Electrical Impedance Tomography: 3D Reconstructions using Scattering Transforms

Publication: Research - peer-reviewJournal article – Annual report year: 2011

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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
Publication date2012
Volume91
Issue4
Pages737-755
ISSN0003-6811
DOIs
StatePublished
CitationsWeb of Science® Times Cited: 1

Keywords

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