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Optimal parameters of a multi-frequency experiment in an inverse problem of determining the dielectric constant of an inclusion in free space and in a waveguide
Moscow State University, Moscow, Russia.
Moscow State University, Moscow, Russia.
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.ORCID iD: 0000-0002-2691-2820
2022 (English)In: Measurement, ISSN 0263-2241, E-ISSN 1873-412X, Vol. 187, article id 110357Article in journal (Refereed) Published
Abstract [en]

A semi-analytical approach to the ill-posed inverse problem of reconstructing the dielectric constant of dielectric objects placed in free space or in a waveguide is proposed. It is shown that the advantage of an experiment, performed at huge frequency array, is the possibility of formulating a well-posed vector problem with attainable experimental parameters. The method substantiates the analysis of the operators of forward scattering problems, which makes it possible to justify the unique solvability of the studied inverse problem. It is proved that a solution to the problem can be found by the least squares method from the measurement data obtained in an imperfect experiment; it converges to the desired parameter of the test material while improving the quality of the experimental setup and reducing noise; the convergence rate grows with an increase in the number of frequencies used in the measurement.

Place, publisher, year, edition, pages
Elsevier, 2022. Vol. 187, article id 110357
Keywords [en]
Ill-posed inverse problem, permittivity, layer, frequency, dielectric, unique solvability, experiment
National Category
Mathematics
Research subject
Intelligent Industry
Identifiers
URN: urn:nbn:se:hig:diva-37286DOI: 10.1016/j.measurement.2021.110357ISI: 000718041900004Scopus ID: 2-s2.0-85118508374OAI: oai:DiVA.org:hig-37286DiVA, id: diva2:1606686
Available from: 2021-10-28 Created: 2021-10-28 Last updated: 2021-11-25Bibliographically approved

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Shestopalov, Yury

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CiteExportLink to record
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Citation style
  • apa
  • harvard-cite-them-right
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
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Language
  • sv-SE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • de-DE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf