Direct sampling methods for isotropic and anisotropic scatterers with point source measurements
Direct sampling methods for isotropic and anisotropic scatterers with point source measurements
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DOI：
10.3934/ipi.2022015
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发表时间：
2021-07
影响因子：
1.3
通讯作者：
I. Harris;Dinh-Liem Nguyen;Thi-Phong Nguyen
中科院分区：
文献类型：
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作者：
I. Harris;Dinh-Liem Nguyen;Thi-Phong Nguyen
本文研究了从测量的点源散射场中恢复各向同性或各向异性散射体的逆散射问题。我们提出了两个新的成像函数来解决逆问题。第一种方法对数据进行“远场”变换，然后我们用它来推导并提供成像函数的显式衰减率。为了分析该成像泛函的行为，我们使用了近场算子的因式分解和Funk-Hecke积分恒等式。对于第二个成像函数，使用柯西数据来定义函数，并使用格林恒等式分析其行为。给出了各向同性散射体和各向异性散射体的二维数值实验。
In this paper, we consider the inverse scattering problem for recovering either an isotropic or anisotropic scatterer from the measured scattered field initiated by a point source. We propose two new imaging functionals for solving the inverse problem. The first one employs a 'far-field' transform to the data which we then use to derive and provide an explicit decay rate for the imaging functional. In order to analyze the behavior of this imaging functional we use the factorization of the near field operator as well as the Funk-Hecke integral identity. For the second imaging functional the Cauchy data is used to define the functional and its behavior is analyzed using the Green's identities. Numerical experiments are given in two dimensions for both isotropic and anisotropic scatterers.