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。