Microlocal inversion of a restricted mixed ray transform for second-order tensor fields in $ {\mathbf {\mathbb {R}}}^{3} $

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发表日期：

2025年3月13日

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Chandni Thakkar

摘要

In this article, we study a restricted mixed ray transform acting on second-order tensor fields in 3-dimensional Euclidean space and prove the invertibility of this integral transform using microlocal techniques. Here, the mixed ray transform is restricted over lines passing through a fixed curve $\gamma $ $γ$ in $\mathbb {R}^3$ $R^{3}$ satisfying certain geometric conditions. The main theorem of the article shows that a second-order tensor field can be recovered from its restricted mixed-ray transform up to the kernel of the transform, a smoothing term, and a known singular term.

Microlocal inversion of a restricted mixed ray transform for second-order tensor fields in \( {\mathbf {\mathbb {R}}}^{3} \)

摘要