Title: Network Based Inversion
Abstract: The electrical impedance tomography problem consists of finding the conductivity in a body from electrical measurements at its surface. It is an inverse problem that arises in medical imaging and geophysical exploration. To image the conductivity, we solve an analogous inverse problem on graphs, where the resistors on the edges of a network are to be found from electrical measurements at certain nodes of the network. We show how this approach of using the solution to a discrete inverse problem to solve a continuum one can be generalized to an inverse problem for the Schroedinger equation.