  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.
