Discrete approach to electrical resistance tomography with applications to distributed network sensing

Most of electrical resistance tomography literature is aimed at biomedical application, where one wishes to estimate the conductivity distribution of some portion of human body in order to detect some health disorder. The solution to this problem often starts considering a continuous media, which requires subsequent discretization through finite element simulations or other sophisticated methods. In this paper, we propose an alternative and purely discrete approach. We pose the problem as a resistor grid, or network, of which only the peripheral elements are accessible for measurements. By injecting known electrical current externally, we want to estimate all the conductances of the network given only boundary voltage measurements. Since the relation between conductance values and voltage measurement is nonlinear, we present two solutions to the problem: one based on iterative linearization and another based on neural network, which solves the problem directly in the nonlinear domain. Finally, we present simulated experiments to demonstrate the viability of the proposed approach and highlight possible applications of the developed technique.