无相近场测量反散射问题的独特确定

IF 1.5 4区数学 Q2 MATHEMATICS, APPLIED

Inverse Problems and Imaging Pub Date : 2020-01-01 DOI:10.3934/ipi.2020026

Deyue Zhang, Yukun Guo, Fenglin Sun, Hongyu Liu

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引用次数: 14

摘要

本文利用近场数据的模量，建立了若干反声散射问题的独特判定结果。利用点源的叠加作为入射波，我们严格地证明了在容许表面上收集的无相近场可以唯一地确定障碍物的位置和形状，以及障碍物的边界条件和介质包体的折射率。我们还建立了由点源叠加引起的无相近场数据确定局部粗糙表面的唯一性。这是无相近场数据反演散射的新颖唯一性结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Unique determinations in inverse scattering problems with phaseless near-field measurements

In this paper, we establish the unique determination results for several inverse acoustic scattering problems using the modulus of the near-field data. By utilizing the superpositions of point sources as the incident waves, we rigorously prove that the phaseless near-fields collected on an admissible surface can uniquely determine the location and shape of the obstacle as well as its boundary condition and the refractive index of a medium inclusion, respectively. We also establish the uniqueness in determining a locally rough surface from the phaseless near-field data due to superpositions of point sources. These are novel uniqueness results in inverse scattering with phaseless near-field data.

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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.