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arXiv · 2402.17683

Inversion of a restricted transverse ray transform with sources on a curve

Rohit Kumar Mishra·Chandni Thakkar
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Abstract

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 $\mathbb{R}^3$ and vector fields in $\mathbb{R}^n$. We restrict the transverse ray transform to all lines going through a fixed curve $\gamma$ 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.

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Rohit Kumar Mishra, Chandni Thakkar. 2024-02-27. Inversion of a restricted transverse ray transform with sources on a curve. https://arxiv.org/abs/2402.17683

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