| Issue |
ESAIM: M2AN
Volume 58, Number 2, March-April 2024
|
|
|---|---|---|
| Page(s) | 545 - 569 | |
| DOI | https://doi.org/10.1051/m2an/2024003 | |
| Published online | 09 April 2024 | |
Invisibility enables super-visibility in electromagnetic imaging
1
Faculty of Computational Mathematics and Cybernetics, Shenzhen MSUBIT University, 518172 Shenzhen, P.R. China
2
Yau Mathematical Sciences Center, Tsinghua University, Beijing, P.R. China
3
Yanqi Lake Beijing Institute of Mathematical Sciences and Applications, Beijing, P.R. China
4
Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong SAR, P.R. China
5
School of Mathematics, Harbin Institute of Technology, Harbin, P.R. China
* Corresponding author: hongyliu@cityu.edu.hk
Received:
29
March
2023
Accepted:
2
January
2024
This paper is concerned with the inverse electromagnetic scattering problem for anisotropic media. We use the interior resonant modes to develop an inverse scattering scheme for imaging the scatterer. The whole procedure consists of three phases. First, we determine the interior Maxwell transmission eigenvalues of the scatterer from a family of far-field data by the mechanism of the linear sampling method. Next, we determine the corresponding transmission eigenfunctions by solving a constrained optimization problem. Finally, based on both global and local geometric properties of the transmission eigenfunctions, we design an imaging functional which can be used to determine the shape of the medium scatterer. We provide rigorous theoretical basis for our method. Numerical experiments verify the effectiveness, better accuracy and super-resolution results of the proposed scheme.
Mathematics Subject Classification: 35Q60 / 35P25 / 35R30 / 78A40
Key words: Inverse electromagnetic scattering / anisotropic media / transmission eigenfunctions / geometric structures / super-resolution
© The authors. Published by EDP Sciences, SMAI 2024
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.