Fourier method for inverse source problem using correlation of passive measurements

被引：0
|
作者：
Triki, Faouzi [1 ]
Linder-Steinlein, Kristoffer [2 ]
Karamehmedovic, Mirza [2 ]
机构：
[1] Univ Grenoble Alpes, Lab Jean Kuntzmann, Grenoble, France
[2] Tech Univ Denmark, Dept Appl Math, Lyngby, Denmark
来源：
INVERSE PROBLEMS | 2024年 / 40卷 / 10期
关键词：
passive imaging; wave equation; stability; inverse source problem; PHASE RETRIEVAL; CONTROLLABILITY;
D O I：
10.1088/1361-6420/ad6fc7
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider the inverse source problem for the time-dependent, constant-coefficient wave equation with Cauchy data and passive cross-correlation data.We propose to consider the cross-correlation as a wave equation itself and reconstruct the cross-correlation in the support of the source for the original Cauchy wave equation. Having access to the cross-correlation in the support of the source, we show that the cross-correlation solves a wave equation, and we reconstruct the cross-correlation from boundary data to recover the source in the original Cauchy wave equation. In addition, we show the inverse source problem is ill-posed and suffers from non-uniqueness when the mean of the source is zero and provide a uniqueness result and stability estimate in case of non-zero mean sources.
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页数：14
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