A reference ball based iterative algorithm for imaging acoustic obstacle from phaseless far-field data

Dong, Heping; Zhang, Deyue; Guo, Yukun

doi:10.3934/ipi.2019010

Cited by 39 publications

(36 citation statements)

References 27 publications

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“…where the scaling factor ρ ≥ 0 is fixed throughout the iterations. Analogously to [9], the regularization parameter λ in (6.7) is chosen as…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…Related phaseless inverse scattering problems as well as numerical methods can be found in [1, 3-5, 18, 24, 31, 42]. Recently, a reference ball technique based nonlinear integral equations method was proposed in [9] to break the translation invariance from phaseless far-field data by one incident plane wave. In our recent work [8], we extended this method to the inverse elastic scattering problem with phaseless far-field data by using a single incident plane wave to recover both the location and shape of a rigid elastic obstacle.…”

Section: Introductionmentioning

confidence: 99%

“…For the inverse problem, motivated by the reference ball technique [32,41] and the recent work [8,9], we give a uniqueness result for the phaseless IAEIP by introducing an elastic reference ball, and also propose a nonlinear integral equations based iterative numerical scheme to solve the phased and phaseless IAEIP. Since the location of reference ball is known, the method breaks the translation invariance and is able to recover the location information of the obstacle with negligible additional computational costs.…”

Section: Introductionmentioning

confidence: 99%

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An inverse acoustic-elastic interaction problem with phased or phaseless far-field data

Dong

Lai

2020

Inverse Problems

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Consider the scattering of a time-harmonic acoustic plane wave by a bounded elastic obstacle which is immersed in a homogeneous acoustic medium. This paper concerns an inverse acoustic-elastic interaction problem, which is to determine the location and shape of the elastic obstacle by using either the phased or phaseless far-field data. By introducing the Helmholtz decomposition, the model problem is reduced to a coupled boundary value problem of the Helmholtz equations. The jump relations are studied for the second derivatives of the single-layer potential in order to establish the corresponding boundary integral equations. The well-posedness is discussed for the solution of the coupled boundary integral equations. An efficient and high order Nyström-type discretization method is proposed for the integral system. A numerical method of nonlinear integral equations is developed for the inverse problem. For the case of phaseless data, we show that the modulus of the far-field pattern is invariant under a translation of the obstacle. To break the translation invariance, an elastic reference ball technique is introduced. We prove that the inverse problem with phaseless far-field pattern has a unique solution under certain conditions. In addition, a numerical method of the reference ball technique based nonlinear integral equations is also proposed for the phaseless inverse problem. Numerical experiments are provided to demonstrate the effectiveness and robustness of the proposed methods.2010 Mathematics Subject Classification. 78A46, 65N21.

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“…where the scaling factor ρ ≥ 0 is fixed throughout the iterations. Analogously to [9], the regularization parameter λ in (6.7) is chosen as…”

Section: Numerical Experimentsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

An inverse acoustic-elastic interaction problem with phased or phaseless far-field data

Dong

Lai

2020

Inverse Problems

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“…The reference ball technique was used in [47] to alleviate the requirement of the a priori assumptions in [46]. Similar strategies of adding reference objects or sources to the scattering system have also been extensively applied to the theoretical analysis and numerical approaches for different models of phaseless inverse scattering problems [13,14,19,20,21,53]. In the absence of any additional reference object, the uniqueness can be established by the superposition of incident point sources and phaseless far-field data, see [43].…”

Section: Introductionmentioning

confidence: 99%

Uniqueness in inverse cavity scattering problems with phaseless near-field data

et al. 2020

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This paper is devoted to the uniqueness of inverse acoustic scattering problems with the modulus of near-field data. By utilizing the superpositions of point sources as the incident waves, we rigorously prove that the phaseless near-fields collected on an admissible surface can uniquely determine the location and shape of the obstacle as well as its boundary condition and the refractive index of a medium inclusion, respectively. We also establish the uniqueness in determining a locally rough surface from the phaseless near-field data due to superpositions of point sources. These are novel uniqueness results in inverse scattering with phaseless near-field data.

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“…Zhang et al [26] developed a reference point source strategy to recovered the radiated near fields via adding extra artificial sources to the inverse source system. Several numerical methods for the inverse scattering from phaseless data can be found in [1,12,14,17,26].…”

Section: Introductionmentioning

confidence: 99%

Retrieval of acoustic sources from multi-frequency phaseless data

Zhang

Guo

et al. 2018

Inverse Problems

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We consider the inverse source problem of determining an acoustic source from multi-frequency phaseless far-field data. By supplementing some reference point sources to the inverse source model, we develop a novel strategy for recovering the phase information of far-field data. This reference source technique leads to an easy-to-implement phase retrieval formula. Mathematically, the stability of the phase retrieval approach is rigorously justified. Then we employ the Fourier method to deal with the multi-frequency inverse source problem with recovered phase information. Finally, some two and three dimensional numerical results are presented to demonstrate the viability and effectiveness of the proposed method.

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A reference ball based iterative algorithm for imaging acoustic obstacle from phaseless far-field data

Cited by 39 publications

References 27 publications

An inverse acoustic-elastic interaction problem with phased or phaseless far-field data

An inverse acoustic-elastic interaction problem with phased or phaseless far-field data

Uniqueness in inverse cavity scattering problems with phaseless near-field data

Retrieval of acoustic sources from multi-frequency phaseless data

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