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The Electrical Impedance Tomography Problem

  • Antonio André NovotnyEmail author
  • Jan Sokołowski
  • Antoni Żochowski
Chapter
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 188)

Abstract

In this chapter the Electrical Impedance Tomography (EIT) is adopted as model problem, which consists in finding the number, size, shape and location of a set of hidden anomalies inside a body from total or partial measurements of the electrical potential on the boundary of the body. Since the EIT problem is written in the form of an overdetermined boundary value problem, the idea is to rewrite it as a topology optimization problem. In particular, a shape functional measuring the misfit between the boundary measurements and the electrical potentials obtained from the model is minimized with respect to a set of ball-shaped anomalies by using the concept of topological derivatives.

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Antonio André Novotny
    • 1
    Email author
  • Jan Sokołowski
    • 2
    • 3
    • 4
  • Antoni Żochowski
    • 3
  1. 1.Coordenação de Métodos Matemáticos e ComputacionaisLaboratório Nacional de Computação Científica LNCC/MCTICPetrópolisBrazil
  2. 2.Institut Élie Cartan de Nancy, UMR 7502Université de Lorraine, CNRSVandœuvre-Lès-NancyFrance
  3. 3.Systems Research InstitutePolish Academy of SciencesWarsawPoland
  4. 4.Universidade Federal da Paraiba, Centro de informaticaJoão PessoaBrazil

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