Inversion of the attenuated momenta ray transform of planar symmetric tensors
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866929337351012352 |
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| author | Fujiwara, Hiroshi Omogbhe, David Sadiq, Kamran Tamasan, Alexandru |
| author_facet | Fujiwara, Hiroshi Omogbhe, David Sadiq, Kamran Tamasan, Alexandru |
| contents | We present a reconstruction method that stably recovers the real valued, symmetric tensors compactly supported in the Euclidean plane, from knowledge of their attenuated momenta ray transform. The problem is recast as an inverse boundary value problem for a system of transport equations, which we solve by an extension of Bukhgeim's $A$-analytic theory. The method of proof is constructive. To illustrate the reconstruction method, we present results obtained in the numerical implementation for the non-attenuated case of 1-tensors. This new version now includes the results of the preprint arXiv: 2307.10758. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_00499 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Inversion of the attenuated momenta ray transform of planar symmetric tensors Fujiwara, Hiroshi Omogbhe, David Sadiq, Kamran Tamasan, Alexandru Analysis of PDEs Primary: 44A12, 35J56, Secondary: 45E05 We present a reconstruction method that stably recovers the real valued, symmetric tensors compactly supported in the Euclidean plane, from knowledge of their attenuated momenta ray transform. The problem is recast as an inverse boundary value problem for a system of transport equations, which we solve by an extension of Bukhgeim's $A$-analytic theory. The method of proof is constructive. To illustrate the reconstruction method, we present results obtained in the numerical implementation for the non-attenuated case of 1-tensors. This new version now includes the results of the preprint arXiv: 2307.10758. |
| title | Inversion of the attenuated momenta ray transform of planar symmetric tensors |
| topic | Analysis of PDEs Primary: 44A12, 35J56, Secondary: 45E05 |
| url | https://arxiv.org/abs/2309.00499 |