用贝叶斯方法求解两层腔体内部逆散射问题

IF 1.2 4区数学 Q2 MATHEMATICS, APPLIED Inverse Problems and Imaging Pub Date : 2021-01-01 DOI:10.3934/ipi.2021069

Yunwen Yin, W. Yin, P. Meng, Hongyu Liu

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引用次数: 12

摘要

本文提出用贝叶斯方法求解两层腔体内部逆散射问题，以重建两层腔体的界面。散射场由位于内部界面内封闭曲线上的点源测量。证明了贝叶斯框架下后验分布的适定性。采用马尔可夫链蒙特卡罗算法来探索后验密度。通过数值实验验证了该方法的有效性。

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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The interior inverse scattering problem for a two-layered cavity using the Bayesian method

In this paper, the Bayesian method is proposed for the interior inverse scattering problem to reconstruct the interface of a two-layered cavity. The scattered field is measured by the point sources located on a closed curve inside the interior interface. The well-posedness of the posterior distribution in the Bayesian framework is proved. The Markov Chain Monte Carlo algorithm is employed to explore the posterior density. Some numerical experiments are presented to demonstrate the effectiveness of the proposed method.

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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.