WIAS Preprint No. 943, (2004)

A regularized Newton method in electrical impedance tomography using shape Hessian information


  • Eppler, Karsten
  • Harbrecht, Helmut

2010 Mathematics Subject Classification

  • 49Q10 49M37 65N38 49K20


  • electrical impedance tomography, shape optimization, integral equation method, Newton type descent


The present paper is concerned with the identification of an obstacle or void of different conductivity included in a two-dimensional domain by measurements of voltage and currents at the boundary. We employ a reformulation of the given identification problem as a shape optimization problem as proposed by Sokolowski and Roche. It turns out that the shape Hessian degenerates at the given hole which gives a further hint on the ill-posedness of the problem. For numerical methods, we propose a preprocessing for detecting the barycenter and a crude approximation of the void or hole. Then, we resolve the shape of the hole by a regularized Newton method.

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