforms for tensor fields. We establish reconstruction results for vector and symmetric 2-tensor fields using appropriate combinations of the defined transforms. This work extends a recent study on the recovery of scalar functions from their GbRt to the recovery of vector and tensor fields from analogously defined generalized GbRts.
