Inversion of generalized V-line transforms of vector fields in $\mathbb{R}^2$
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910415053651968 |
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| author | Bhardwaj, Rahul Mishra, Rohit Kumar Vashisth, Manmohan |
| author_facet | Bhardwaj, Rahul Mishra, Rohit Kumar Vashisth, Manmohan |
| contents | This article studies the inverse problem of recovering a vector field supported in $\mathbb{D}_R$, the disk of radius $R$ centered at the origin, through a set of generalized broken ray/V-line transforms, namely longitudinal and transverse V-line transforms. Geometrically, we work with broken lines that start from the boundary of a disk and break at a fixed angle after traveling a distance along the diameter. We derive two inversion algorithms to recover a vector field in $\mathbb{R}^2$ from the knowledge of its longitudinal and transverse V-line transforms over two different subsets of aforementioned broken lines in $\mathbb{R}^2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_12479 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Inversion of generalized V-line transforms of vector fields in $\mathbb{R}^2$ Bhardwaj, Rahul Mishra, Rohit Kumar Vashisth, Manmohan Classical Analysis and ODEs This article studies the inverse problem of recovering a vector field supported in $\mathbb{D}_R$, the disk of radius $R$ centered at the origin, through a set of generalized broken ray/V-line transforms, namely longitudinal and transverse V-line transforms. Geometrically, we work with broken lines that start from the boundary of a disk and break at a fixed angle after traveling a distance along the diameter. We derive two inversion algorithms to recover a vector field in $\mathbb{R}^2$ from the knowledge of its longitudinal and transverse V-line transforms over two different subsets of aforementioned broken lines in $\mathbb{R}^2$. |
| title | Inversion of generalized V-line transforms of vector fields in $\mathbb{R}^2$ |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2404.12479 |