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2009, Volume 3, Issue 2: 353-371. Doi: 10.3934/ipi.2009.3.353
This issue Previous Article An estimate for the free Helmholtz equation that scales Next Article

A Newton method for reconstructing non star-shaped domains in electrical impedance tomography

  • 1.

    Institut für Numerische Simulation, Universität Bonn, Wegelerstr. 6, 53115 Bonn

  • 2.

    Institut für Numerische und Angewandte Mathematik, Lotzestr. 16-18 D-37083 Göttingen

Received:  December 31, 2008
Revised:  February 28, 2009
Published:  April 2009
Abstract Related Papers Cited by
    Abstract
  • We study the reconstruction of the shape of a perfectly conducting inclusion in three dimensional electrical impedance tomography (EIT) using a regularized Newton method. This method involves a least squares penalty in the form of an additional nonlinear operator to cope with the non-uniqueness of general parametrizations of the unknown boundary. We provide a convergence result for this method in the general framework of nonlinear ill-posed operator equations. Moreover, we discuss the evaluation of the forward operator in EIT, its derivative, and the adjoint of the derivative using a wavelet based boundary element method. Numerical examples illustrate the performance of our method.
    Mathematics Subject Classification: Primary: 65J22; Secondary: 65J15, 65J20, 65R20.

    Citation:
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