Inverse electromagnetic obstacle scattering problems with multi-frequency sparse backscattering far field data. (24th September 2020)

• Record Type: Journal Article
• Authors: Arens, Tilo; Ji, Xia; Liu, Xiaodong
• Is Part Of: Inverse problems. Volume 36:Number 10(2020)
• Publication Date: 2020-09-24
• Subjects: electromagnetic obstacle scattering -- sparse backscattering data -- uniqueness -- direct sampling methods; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/abb5e2
• Languages: English
• ISSNs: 0266-5611

Abstract

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 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.