The Linear Sampling Method for Data Generated by Small Random Scatterers\ast

被引：0

作者：

Garnier, Josselin ^{[1
]}

Haddar, Houssem ^{[2
]}

Montanelli, Hadrien ^{[2
]}

机构：

[1] Ecole Polytech, CMAP, IP Paris, F-91120 Palaiseau, France

[2] Inria, UMA, ENSTA Paris, IP Paris, F-91120 Palaiseau, France

来源：

SIAM JOURNAL ON IMAGING SCIENCES | 2024年 / 17卷 / 04期

关键词：

active (controlled sources); inverse acoustic scattering problem; Helmholtz equation; linear sampling method; passive imaging; singular value decomposition; Tikhonov regularization; ill-posed problems; INVERSE SCATTERING; WAVE TOMOGRAPHY; FIELDS;

D O I：

10.1137/24M1650417

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

We present an extension of the linear sampling method for solving the sound-soft inverse scattering problem in two dimensions with data generated by randomly distributed small scatterers. The theoretical justification of our novel sampling method is based on a rigorous asymptotic model, a modified Helmholtz-Kirchhoff identity, and our previous work on the linear sampling method for random sources. Our numerical implementation incorporates boundary elements, singular value decomposition, Tikhonov regularization, and Morozov's discrepancy principle. We showcase the robustness and accuracy of our algorithms with a series of numerical experiments.

引用

页码：2142 / 2173

页数：32

共 33 条

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