The factorization and monotonicity method for the defect in an open periodic waveguide
The factorization and monotonicity method for the defect in an open periodic waveguide
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DOI：
10.1515/jiip-2019-0088
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发表时间：
2019-07
影响因子：
1.1
通讯作者：
Takashi Furuya
中科院分区：
文献类型：
--
作者：
Takashi Furuya
摘要本文研究了由近场数据重建上半空间具有周期性的无限介质中缺陷的逆散射问题。本文有两个贡献。首先指出了文献[A. Lechleiter，The factorization method is independent of transmission eigenvalues，Inverse Probl. Imaging 3 2009，1，123-138]，并给出正确的一个。其次，结合因子分解法和单调性法给出了两种未知缺陷的重建算法。文中还给出了基于前一算法的数值例子。
Abstract We consider the inverse scattering problem to reconstruct the defect in an infinite medium with periodicity in the upper half space from near field data. This paper has two contributions. Firstly, we mention that there is a mistake in the factorization method of the earlier paper [A. Lechleiter, The factorization method is independent of transmission eigenvalues, Inverse Probl. Imaging 3 2009, 1, 123–138] and give the correct one. Secondly, we give two reconstruction algorithms for the unknown defect by a combination of the factorization method and the monotonicity method. We also give numerical examples based on the former algorithm.