Muti-frequency extended sampling method for the inverse acoustic source problem

Jiyu Sun; Jitao Zhang; Jiyu Sun; Jitao Zhang

doi:10.3934/era.2023214

Electronic Research Archive

2023, Volume 31, Issue 7: 4216-4231. doi: 10.3934/era.2023214

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Research article

Muti-frequency extended sampling method for the inverse acoustic source problem

Jiyu Sun ^,,
Jitao Zhang

School of Measurement-Control Technology and Communications Engineering, Harbin University of Science and Technology, Harbin 150080, China

Received: 18 April 2023 Revised: 15 May 2023 Accepted: 28 May 2023 Published: 01 June 2023

We consider the reconstruction of the compact support of an acoustic source given multiple frequency far field data. We propose a multi-frequency extended sampling method (MESM). The MESM computes the solutions of some ill-posed integral equations and constructs an indicator function to image the source. The behavior of the indicator function is justified. The method is fast and easy to implement. Various numerical examples are presented to show the effectiveness of the MESM for both frequency-independent and frequency-dependent sources.
- inverse source problem,
- extended sampling method,
- multiple frequency data
Citation: Jiyu Sun, Jitao Zhang. Muti-frequency extended sampling method for the inverse acoustic source problem[J]. Electronic Research Archive, 2023, 31(7): 4216-4231. doi: 10.3934/era.2023214

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Abstract

We consider the reconstruction of the compact support of an acoustic source given multiple frequency far field data. We propose a multi-frequency extended sampling method (MESM). The MESM computes the solutions of some ill-posed integral equations and constructs an indicator function to image the source. The behavior of the indicator function is justified. The method is fast and easy to implement. Various numerical examples are presented to show the effectiveness of the MESM for both frequency-independent and frequency-dependent sources.

References

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