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

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

54 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

Scopus Subject Areas

Theoretical Computer Science
Signal Processing
Mathematical Physics
Computer Science Applications
Applied Mathematics

User-Defined Keywords

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

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10.1088/1361-6420/aa573c

Cite this

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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",

note = "Funding Information: The work of X Wang was supported by the NSFC grant under No. 11671113. The work of Y Guo was supported by the NSFC grants under Nos. 11671111, 11601107 and 41474102. The work of D Zhang was supported by the NSFC grants under No. 11671170. The work of H Liu was supported by the FRG grants from Hong Kong Baptist University, Hong Kong RGC General Research Funds, No. 12302415, and the NSFC grant under No. 11371115.",

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doi = "10.1088/1361-6420/aa573c",

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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

N1 - Funding Information: The work of X Wang was supported by the NSFC grant under No. 11671113. The work of Y Guo was supported by the NSFC grants under Nos. 11671111, 11601107 and 41474102. The work of D Zhang was supported by the NSFC grants under No. 11671170. The work of H Liu was supported by the FRG grants from Hong Kong Baptist University, Hong Kong RGC General Research Funds, No. 12302415, and the NSFC grant under No. 11371115.

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

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U2 - 10.1088/1361-6420/aa573c

DO - 10.1088/1361-6420/aa573c

M3 - Journal article

AN - SCOPUS:85014664993

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

Abstract

Scopus Subject Areas

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