On a novel inverse scattering scheme using resonant modes with enhanced imaging resolution

doi:10.1088/1361-6420/ab2932

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	On a novel inverse scattering scheme using resonant modes with enhanced imaging resolution
	Liu,Hongyu 1; Liu,Xiaodong2 ; Wang,Xianchao 3; Wang,Yuliang 1
	2019-11-20
发表期刊	Inverse Problems
ISSN	0266-5611
卷号	35 期号:12
摘要	Abstract We develop a novel wave imaging scheme for reconstructing the shape of an inhomogeneous scatterer and we consider the inverse acoustic obstacle scattering problem as a prototype model for our study. There exists a wealth of reconstruction methods for the inverse obstacle scattering problem and many of them intentionally avoid the interior resonant modes. Indeed, the occurrence of the interior resonance may cause the failure of the corresponding reconstruction. However, based on the observation that the interior resonant modes actually carry the geometrical information of the underlying obstacle, we propose an inverse scattering scheme of using those resonant modes for the reconstruction. To that end, we first develop a numerical procedure in determining the interior eigenvalues associated with an unknown obstacle from its far-field data based on the validity of the factorization method. Then we propose two efficient optimization methods in further determining the corresponding eigenfunctions. Using the afore-determined interior resonant modes, we show that the shape of the underlying obstacle can be effectively recovered. Moreover, the reconstruction yields enhanced imaging resolution, especially for the concave part of the obstacle. We provide rigorous theoretical justifications for the proposed method. Numerical examples in 2D and 3D verify the theoretically predicted effectiveness and efficiency of the method.
关键词	wave imaging shape reconstruction interior resonant modes eigenvalue and eigenfunction reconstruction
DOI	10.1088/1361-6420/ab2932
语种	英语
WOS记录号	IOP:0266-5611-35-12-ab2932
出版者	IOP Publishing
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/50286
专题	应用数学研究所
作者单位	1.Department of Mathematics, Hong Kong Baptist University, Kowloon, Hong Kong Special Administrative Region of China 2.Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, 100190 Beijing, People’s Republic of China 3.Department of Mathematics, Harbin Institute of Technology, Harbin, Republic of China
推荐引用方式 GB/T 7714	Liu,Hongyu,Liu,Xiaodong,Wang,Xianchao,et al. On a novel inverse scattering scheme using resonant modes with enhanced imaging resolution[J]. Inverse Problems,2019,35(12).
APA	Liu,Hongyu,Liu,Xiaodong,Wang,Xianchao,&Wang,Yuliang.(2019).On a novel inverse scattering scheme using resonant modes with enhanced imaging resolution.Inverse Problems,35(12).
MLA	Liu,Hongyu,et al."On a novel inverse scattering scheme using resonant modes with enhanced imaging resolution".Inverse Problems 35.12(2019).