Fourier method for recovering acoustic sources from multi-frequency far-field data

Xianchao Wang; Yukun Guo; Deyue Zhang; Hongyu Liu

doi:10.1088/1361-6420/aa573c

Fourier method for recovering acoustic sources from multi-frequency far-field data

Xianchao Wang, Yukun Guo, Deyue Zhang, Hongyu Liu^*

^*Corresponding author for this work

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

56 Citations (Scopus)

Abstract

We consider an inverse source problem of determining a source term in the Helmholtz equation from multi-frequency far-field measurements. Based on the Fourier series expansion, we develop a novel non-iterative reconstruction method for solving the problem. A promising feature of this method is that it utilizes the data from only a few observation directions for each frequency. Theoretical uniqueness and stability analysis are provided. Numerical experiments are conducted to illustrate the effectiveness and efficiency of the proposed method in both two and three dimensions.

Original language	English
Article number	035001
Journal	Inverse Problems
Volume	33
Issue number	3
DOIs	https://doi.org/10.1088/1361-6420/aa573c
Publication status	Published - 1 Feb 2017
Externally published	Yes

Research Keywords

far-field
Fourier expansion
Helmholtz equation
inverse source problem
multi-frequency

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10.1088/1361-6420/aa573c

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title = "Fourier method for recovering acoustic sources from multi-frequency far-field data",

abstract = "We consider an inverse source problem of determining a source term in the Helmholtz equation from multi-frequency far-field measurements. Based on the Fourier series expansion, we develop a novel non-iterative reconstruction method for solving the problem. A promising feature of this method is that it utilizes the data from only a few observation directions for each frequency. Theoretical uniqueness and stability analysis are provided. Numerical experiments are conducted to illustrate the effectiveness and efficiency of the proposed method in both two and three dimensions.",

keywords = "far-field, Fourier expansion, Helmholtz equation, inverse source problem, multi-frequency",

author = "Xianchao Wang and Yukun Guo and Deyue Zhang and Hongyu Liu",

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T1 - Fourier method for recovering acoustic sources from multi-frequency far-field data

AU - Wang, Xianchao

AU - Guo, Yukun

AU - Zhang, Deyue

AU - Liu, Hongyu

PY - 2017/2/1

Y1 - 2017/2/1

N2 - We consider an inverse source problem of determining a source term in the Helmholtz equation from multi-frequency far-field measurements. Based on the Fourier series expansion, we develop a novel non-iterative reconstruction method for solving the problem. A promising feature of this method is that it utilizes the data from only a few observation directions for each frequency. Theoretical uniqueness and stability analysis are provided. Numerical experiments are conducted to illustrate the effectiveness and efficiency of the proposed method in both two and three dimensions.

AB - We consider an inverse source problem of determining a source term in the Helmholtz equation from multi-frequency far-field measurements. Based on the Fourier series expansion, we develop a novel non-iterative reconstruction method for solving the problem. A promising feature of this method is that it utilizes the data from only a few observation directions for each frequency. Theoretical uniqueness and stability analysis are provided. Numerical experiments are conducted to illustrate the effectiveness and efficiency of the proposed method in both two and three dimensions.

KW - far-field

KW - Fourier expansion

KW - Helmholtz equation

KW - inverse source problem

KW - multi-frequency

UR - http://www.scopus.com/inward/record.url?scp=85014664993&partnerID=8YFLogxK

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85014664993&origin=recordpage

U2 - 10.1088/1361-6420/aa573c

DO - 10.1088/1361-6420/aa573c

M3 - RGC 21 - Publication in refereed journal

SN - 0266-5611

VL - 33

JO - Inverse Problems

JF - Inverse Problems

IS - 3

M1 - 035001

ER -

Fourier method for recovering acoustic sources from multi-frequency far-field data

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Research Keywords

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