The Linear Sampling Method for Data Generated by Small Random Scatterers

Josselin Garnier; Houssem Haddar; Hadrien Montanelli

doi:10.1137/24M1650417

The Linear Sampling Method for Data Generated by Small Random Scatterers

Josselin Garnier, Houssem Haddar, Hadrien Montanelli

Ecole polytechnique

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	2142-2173
Number of pages	32
Journal	SIAM Journal on Imaging Sciences
Volume	17
Issue number	4
DOIs	https://doi.org/10.1137/24M1650417
Publication status	Published - 1 Jan 2024

Keywords

Helmholtz equation
Tikhonov regularization
ill-posed problems
inverse acoustic scattering problem
linear sampling method
passive imaging
singular value decomposition

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10.1137/24M1650417

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title = "The Linear Sampling Method for Data Generated by Small Random Scatterers",

abstract = "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.",

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N2 - 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.

AB - 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.

KW - Helmholtz equation

KW - Tikhonov regularization

KW - ill-posed problems

KW - inverse acoustic scattering problem

KW - linear sampling method

KW - passive imaging

KW - singular value decomposition

U2 - 10.1137/24M1650417

DO - 10.1137/24M1650417

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EP - 2173

JO - SIAM Journal on Imaging Sciences

JF - SIAM Journal on Imaging Sciences

IS - 4

ER -

The Linear Sampling Method for Data Generated by Small Random Scatterers

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Keywords

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