@MASTERSTHESIS\{IMM2013-06698,
    author       = "R. M. Loving",
    title        = "Magnetic Resonance Electric Impedance Tomography for Anisotropic Conductivity Distribution",
    year         = "2013",
    school       = "Technical University of Denmark, Department of Applied Mathematics and Computer Science",
    address      = "Matematiktorvet, Building 303B, {DK-}2800 Kgs. Lyngby, Denmark, compute@compute.dtu.dk",
    type         = "",
    note         = "{DTU} supervisors: Anton Evgrafov, aaev@dtu.dk, and Kim Knudsen, kiknu@dtu.dk, {DTU} Compute",
    url          = "http://www.compute.dtu.dk/English.aspx",
    abstract     = "The goal of the thesis is to investigate the problem of having an anisotropic conductivity distribution when working with impedance image reconstruction for Magnetic Resonance Electrical Impedance Tomography(MREIT). 
The underlying physics of {MREIT} is introduced with the aim to show how an actual {MREIT} experiment would occur. Two models describing the forward problem of having known conductivity distribution and attaining the resultant z-component of the induced magnetic field are investigated. A simplified geometry for the conducting media is assumed to ease computational efforts and complexity of the reconstruction. The conducting media is assumed to have known sub-domains with different conductivity. A {L-BFGS-B} optimization algorithm is applied to solve the resultant non-linear constrained optimization problem of recovering the conductivity distribution.
Several aspects are investigated, including accuracy, sensitivity on initial guess, sensitivity on contrast between conductivities of the sub-domains and gain from adding more data. It is shown that using a general optimization scheme for finding anisotropic conductivity distributions when applying {MREIT} is a viable method where, when the choice of initial guess is good, the estimated parameters only suffer from a few \% relative error. There is shown to be a threshold of needing at least three pairs of electrodes for viable estimation. It is shown that the geometry of the interior sub-domains influence the estimated parameters. Furthermore, it is shown that high contrast between conductivities of interior sub-domains produce a small bias in the estimated parameters."
}