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Inverse electromagnetic obstacle scattering problems with multi-frequency sparse backscattering far field data
Arens,Tilo1; Ji,Xia2,3; Liu,Xiaodong4
2020-09-24
Source PublicationInverse Problems
ISSN0266-5611
Volume36Issue:10
AbstractAbstractThis 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 boundaries of perfectly conducting obstacles. We show that the 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, even with moderately sized frequencies. 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.
Keywordelectromagnetic obstacle scattering sparse backscattering data uniqueness direct sampling methods
DOI10.1088/1361-6420/abb5e2
Language英语
WOS IDIOP:0266-5611-36-10-abb5e2
PublisherIOP Publishing
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/52127
Collection中国科学院数学与系统科学研究院
Affiliation1.Department of Mathematics, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany
2.School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, People’s Republic of China
3.Beijing Key Laboratory on MCAACI, Beijing Institute of Technology, Beijing 100081, People’s Republic of China
4.Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, 100190 Beijing, People’s Republic of China
Recommended Citation
GB/T 7714
Arens,Tilo,Ji,Xia,Liu,Xiaodong. Inverse electromagnetic obstacle scattering problems with multi-frequency sparse backscattering far field data[J]. Inverse Problems,2020,36(10).
APA Arens,Tilo,Ji,Xia,&Liu,Xiaodong.(2020).Inverse electromagnetic obstacle scattering problems with multi-frequency sparse backscattering far field data.Inverse Problems,36(10).
MLA Arens,Tilo,et al."Inverse electromagnetic obstacle scattering problems with multi-frequency sparse backscattering far field data".Inverse Problems 36.10(2020).
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