Error estimation to the direct sampling method for the inverse acoustic source problem with multi-frequency data

IF 1.2 4区数学 Q2 MATHEMATICS, APPLIED

Inverse Problems and Imaging Pub Date : 2023-01-01 DOI:10.3934/ipi.2023042

Xia Ji, Yuling Jiao, Xiliang Lu, Fengru Wang

引用次数: 0

Abstract

In this article, we introduce a novel direct sampling indicator function for solving the inverse source problem (ISP) associated with the Helmholtz equation. The proposed method is rigorously evaluated through numerical analysis of both singular and general sources, providing a comprehensive assessment of its performance. Several numerical examples are given to validate the theoretical estimations.

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多频数据反声源问题直接采样方法的误差估计

在本文中，我们引入了一种新的直接抽样指示函数来解决与亥姆霍兹方程相关的逆源问题。通过对单一源和一般源的数值分析，对所提出的方法进行了严格的评估，对其性能进行了全面的评估。给出了几个数值算例来验证理论估计。

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.