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

    Fingerprint

    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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