Electrical Impedance Tomography: 3D Reconstructions using Scattering Transforms

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    Abstract

    In three dimensions the Calderon problem was addressed and solved in theory in the 1980s. The main ingredients in the solution of the problem are complex geometrical optics solutions to the conductivity equation and a (non-physical) scattering transform. The resulting reconstruction algorithm is in principle direct and addresses the full non-linear problem immediately. In this paper a new simplication of the algorithm is suggested. The method is based on solving a boundary integral equation for the complex geometrical optics solutions, and the method is implemented numerically using a Nystrom method. Convergence estimates are obtained using hyperinterpolation operators. We compare the method numerically to two other approximations by evaluation on two numerical examples. In addition a moment method for the numerical solution of the forward problem is given.
    Original languageEnglish
    JournalApplicable Analysis
    Volume91
    Issue number4
    Pages (from-to)737-755
    ISSN0003-6811
    DOIs
    Publication statusPublished - 2012

    Keywords

    • Numerical solution
    • Calderon problem
    • Moment method
    • Hyperinterpolation
    • Reconstruction algorithm
    • Electrical Impedance Tomography

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