Inversion of a restricted transverse ray transform with sources on a curve
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911785031827456 |
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| author | Mishra, Rohit Kumar Thakkar, Chandni |
| author_facet | Mishra, Rohit Kumar Thakkar, Chandni |
| contents | 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 $γ$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_17683 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Inversion of a restricted transverse ray transform with sources on a curve Mishra, Rohit Kumar Thakkar, Chandni Classical Analysis and ODEs 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 $γ$ 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. |
| title | Inversion of a restricted transverse ray transform with sources on a curve |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2402.17683 |