Bounds on the volume of an inclusion in a body from a complex conductivity measurement

Andrew E. Thaler, Graeme W. Milton

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

We derive bounds on the volume of an inclusion in a body in two or three dimensions when the conductivities of the inclusion and the surrounding body are complex and assumed to be known. The bounds are derived in terms of average values of the electric field, current, and certain products of the electric field and current. All of these average values are computed from a single electrical impedance tomography measurement of the voltage and current on the boundary of the body. Additionally, the bounds are tight in the sense that at least one of the bounds gives the exact volume of the inclusion for certain geometries and boundary conditions.

Original languageEnglish (US)
Pages (from-to)863-892
Number of pages30
JournalCommunications in Mathematical Sciences
Volume13
Issue number4
DOIs
StatePublished - 2015

Bibliographical note

Publisher Copyright:
© 2015 International Press.

Keywords

  • Electrical impedance tomography
  • Size estimation
  • Volume fraction bounds

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