@MASTERSTHESIS\{IMM2016-07016,
    author       = "C. Kragh",
    title        = "Computational Methods for Hybrid Impedance Tomography",
    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     = "This thesis investigates a hybrid impedance inverse problem where the conductivity in a planar domain is reconstructed from noise-free interior data of the current density and power density types. Two algorithms are implemented for reconstructing C2–conductivities. The first algorithm performs well for the current density problem using a single measurement. The second algorithm produces good reconstructions for the power density problem using two measurements. The results indicate that both algorithms are convergent for the current density problem. The second algorithm is the only one which performs well for the power density problem but is only semi-convergent in that case. The effect of highly oscillating Neumann conditions is investigated, where the results indicate that higher frequencies lead to poorer reconstructions. The numerical results moreover indicate that L2–regularization for the power density problem does not have any positive impact. Finally, the second algorithm is tested for the reconstruction of a piece-wise constant conductivity, with results that are comparable to the case of a C2–conductivity."
}