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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2312.11721 |
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| _version_ | 1866909274697891840 |
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| author | Carmona, Ángeles Encinas, Andrés M. Jiménez, María José Samperio, Álvaro |
| author_facet | Carmona, Ángeles Encinas, Andrés M. Jiménez, María José Samperio, Álvaro |
| contents | We address the discrete inverse conductance problem for well-connected spider networks; that is, to recover the conductance function on a well-connected spider network from the Dirichlet-to-Neumann map. It is well-known that this inverse problem is exponentially ill-posed, requiring the implementation of a regularization strategy for numerical solutions. Our focus lies in exploring whether prior knowledge of the conductance being piecewise constant within a partition of the edge set comprising few subsets enables stable conductance recovery. To achieve this, we propose formulating the problem as a polynomial optimization one, incorporating a regularization term that accounts for the piecewise constant hypothesis. We show several experimental examples in which the stable conductance recovery under the aforementioned hypothesis is feasible. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_11721 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Stable recovery of piecewise constant conductance on spider networks Carmona, Ángeles Encinas, Andrés M. Jiménez, María José Samperio, Álvaro Combinatorics We address the discrete inverse conductance problem for well-connected spider networks; that is, to recover the conductance function on a well-connected spider network from the Dirichlet-to-Neumann map. It is well-known that this inverse problem is exponentially ill-posed, requiring the implementation of a regularization strategy for numerical solutions. Our focus lies in exploring whether prior knowledge of the conductance being piecewise constant within a partition of the edge set comprising few subsets enables stable conductance recovery. To achieve this, we propose formulating the problem as a polynomial optimization one, incorporating a regularization term that accounts for the piecewise constant hypothesis. We show several experimental examples in which the stable conductance recovery under the aforementioned hypothesis is feasible. |
| title | Stable recovery of piecewise constant conductance on spider networks |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2312.11721 |