American Institute of Mathematical Sciences

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May  2009, 3(2): 353-371. doi: 10.3934/ipi.2009.3.353

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

Helmut Harbrecht 1, and  Thorsten Hohage 2,

1. 

Institut für Numerische Simulation, Universität Bonn, Wegelerstr. 6, 53115 Bonn, Germany
2. 

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

Received  January 2009 Revised  March 2009 Published  May 2009

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, inverse obstacle problems., electrical impedance tomography.
Mathematics Subject Classification: Primary: 65J22; Secondary: 65J15, 65J20, 65R2.
Citation: Helmut Harbrecht, Thorsten Hohage. A Newton method for reconstructing non star-shaped domains in electrical impedance tomography. Inverse Problems & Imaging, 2009, 3 (2) : 353-371. doi: 10.3934/ipi.2009.3.353
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