On a quantitative partial imaging problem in vector tomography
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918065659183104 |
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| author | Fujiwara, Hiroshi Sadiq, Kamran Tamasan, Alexandru |
| author_facet | Fujiwara, Hiroshi Sadiq, Kamran Tamasan, Alexandru |
| contents | In two dimensions, we consider the problem of reconstructing a vector field from partial knowledge of its zeroth and first moment ray transforms. Different from existing works the data is known on a subset of lines, namely the ones intersecting a given arc. The problem is non-local and, for partial data, severely ill-posed. We present a reconstruction method which recovers the vector field in the convex hull of the arc. An algorithm based on this method is implemented on some numerical experiments. While still ill-posed the discretization stabilizes the numerical reconstruction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_16455 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On a quantitative partial imaging problem in vector tomography Fujiwara, Hiroshi Sadiq, Kamran Tamasan, Alexandru Numerical Analysis Analysis of PDEs In two dimensions, we consider the problem of reconstructing a vector field from partial knowledge of its zeroth and first moment ray transforms. Different from existing works the data is known on a subset of lines, namely the ones intersecting a given arc. The problem is non-local and, for partial data, severely ill-posed. We present a reconstruction method which recovers the vector field in the convex hull of the arc. An algorithm based on this method is implemented on some numerical experiments. While still ill-posed the discretization stabilizes the numerical reconstruction. |
| title | On a quantitative partial imaging problem in vector tomography |
| topic | Numerical Analysis Analysis of PDEs |
| url | https://arxiv.org/abs/2506.16455 |