{"title":"Error estimation to the direct sampling method for the inverse acoustic source problem with multi-frequency data","authors":"Xia Ji, Yuling Jiao, Xiliang Lu, Fengru Wang","doi":"10.3934/ipi.2023042","DOIUrl":null,"url":null,"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.","PeriodicalId":50274,"journal":{"name":"Inverse Problems and Imaging","volume":null,"pages":null},"PeriodicalIF":1.2000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Inverse Problems and Imaging","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3934/ipi.2023042","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
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.
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.
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