Size estimates for the EIT problem with one measurement: The complex case

Elena Beretta, Elisa Francini, Sergio Vessella

Research output: Contribution to journalArticle

Abstract

In this paper we estimate the size of a measurable inclusion in terms of power measurements for a single applied boundary current. This problem arises in medical imaging for the screening of organs (see [17]). For this kind of problem one has to deal mathematically with the complex conductivity (admittivity) equation. In this case we are able to establish, for certain classes of admittivities, lower and upper bounds of the measure of the inclusion in terms of the power measurements. A novelty of our result is that we are also able to estimate the volume of an inclusion having part of its boundary in common with the reference body. Our analysis is based on the derivation of energy bounds and fine quantitative estimates of unique continuation for solutions to elliptic equations.

Original languageEnglish (US)
Pages (from-to)551-580
Number of pages30
JournalRevista Matematica Iberoamericana
Volume30
Issue number2
DOIs
StatePublished - Jan 1 2014

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Inclusion
Estimate
Unique Continuation
Medical Imaging
Elliptic Equations
Conductivity
Screening
Upper and Lower Bounds
Energy
Class

Keywords

  • Inverse boundary problems
  • Size estimates
  • Ucontinuation

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Size estimates for the EIT problem with one measurement : The complex case. / Beretta, Elena; Francini, Elisa; Vessella, Sergio.

In: Revista Matematica Iberoamericana, Vol. 30, No. 2, 01.01.2014, p. 551-580.

Research output: Contribution to journalArticle

Beretta, Elena ; Francini, Elisa ; Vessella, Sergio. / Size estimates for the EIT problem with one measurement : The complex case. In: Revista Matematica Iberoamericana. 2014 ; Vol. 30, No. 2. pp. 551-580.
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