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Inverse electromagnetic obstacle scattering problems with multi-frequency sparse backscattering far field data

Arens, Tilo; Ji, Xia; Liu, Xiaodong

Abstract:
This paper is dedicated to design a direct sampling method of inverse electromagnetic scattering problems, which uses multi-frequency sparse backscattering far field data for reconstructing the boundary of perfectly conducting obstacles. We show that a smallest strip containing the unknown object can be approximately determined by the multi-frequency backscattering far field data at two opposite observation directions. The proof is based on the Kirchhoff approximation and Fourier transform. Such a strip is then reconstructed by an indicator, which is the absolute value of an integral of the product of the data and some properly chosen function over the frequency interval. With the increase of the number of the backscattering data, the location and shape of the underlying object can be reconstructed. Numerical examples are conducted to show the validity and robustness of the proposed sampling method. The numerical examples also show that the concave part of the underlying object can be well reconstructed, and the different connected components of the underlying object can be well separated.

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Volltext §
DOI: 10.5445/IR/1000118149
Veröffentlicht am 09.04.2020
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht/Preprint
Publikationsjahr 2020
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000118149
Verlag KIT, Karlsruhe
Umfang 18 S.
Serie CRC Preprint ; 2020/12
Projektinformation SFB 1173/2 (DFG, DFG KOORD, SFB 1173/2 2019)
Externe Relationen Abstract/Volltext
Schlagwörter electromagnetic obstacle scattering, sparse backscattering data, uniqueness, direct sampling methods
Nachgewiesen in arXiv
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