Distinguishability Revisited: Depth Dependent Bounds on Reconstruction Quality in Electrical Impedance Tomography: Depth dependent bounds on reconstruction quality in electrical impedance tomography

Henrik Garde, Kim Knudsen

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Abstract

The reconstruction problem in electrical impedance tomography is highly ill-posed, and it is often observed numerically that reconstructions have poor resolution far away from the measurement boundary but better resolution near the measurement boundary. The observation can be quantified by the concept of distinguishability of inclusions. This paper provides mathematically rigorous results supporting the intuition. Indeed, for a model problem lower and upper bounds on the distinguishability of an inclusion are derived in terms of the boundary data. These bounds depend explicitly on the distance of the inclusion to the boundary, i.e. the depth of the inclusion. The results are obtained for disk inclusions in a homogeneous background in the unit disk. The theoretical bounds are veried numerically using a novel, exact characterization of the forward map as a tridiagonal matrix.
Original languageEnglish
JournalS I A M Journal on Applied Mathematics
Volume77
Issue number2
Pages (from-to)697-720
ISSN0036-1399
DOIs
Publication statusPublished - 2017

Keywords

  • Electrical impedance tomography
  • Depth dependence
  • Harmonic morphism
  • Sigenvalue bounds
  • Distinguishability

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