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

Yan Chang; Yukun Guo; Yan Chang; Yukun Guo

doi:10.3934/era.2022068

Electronic Research Archive

2022, Volume 30, Issue 4: 1296-1321. doi: 10.3934/era.2022068

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

Yan Chang ,
Yukun Guo ^,

School of Mathematics, Harbin Institute of Technology, Harbin, China

Received: 19 December 2021 Revised: 17 February 2022 Accepted: 07 March 2022 Published: 17 March 2022

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. Several numerical examples are presented to show the effectiveness of the proposed method.
- inverse scattering,
- inverse source problem,
- near field,
- optimization method,
- direct sampling,
- reverse time migration
Citation: Yan Chang, Yukun Guo. Simultaneous recovery of an obstacle and its excitation sources from near-field scattering data[J]. Electronic Research Archive, 2022, 30(4): 1296-1321. doi: 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. Several numerical examples are presented to show the effectiveness of the proposed method.

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