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arXiv · 2312.11721

Stable recovery of piecewise constant conductance on spider networks

Ángeles Carmona·Andrés M. Encinas·María José Jiménez·Álvaro Samperio
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Abstract

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.

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Ángeles Carmona, Andrés M. Encinas, María José Jiménez, Álvaro Samperio. 2023-12-18. Stable recovery of piecewise constant conductance on spider networks. https://doi.org/10.1080/00207160.2024.2385631

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