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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2504.17592 |
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| _version_ | 1866910918052413440 |
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| author | Chen, Gaoming Santosa, Fadil Symes, William W. |
| author_facet | Chen, Gaoming Santosa, Fadil Symes, William W. |
| contents | Professor Pierre Sabatier contributed much to the study of inverse problems in theory and practice. Two of these contributions were a focus on theory that actually supports practice, and the identification of well-posed aspects of inverse problems that may quite ill-posed. This paper illustrates these two themes in the context of Electrical Impedance Tomography (EIT), which is both very ill-posed and very practical. We show that for a highly constrained version of this inverse problem, in which a small elliptical inclusion in a homogeneous background is to be identified, optimization of the experimental design (that is, electrode locations) vastly improves the stability of the solution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_17592 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Well-posed Questions for Ill-posed Inverse Problems: a Note in Memory of Pierre Sabatier Chen, Gaoming Santosa, Fadil Symes, William W. Analysis of PDEs Professor Pierre Sabatier contributed much to the study of inverse problems in theory and practice. Two of these contributions were a focus on theory that actually supports practice, and the identification of well-posed aspects of inverse problems that may quite ill-posed. This paper illustrates these two themes in the context of Electrical Impedance Tomography (EIT), which is both very ill-posed and very practical. We show that for a highly constrained version of this inverse problem, in which a small elliptical inclusion in a homogeneous background is to be identified, optimization of the experimental design (that is, electrode locations) vastly improves the stability of the solution. |
| title | Well-posed Questions for Ill-posed Inverse Problems: a Note in Memory of Pierre Sabatier |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2504.17592 |