On a novel inverse scattering scheme using resonant modes with enhanced imaging resolution
Liu,Hongyu1; Liu,Xiaodong2; Wang,Xianchao3; Wang,Yuliang1
Source PublicationInverse Problems
AbstractAbstract 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.
Keywordwave imaging shape reconstruction interior resonant modes eigenvalue and eigenfunction reconstruction
WOS IDIOP:0266-5611-35-12-ab2932
PublisherIOP Publishing
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Document Type期刊论文
Affiliation1.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
Recommended Citation
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).
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