TWO SINGLE-MEASUREMENT UNIQUENESS RESULTS FOR INVERSE SCATTERING PROBLEMS WITHIN POLYHEDRAL GEOMETRIES

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

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Detail(s)

Original languageEnglish
Pages (from-to)1501–1528
Number of pages28
Journal / PublicationInverse Problems and Imaging
Volume16
Issue number6
Online publishedApr 2022
Publication statusPublished - Dec 2022

Abstract

We consider the unique determinations of impenetrable obstacles or diffraction grating profiles in R3 by a single far-field measurement within polyhedral geometries. We are particularly interested in the case that the scattering objects are of impedance type. We derive two new unique identifiability results by a single measurement for the inverse scattering problem in the aforementioned two challenging setups. The main technical idea is to exploit certain quantitative geometric properties of the Laplacian eigenfunctions which were initiated in our recent works [12, 13]. In this paper, we derive novel geometric properties that generalize and extend the related results in [13], which further enable us to establish the new unique identifiability results. It is pointed out that in addition to the shape of the obstacle or the grating profile, we can simultaneously recover the boundary impedance parameters.

Research Area(s)

  • Unique identifiability, inverse obstacle scattering, inverse grating, single far-field pattern, Laplacian eigenfunction, geometric structure, LAPLACIAN EIGENFUNCTIONS, STABLE DETERMINATION, SOUND-HARD, OBSTACLE, PRINCIPLE, EQUATIONS, THEOREMS

Citation Format(s)

TWO SINGLE-MEASUREMENT UNIQUENESS RESULTS FOR INVERSE SCATTERING PROBLEMS WITHIN POLYHEDRAL GEOMETRIES. / CAO, Xinlin; DIAO, Huaian; LIU, Hongyu et al.
In: Inverse Problems and Imaging, Vol. 16, No. 6, 12.2022, p. 1501–1528.

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review