Inversion of generalized Radon transform over symmetric $m$-tensor fields in $\mathbb{R}^n$
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909475702571008 |
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| author | Abhishek, Anuj Mishra, Rohit Kumar Thakkar, Chandni |
| author_facet | Abhishek, Anuj Mishra, Rohit Kumar Thakkar, Chandni |
| contents | In this work, we study a set of generalized Radon transforms over symmetric $m$-tensor fields in $\mathbb{R}^n$. The longitudinal/transversal Radon transform and corresponding weighted integral transforms for symmetric $m$-tensor field are introduced. We give the kernel descriptions for the longitudinal and transversal Radon transform. Further, we also prove that a symmetric $m$-tensor field can be recovered uniquely from certain combinations of these integral transforms of the unknown tensor field. This generalizes a recent study done for the recovery of vector fields from its weighted Radon transform data to recovery of a symmetric $m$-tensor field from analogously defined weighted Radon transforms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_02058 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Inversion of generalized Radon transform over symmetric $m$-tensor fields in $\mathbb{R}^n$ Abhishek, Anuj Mishra, Rohit Kumar Thakkar, Chandni Analysis of PDEs 44A12, 44A30, 46F12, 47G10 In this work, we study a set of generalized Radon transforms over symmetric $m$-tensor fields in $\mathbb{R}^n$. The longitudinal/transversal Radon transform and corresponding weighted integral transforms for symmetric $m$-tensor field are introduced. We give the kernel descriptions for the longitudinal and transversal Radon transform. Further, we also prove that a symmetric $m$-tensor field can be recovered uniquely from certain combinations of these integral transforms of the unknown tensor field. This generalizes a recent study done for the recovery of vector fields from its weighted Radon transform data to recovery of a symmetric $m$-tensor field from analogously defined weighted Radon transforms. |
| title | Inversion of generalized Radon transform over symmetric $m$-tensor fields in $\mathbb{R}^n$ |
| topic | Analysis of PDEs 44A12, 44A30, 46F12, 47G10 |
| url | https://arxiv.org/abs/2502.02058 |