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Microlocal inversion of a 3-dimensional restricted transverse ray transform on symmetric tensor fields
Journal of Mathematical Analysis and Applications ( IF 1.2 ) Pub Date : 2021-03-01 , DOI: 10.1016/j.jmaa.2020.124700
Venkateswaran P. Krishnan , Rohit Kumar Mishra , Suman Kumar Sahoo

We study the problem of inverting a restricted transverse ray transform to recover a symmetric $m$-tensor field in $\mathbb{R}^3$ using microlocal analysis techniques. More precisely, we prove that a symmetric $m$-tensor field can be recovered up to a known singular term and a smoothing term if its transverse ray transform is known along all lines intersecting a fixed smooth curve satisfying the Kirillov-Tuy condition.

中文翻译:

对称张量场上 3 维受限横向射线变换的微局域反演

我们研究了使用微局部分析技术反转受限横向射线变换以恢复 $\mathbb{R}^3$ 中的对称 $m$-张量场的问题。更准确地说,我们证明对称的 $m$-张量场可以恢复到已知的奇异项和平滑项,如果它的横向射线变换沿着满足 Kirillov-Tuy 条件的固定平滑曲线相交的所有线都是已知的。
更新日期:2021-03-01
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