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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.00738 |
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| _version_ | 1866916945307107328 |
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| author | Jathar, Shubham R. Kar, Manas Krishnan, Venkateswaran P. Pattar, Rahul Raju |
| author_facet | Jathar, Shubham R. Kar, Manas Krishnan, Venkateswaran P. Pattar, Rahul Raju |
| contents | In this article, we establish that any symmetric $m$-tensor field can be recovered pointwise from partial data of the $k$-th weighted divergent ray transform for any $k \in \mathbb{Z}^{+} \cup\{0\}$. Using the unique continuation property of the fractional Laplacian, we further prove the unique continuation of the fractional divergent beam ray transform for both vector fields and symmetric 2-tensor fields. Additionally, we derive explicit reconstruction formulas and stability results for vector fields and symmetric 2-tensor fields in terms of fractional divergent beam ray transform data. Finally, we conclude by proving a unique continuation result for the divergent beam ray transform for functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_00738 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Weighted Divergent Beam Ray Transform: Reconstruction, Unique continuation and Stability Jathar, Shubham R. Kar, Manas Krishnan, Venkateswaran P. Pattar, Rahul Raju Analysis of PDEs Differential Geometry Primary 46F12, 45Q05, 35R11 In this article, we establish that any symmetric $m$-tensor field can be recovered pointwise from partial data of the $k$-th weighted divergent ray transform for any $k \in \mathbb{Z}^{+} \cup\{0\}$. Using the unique continuation property of the fractional Laplacian, we further prove the unique continuation of the fractional divergent beam ray transform for both vector fields and symmetric 2-tensor fields. Additionally, we derive explicit reconstruction formulas and stability results for vector fields and symmetric 2-tensor fields in terms of fractional divergent beam ray transform data. Finally, we conclude by proving a unique continuation result for the divergent beam ray transform for functions. |
| title | Weighted Divergent Beam Ray Transform: Reconstruction, Unique continuation and Stability |
| topic | Analysis of PDEs Differential Geometry Primary 46F12, 45Q05, 35R11 |
| url | https://arxiv.org/abs/2412.00738 |