Shape Reconstruction in Inverse Scattering by an Inhomogeneous Cavity with Internal Measurements

Qu, Fenglong; Yang, Jiaqing; Zhang, Haiwen

doi:10.1137/18m1232401

Cited by 16 publications

(8 citation statements)

References 30 publications

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“…[5, 10, 11, 16-18, 25, 29] and the references therein). Recently, based on a technique of the detailed description of the kernel space of the related solution operator, the factorization method has been justified in [26] for the inverse problem of reconstructing the interior interface of a two-layered cavity in the case when the solution is discontinuous across the interior interface, that is, u|…”

Section: Introductionmentioning

confidence: 99%

Near-Field Imaging of an Inhomogeneous Cavity with a Modified Factorization Method

Cui,

2024

JCM

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This paper is concerned with the inverse problem of scattering of time-harmonic acoustic waves by an inhomogeneous cavity. We shall develop a modified factorization method to reconstruct the shape and location of the interior interface of the inhomogeneous cavity by means of many internal measurements of the near-field data. Numerical examples are carried out to illustrate the practicability of the inversion algorithm.

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Section: Introductionmentioning

confidence: 99%

Near-Field Imaging of an Inhomogeneous Cavity with a Modified Factorization Method

Cui,

2024

JCM

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“…For a survey of these methods we refer to [7,11,16]. There have been recent interests in the inverse scattering problem for cavities using measurements inside [15,20,21,[24][25][26]28]. Such inverse scattering problems have potential applications in monitoring the structural integrity of the fusion reactor.…”

Section: Introductionmentioning

confidence: 99%

The interior inverse electromagnetic scattering for an inhomogeneous cavity

Zeng

Meng

2021

Inverse Problems

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In this paper we consider the inverse electromagnetic scattering for a cavity surrounded by an inhomogeneous medium in three dimensions. The measurements are scattered wave fields measured on some surface inside the cavity, where such scattered wave fields are due to sources emitted on the same surface. We first prove that the measurements uniquely determine the shape of the cavity, where we make use of a boundary value problem called the exterior transmission problem. We then complete the inverse scattering problem by designing the linear sampling method to reconstruct the cavity. Numerical examples are further provided to illustrate the viability of our algorithm.

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“…In this paper we intend to develop a novel method, which differs from the approach used in [34], to prove the uniqueness on the identification of the penetrable periodic structure in the three-dimensional space from the measured data only above the structure with respect to a countably infinite number of quasiperiodic incident plane waves. The technique developed in this paper can date back to the work [27,36] on the inverse scattering problems of determining the support of penetrable electromagnetic obstacles or to [28] for the fluid-solid interaction problem of identifying the bounded solid obstacle, [29] for the cavity scattering case.…”

Section: Introductionmentioning

confidence: 99%

A novel method in determining a layered periodic structure

Cui

2020

Bound Value Probl

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This paper is concerned with the inverse scattering of time-harmonic waves by a penetrable structure. By applying the integral equation method, we establish the uniform $L^{p}_{\alpha }\ (1< p\leq 2)$ L α p ( 1 < p ≤ 2 ) estimates for the scattered and transmitted wave fields corresponding to a series of incident point sources. Based on these a priori estimates and a mixed reciprocity relation, we prove that the penetrable structure can be uniquely identified by means of the scattered field measured only above the structure induced by a countably infinite number of quasi-periodic incident plane waves.

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Shape Reconstruction in Inverse Scattering by an Inhomogeneous Cavity with Internal Measurements

Cited by 16 publications

References 30 publications

Near-Field Imaging of an Inhomogeneous Cavity with a Modified Factorization Method

Near-Field Imaging of an Inhomogeneous Cavity with a Modified Factorization Method

The interior inverse electromagnetic scattering for an inhomogeneous cavity

A novel method in determining a layered periodic structure

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