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    Numerical methods of electrical impedance tomography

    Author
    Muller, Peter
    View/Open
    177160_Muller_rpi_0185E_10413.pdf (4.395Mb)
    Other Contributors
    Isaacson, David; Saulnier, Gary J.; Newell, Jonathan C.; Schwendeman, Donald W.; Holmes, Mark H.;
    Date Issued
    2014-08
    Subject
    Mathematics
    Degree
    PhD;
    Terms of Use
    This electronic version is a licensed copy owned by Rensselaer Polytechnic Institute, Troy, NY. Copyright of original work retained by author.;
    Metadata
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    URI
    https://hdl.handle.net/20.500.13015/1645
    Abstract
    The second reconstruction algorithm this thesis considers is the D-bar method. The D-bar method solves the full non-linear inverse problem. This method relies on solving for the complex geometrical optics (CGO) solutions to Schrödinger equation. To compute these CGO solutions, the D-bar equation must be solved numerically. This thesis introduces and analyzes a simple, easy-to-use finite difference solver for the D-bar equation. This solver is proven to be convergent with second-order accuracy. The D-bar method via this finite difference solver is then compared to Calderón's method.; Lastly, using both of these methods, a first attempt at recovering a ventilation-perfusion index from human data is explored.; The first direct method considered is a linearized reconstruction algorithm called Calderón's method. The original theory does not specify any particular domain, but previous numerical implementations of this algorithm rely on a circular domain. I developed a numerical implementation that works for non-circular domains, since the domains of interest in medical imaging applications are non-circular. When the boundary is modeled with a radius that changes with the angle, the data function is approximated by a similar series to the circular case, except now the inner products, which themselves need to be expanded into series, represent the entries of a transformation of the discrete Dirichlet-to-Neumann map. Qualitative and quantitative effects of correct domain modeling are demonstrated.; In electrical impedance tomography (EIT), the internal conductivity of a body is determined from measurements made on the boundary of the body. The goal of EIT is to reconstruct the conductivity inside the body from a dataset of boundary currents and voltages. This thesis is focused on numerical implementations of direct methods for reconstructing the conductivity.;
    Description
    August 2014; School of Science
    Department
    Dept. of Mathematical Sciences;
    Publisher
    Rensselaer Polytechnic Institute, Troy, NY
    Relationships
    Rensselaer Theses and Dissertations Online Collection;
    Access
    Restricted to current Rensselaer faculty, staff and students. Access inquiries may be directed to the Rensselaer Libraries.;
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