Stable recovery of piecewise constant conductance on spider networks

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.

arXiv commentSubmitted to Applied Mathematics and Computation

References in corpus (5)

• Uniform stability estimates for the discrete Calderon problems
• Discrete approximation and regularisation for the inverse conductivity problem
• Optical tomography on graphs
• Study of noise effects in electrical impedance tomography with resistor networks
• A discrete Liouville identity for numerical reconstruction of Schrödinger potentials