Tensor tomography using V-line transforms with vertices restricted to a circle
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866913573111857152 |
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| author | Mishra, Rohit Kumar Purohit, Anamika Zamindar, Indrani |
| author_facet | Mishra, Rohit Kumar Purohit, Anamika Zamindar, Indrani |
| contents | In this article, we study the problem of recovering symmetric $m$-tensor fields (including vector fields) supported in a unit disk $\mathbb{D}$ from a set of generalized V-line transforms, namely longitudinal, transverse, and mixed V-line transforms, and their integral moments. We work in a circular geometric setup, where the V-lines have vertices on a circle, and the axis of symmetry is orthogonal to the circle. We present two approaches to recover a symmetric $m$-tensor field from the combination of longitudinal, transverse, and mixed V-line transforms. With the help of these inversion results, we are able to give an explicit kernel description for these transforms. We also derive inversion algorithms to reconstruct a symmetric $m$-tensor field from its first $(m+1)$ moment longitudinal/transverse V-line transforms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_04145 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Tensor tomography using V-line transforms with vertices restricted to a circle Mishra, Rohit Kumar Purohit, Anamika Zamindar, Indrani Numerical Analysis Classical Analysis and ODEs In this article, we study the problem of recovering symmetric $m$-tensor fields (including vector fields) supported in a unit disk $\mathbb{D}$ from a set of generalized V-line transforms, namely longitudinal, transverse, and mixed V-line transforms, and their integral moments. We work in a circular geometric setup, where the V-lines have vertices on a circle, and the axis of symmetry is orthogonal to the circle. We present two approaches to recover a symmetric $m$-tensor field from the combination of longitudinal, transverse, and mixed V-line transforms. With the help of these inversion results, we are able to give an explicit kernel description for these transforms. We also derive inversion algorithms to reconstruct a symmetric $m$-tensor field from its first $(m+1)$ moment longitudinal/transverse V-line transforms. |
| title | Tensor tomography using V-line transforms with vertices restricted to a circle |
| topic | Numerical Analysis Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2411.04145 |