V-line 2-tensor tomography in the plane
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866916099225812992 |
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| author | Ambartsoumian, Gaik Mishra, Rohit Kumar Zamindar, Indrani |
| author_facet | Ambartsoumian, Gaik Mishra, Rohit Kumar Zamindar, Indrani |
| contents | In this article, we introduce and study various V-line transforms (VLTs) defined on symmetric 2-tensor fields in $\mathbb{R}^2$. The operators of interest include the longitudinal, transverse, and mixed VLTs, their integral moments, and the star transform. With the exception of the star transform, all these operators are natural generalizations to the broken-ray trajectories of the corresponding well studied concepts defined for straight-line paths of integration. We characterize the kernels of the VLTs and derive exact formulas for reconstruction of tensor fields from various combinations of these transforms. The star transform on tensor fields is an extension of the corresponding concepts that have been previously studied on vector fields and scalar fields (functions). We describe all injective configurations of the star transform on symmetric 2-tensor fields and derive an exact, closed-form inversion formula for that operator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_13245 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | V-line 2-tensor tomography in the plane Ambartsoumian, Gaik Mishra, Rohit Kumar Zamindar, Indrani Classical Analysis and ODEs Mathematical Physics 44A12, 44A60, 44A30, 47G10 In this article, we introduce and study various V-line transforms (VLTs) defined on symmetric 2-tensor fields in $\mathbb{R}^2$. The operators of interest include the longitudinal, transverse, and mixed VLTs, their integral moments, and the star transform. With the exception of the star transform, all these operators are natural generalizations to the broken-ray trajectories of the corresponding well studied concepts defined for straight-line paths of integration. We characterize the kernels of the VLTs and derive exact formulas for reconstruction of tensor fields from various combinations of these transforms. The star transform on tensor fields is an extension of the corresponding concepts that have been previously studied on vector fields and scalar fields (functions). We describe all injective configurations of the star transform on symmetric 2-tensor fields and derive an exact, closed-form inversion formula for that operator. |
| title | V-line 2-tensor tomography in the plane |
| topic | Classical Analysis and ODEs Mathematical Physics 44A12, 44A60, 44A30, 47G10 |
| url | https://arxiv.org/abs/2306.13245 |