点源测量各向同性和各向异性散射体的直接采样方法

IF 1.2 4区数学 Q2 MATHEMATICS, APPLIED

Inverse Problems and Imaging Pub Date : 2021-07-16 DOI:10.3934/ipi.2022015

I. Harris, Dinh-Liem Nguyen, Thi-Phong Nguyen

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引用次数: 9

摘要

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。

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Direct sampling methods for isotropic and anisotropic scatterers with point source measurements

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.

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来源期刊

Inverse Problems and Imaging 数学-物理：数学物理

CiteScore

2.50

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Inverse Problems and Imaging publishes research articles of the highest quality that employ innovative mathematical and modeling techniques to study inverse and imaging problems arising in engineering and other sciences. Every published paper has a strong mathematical orientation employing methods from such areas as control theory, discrete mathematics, differential geometry, harmonic analysis, functional analysis, integral geometry, mathematical physics, numerical analysis, optimization, partial differential equations, and stochastic and statistical methods. The field of applications includes medical and other imaging, nondestructive testing, geophysical prospection and remote sensing as well as image analysis and image processing. This journal is committed to recording important new results in its field and will maintain the highest standards of innovation and quality. To be published in this journal, a paper must be correct, novel, nontrivial and of interest to a substantial number of researchers and readers.