Electrical Conductivity Reconstruction using Non-Local Boundary Conditions

In this paper we study existence, uniqueness and solution estimates to the mixed problem r \Delta oeru = 0 with Dirichlet to Neumann map boundary conditions and Neumann boundary conditions. We then show how this can be used in the reconstruction of oe, given the relationship between u and its normal derivative on the boundary portion where we do not apply the Dirichlet to Neumann map. A numerical reconstruction scheme is also derived. 1 Introduction In impedance imaging, see [1], [2], [3], [4] , and [5], we inject small currents to electrodes attached to the skin around the body. This induces voltages on the skin that are related to the internal conductivities. The conductivities are then reconstructed from the current to voltage data on the skin, which is our 1 This work was done as part of the author's doctoral thesis at Rensselaer Polytechnic Institute. boundary information. Since different tissue types exhibit different electrical conductivities, displaying the conductivities..