The Linear Sampling Method for Random Sources

Josselin Garnier; Houssem Haddar; Hadrien Montanelli

doi:10.1137/22M1531336

The Linear Sampling Method for Random Sources

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 acoustic scattering problem with randomly distributed point sources. The theoretical justification of our sampling method is based on the Helmholtz--Kirchhoff identity, the cross-correlation between measurements, and the volume and imaginary near-field operators, which we introduce and analyze. Implementations in MATLAB using boundary elements, the SVD, Tikhonov regularization, and Morozov's discrepancy principle are also discussed. We demonstrate the robustness and accuracy of our algorithms with several numerical experiments in two dimensions.

Original language	English
Pages (from-to)	1572-1593
Number of pages	22
Journal	SIAM Journal on Imaging Sciences
Volume	16
Issue number	3
DOIs	https://doi.org/10.1137/22M1531336
Publication status	Published - 1 Jan 2023

Keywords

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

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10.1137/22M1531336

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title = "The Linear Sampling Method for Random Sources",

abstract = "We present an extension of the linear sampling method for solving the sound-soft inverse acoustic scattering problem with randomly distributed point sources. The theoretical justification of our sampling method is based on the Helmholtz--Kirchhoff identity, the cross-correlation between measurements, and the volume and imaginary near-field operators, which we introduce and analyze. Implementations in MATLAB using boundary elements, the SVD, Tikhonov regularization, and Morozov's discrepancy principle are also discussed. We demonstrate the robustness and accuracy of our algorithms with several numerical experiments in two dimensions.",

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

author = "Josselin Garnier and Houssem Haddar and Hadrien Montanelli",

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AU - Montanelli, Hadrien

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N2 - We present an extension of the linear sampling method for solving the sound-soft inverse acoustic scattering problem with randomly distributed point sources. The theoretical justification of our sampling method is based on the Helmholtz--Kirchhoff identity, the cross-correlation between measurements, and the volume and imaginary near-field operators, which we introduce and analyze. Implementations in MATLAB using boundary elements, the SVD, Tikhonov regularization, and Morozov's discrepancy principle are also discussed. We demonstrate the robustness and accuracy of our algorithms with several numerical experiments in two dimensions.

AB - We present an extension of the linear sampling method for solving the sound-soft inverse acoustic scattering problem with randomly distributed point sources. The theoretical justification of our sampling method is based on the Helmholtz--Kirchhoff identity, the cross-correlation between measurements, and the volume and imaginary near-field operators, which we introduce and analyze. Implementations in MATLAB using boundary elements, the SVD, Tikhonov regularization, and Morozov's discrepancy principle are also discussed. We demonstrate the robustness and accuracy of our algorithms with several numerical experiments in two dimensions.

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 - 10.1137/22M1531336

DO - 10.1137/22M1531336

M3 - Article

AN - SCOPUS:85179182408

SN - 1936-4954

VL - 16

SP - 1572

EP - 1593

JO - SIAM Journal on Imaging Sciences

JF - SIAM Journal on Imaging Sciences

IS - 3

ER -

The Linear Sampling Method for Random Sources

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Keywords

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