基于边界控制方法的变密度重构逆问题的深度学习与连续迭代

IF 0.6 Q4 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Eurasian Journal of Mathematical and Computer Applications Pub Date : 2022-09-27 DOI:10.32523/2306-6172-2022-10-3-37-57

Klibanov Michael V, Timonov Alexandre

{"title":"基于边界控制方法的变密度重构逆问题的深度学习与连续迭代","authors":"Klibanov Michael V, Timonov Alexandre","doi":"10.32523/2306-6172-2022-10-3-37-57","DOIUrl":null,"url":null,"abstract":"For the first time, two approaches, the deep learning and successive iterations, are proposed for use and implemented for enhancing the images reconstructed by the boundary control method. The construction of successive iterations is based on the reduction of a nonlinear inverse problem for a time-domain wave equation to a linear integral equation of the first kind. The computational effectiveness of the numerical techniques is demonstrated in the numerical experiments in two and three dimensions.","PeriodicalId":42910,"journal":{"name":"Eurasian Journal of Mathematical and Computer Applications","volume":"1 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2022-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"DEEP LEARNING AND SUCCESSIVE ITERATIONS FOR AN INVERSE PROBLEM OF THE VARIABLE DENSITY RECONSTRUCTION BY THE BOUNDARY CONTROL METHOD\",\"authors\":\"Klibanov Michael V, Timonov Alexandre\",\"doi\":\"10.32523/2306-6172-2022-10-3-37-57\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"For the first time, two approaches, the deep learning and successive iterations, are proposed for use and implemented for enhancing the images reconstructed by the boundary control method. The construction of successive iterations is based on the reduction of a nonlinear inverse problem for a time-domain wave equation to a linear integral equation of the first kind. The computational effectiveness of the numerical techniques is demonstrated in the numerical experiments in two and three dimensions.\",\"PeriodicalId\":42910,\"journal\":{\"name\":\"Eurasian Journal of Mathematical and Computer Applications\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2022-09-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Eurasian Journal of Mathematical and Computer Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.32523/2306-6172-2022-10-3-37-57\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Eurasian Journal of Mathematical and Computer Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.32523/2306-6172-2022-10-3-37-57","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}

引用次数: 0

摘要

首次提出并实现了两种方法，即深度学习和连续迭代，用于增强边界控制方法重建的图像。连续迭代的构造是基于将时域波动方程的非线性逆问题简化为第一类线性积分方程。在二维和三维数值实验中证明了数值技术的计算有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

DEEP LEARNING AND SUCCESSIVE ITERATIONS FOR AN INVERSE PROBLEM OF THE VARIABLE DENSITY RECONSTRUCTION BY THE BOUNDARY CONTROL METHOD

For the first time, two approaches, the deep learning and successive iterations, are proposed for use and implemented for enhancing the images reconstructed by the boundary control method. The construction of successive iterations is based on the reduction of a nonlinear inverse problem for a time-domain wave equation to a linear integral equation of the first kind. The computational effectiveness of the numerical techniques is demonstrated in the numerical experiments in two and three dimensions.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Eurasian Journal of Mathematical and Computer Applications MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-

CiteScore

1.40

自引率

0.00%

发文量

期刊介绍： Eurasian Journal of Mathematical and Computer Applications (EJMCA) publishes carefully selected original research papers in all areas of Applied mathematics first of all from Europe and Asia. However papers by mathematicians from other continents are also welcome. From time to time Eurasian Journal of Mathematical and Computer Applications (EJMCA) will also publish survey papers. Eurasian Mathematical Journal publishes 4 issues in a year. A working language of the journal is English. Main topics are: - Mathematical methods and modeling in mechanics, mining, biology, geophysics, electrodynamics, acoustics, industry. - Inverse problems of mathematical physics: theory and computational approaches. - Medical and industry tomography. - Computer applications: distributed information systems, decision-making systems, embedded systems, information security, graphics.