Inverse Problems and Imaging (IPI)

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

Pages: 353 - 371, Volume 3, Issue 2, May 2009      doi:10.3934/ipi.2009.3.353

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Helmut Harbrecht - Institut für Numerische Simulation, Universität Bonn, Wegelerstr. 6, 53115 Bonn, Germany (email)
Thorsten Hohage - Institut für Numerische und Angewandte Mathematik, Lotzestr. 16-18 D-37083 Göttingen, Germany (email)

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.

Keywords:  nonlinear inverse problems, regularization, electrical impedance tomography, inverse obstacle problems.
Mathematics Subject Classification:  Primary: 65J22; Secondary: 65J15, 65J20, 65R20.

Received: January 2009;      Revised: March 2009;      Available Online: May 2009.