Identifying multipolar acoustic sources by the direct sampling method

Bousba, Sara; Guo, Yukun; Wang, Xianchao; Li, Longsuo

doi:10.1080/00036811.2018.1514019

Cited by 14 publications

(14 citation statements)

References 25 publications

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“…Recently, some non-iterative methods have been proposed. In particular, [36,37] studied a Fourier method to reconstruct the source function and [11,38] investigated the direct sampling methods for identifying the point sources. One practical situation involves sparse measurements, i.e.…”

Section: Introductionmentioning

confidence: 99%

A multi-frequency sampling method for the inverse source problems with sparse measurements

Liu¹,

Meng²

2021

Preprint

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We consider the inverse source problems with multi-frequency sparse near field measurements. In contrast to the existing near field operator based on the integral over the space variable, a multi-frequency near field operator is introduced based on the integral over the frequency variable. A factorization of this multi-frequency near field operator is further given and analysed. Motivated by such a factorization, we introduce a multi-frequency sampling method to reconstruct the source support. Its theoretical foundation is then derived from the properties of the factorized operators and a properly chosen point spread function. Numerical examples are provided to illustrate the multi-frequency sampling method with sparse near field measurements. Finally we briefly discuss how to extend the near field case to the far field case.

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Section: Introductionmentioning

confidence: 99%

A multi-frequency sampling method for the inverse source problems with sparse measurements

Liu¹,

Meng²

2021

Preprint

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“…Zhang et al [30] used the direct sampling method to locate multipolar acoustic sources for the Helmholtz equation from near-field Cauchy data. Bousba et al [7] utilized the direct sampling method to identify point sources for the Helmholtz equation from far-field data. The algebraic method has also been applied to the Helmholtz equation for determining monopolar sources [3].…”

Section: Introductionmentioning

confidence: 99%

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

Yan¹,

Guo²

2021

Preprint

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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 indicating behaviors of the indicator functions. Several numerical examples are presented to show the effectiveness of the proposed method.

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“…To our best knowledge, this is the first sampling scheme to reconstruct multiple moment tensor point sources from time-harmonic elastic measurements. Interested readers could refer to [1,13,16,26] for some theoretical and computational results on recovering multiple point sources for the Poisson equation, the Helmholtz equation and the Maxwell system.…”

Section: Introductionmentioning

confidence: 99%

Direct imaging for the moment tensor point sources of elastic waves

Wang,

Guo,

Bousba

2021

Preprint

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We investigate an inverse source problem of the time-harmonic elastic wave equation. Some novel sampling-type numerical schemes are proposed to identify the moment tensor point sources in the Lamé system from near-field measurements. Rigorous theoretical justifications are provided to show that the locations and moment tensors of the elastic sources can be uniquely determined from the multi-frequency displacement data.Several numerical examples are also presented to illustrate the validity and robustness of the proposed method.

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Identifying multipolar acoustic sources by the direct sampling method

Cited by 14 publications

References 25 publications

A multi-frequency sampling method for the inverse source problems with sparse measurements

A multi-frequency sampling method for the inverse source problems with sparse measurements

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

Direct imaging for the moment tensor point sources of elastic waves

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