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Monotonicity-based reconstruction of extreme inclusions in electrical impedance tomography

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  • Valentina Candiani, Department of Mathematics and Systems Analysis, Aalto University, Finland
  • Jérémi Dardé, Université Paul Sabatier, Frankrig
  • Henrik Garde
  • Nuutti Hyvönen, Department of Mathematics and Systems Analysis, Aalto University, Finland
The monotonicity-based approach has become one of the fundamental methods for reconstructing inclusions in the inverse problem of electrical impedance tomography. Thus far the method has not been proven to be able to handle extreme inclusions that correspond to some parts of the studied domain becoming either perfectly conducting or perfectly insulating. The main obstacle has arguably been establishing suitable monotonicity principles for the corresponding Neumann-to-Dirichlet boundary maps. In this work, we tackle this shortcoming by first giving a convergence result in the operator norm for the Neumann-to-Dirichlet map when the conductivity coefficient decays to zero and/or grows to infinity in some given parts of the domain. This allows passing the necessary monotonicity principles to the limiting case. Subsequently, we show how the monotonicity method generalizes to the definite case of reconstructing either perfectly conducting or perfectly insulating inclusions, as well as to the indefinite case where the perturbed conductivity can take any values between, and including, zero and infinity.
OriginalsprogEngelsk
TidsskriftSIAM Journal on Mathematical Analysis
Vol/bind52
Nummer6
Sider (fra-til)6234–6259
Antal sider26
ISSN0036-1410
DOI
StatusUdgivet - dec. 2020

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