@MASTERSTHESIS\{IMM2016-07018,
    author       = "J. B. Andersen",
    title        = "Hybrid Data Impedance Tomography with the Complete Electrode Model",
    year         = "2016",
    school       = "Technical University of Denmark, Department of Applied Mathematics and Computer Science",
    address      = "Richard Petersens Plads, Building 324, {DK-}2800 Kgs. Lyngby, Denmark, compute@compute.dtu.dk",
    type         = "",
    note         = "{DTU} supervisor: Kim Knudsen, kiknu@dtu.dk, {DTU} Compute",
    url          = "http://www.compute.dtu.dk/English.aspx",
    abstract     = "We consider the Complete Electrode Model (CEM) as a model for the scenario where one apply currents to electrodes attached at the surface of the body. We show, using two different approaches, that the forward problem for the {CEM} has a unique solution. Firstly, by Lax-Milgram Theorem, we identify the forward problem by the variational formulation (2.1). Secondly, via a minimization approach, by associating the forward problem with the functional (2.52). Using the magnitude of the current density, we show non-uniqueness of the inverse problem of finding the conductivity. We characterize this nonuniqueness and state when reconstruction of the conductivity is possible. Numerical experiments of both problems show that errors occur at discontinuities of the conductivity and around the electrodes."
}