Simultaneous recovery of an obstacle and its excitation sources from near-field scattering data

Yan Chang; Yukun Guo

doi:10.3934/era.2022068

Simultaneous recovery of an obstacle and its excitation sources from near-field scattering data

Yan Chang
, Yukun Guo^*

^*Corresponding author for this work

School of Mathematics, Harbin Institute of Technology

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

11 Scopus citations

Abstract

This paper is concerned with the inverse problem of determining an obstacle and the corresponding incident point sources in the Helmholtz equation from near-field scattering data. An optimization method is proposed to simultaneously recover both the obstacle and source locations. Moreover, a two-step sampling scheme with novel indicator functions is proposed to produce a good initial guess for solving the optimization problem. Theoretically, we analyze the convergence properties of the optimization method and the behaviors of the indicator functions.

Original language	English
Pages (from-to)	1296-1321
Number of pages	26
Journal	Electronic Research Archive
Volume	30
Issue number	4
DOIs	https://doi.org/10.3934/era.2022068
State	Published - 2022
Externally published	Yes

Keywords

Direct sampling
Inverse scattering
Inverse source problem
Near field
Optimization method
Reverse time migration

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10.3934/era.2022068

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abstract = "This paper is concerned with the inverse problem of determining an obstacle and the corresponding incident point sources in the Helmholtz equation from near-field scattering data. An optimization method is proposed to simultaneously recover both the obstacle and source locations. Moreover, a two-step sampling scheme with novel indicator functions is proposed to produce a good initial guess for solving the optimization problem. Theoretically, we analyze the convergence properties of the optimization method and the behaviors of the indicator functions.",

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author = "Yan Chang and Yukun Guo",

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AU - Chang, Yan

AU - Guo, Yukun

N1 - Publisher Copyright: © 2022. the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)

PY - 2022

Y1 - 2022

N2 - This paper is concerned with the inverse problem of determining an obstacle and the corresponding incident point sources in the Helmholtz equation from near-field scattering data. An optimization method is proposed to simultaneously recover both the obstacle and source locations. Moreover, a two-step sampling scheme with novel indicator functions is proposed to produce a good initial guess for solving the optimization problem. Theoretically, we analyze the convergence properties of the optimization method and the behaviors of the indicator functions.

AB - This paper is concerned with the inverse problem of determining an obstacle and the corresponding incident point sources in the Helmholtz equation from near-field scattering data. An optimization method is proposed to simultaneously recover both the obstacle and source locations. Moreover, a two-step sampling scheme with novel indicator functions is proposed to produce a good initial guess for solving the optimization problem. Theoretically, we analyze the convergence properties of the optimization method and the behaviors of the indicator functions.

KW - Direct sampling

KW - Inverse scattering

KW - Inverse source problem

KW - Near field

KW - Optimization method

KW - Reverse time migration

UR - https://www.scopus.com/pages/publications/85129744885

U2 - 10.3934/era.2022068

DO - 10.3934/era.2022068

M3 - 文章

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SN - 2688-1594

VL - 30

SP - 1296

EP - 1321

JO - Electronic Research Archive

JF - Electronic Research Archive

IS - 4

ER -

Simultaneous recovery of an obstacle and its excitation sources from near-field scattering data

Abstract

Keywords

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