A stable non-iterative reconstruction algorithm for the acoustic inverse boundary value problem

IF 1.2 4区数学 Q2 MATHEMATICS, APPLIED

Inverse Problems and Imaging Pub Date : 2021-01-01 DOI:10.3934/IPI.2021038

Tianyu Yang, Yang Yang

引用次数: 1

Abstract

We present a non-iterative algorithm to reconstruct the isotropic acoustic wave speed from the measurement of the Neumann-to-Dirichlet map. The algorithm is designed based on the boundary control method and involves only computations that are stable. We prove the convergence of the algorithm and present its numerical implementation. The effectiveness of the algorithm is validated on both constant speed and variable speed, with full and partial boundary measurement as well as different levels of noise.

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声学反边值问题的稳定非迭代重构算法

我们提出了一种非迭代算法，从诺伊曼-狄利克雷映射的测量中重建各向同性声波速度。该算法是基于边界控制方法设计的，只涉及稳定的计算。证明了算法的收敛性，并给出了算法的数值实现。在等速和变速、全边界和局部边界测量以及不同噪声水平下验证了算法的有效性。

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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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.