Toward a time domain approach to the linear sampling method

Guo, Yukun; Monk, Peter; Colton, David

doi:10.1088/0266-5611/29/9/095016

Cited by 46 publications

(58 citation statements)

References 14 publications

(22 reference statements)

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“…The Nyström method is used for the spatial discretization of the Helmholtz problems. Then, with the boundary data ψ + n ( · ), the scattered data u s + can be obtained from Equation (19).…”

Section: Downloaded By [University Of Bath] At 05:40 21 June 2016mentioning

confidence: 99%

“…In recent years, the time domain version of LSM has been successfully applied to the time-dependent inverse scattering problems of recovering bounded objects. [5,19,20] However, to the best of our knowledge, there is no attempt to apply the LSM to the time domain inverse scattering problems of determinating unbounded scatterers. Therefore, we aim to investigate the feasibility of the time domain LSM for the inverse scattering problem in a locally perturbed half-plane.…”

Section: Introductionmentioning

confidence: 99%

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Time domain scattering and inverse scattering problems in a locally perturbed half-plane

Chen

Guo

2016

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This paper is concerned with efficient numerical methods for solving the time-dependent scattering and inverse scattering problems of acoustic waves in a locally perturbed half-plane. By symmetric continuation, the scattering problem is reformulated as an equivalent symmetric problem defined in the whole plane. The retarded potential boundary integral equation method is modified to solve the forward problem. Then we consider the inverse scattering problem of determinating the local perturbation from the measured scattered data. The time domain linear sampling method is employed to deal with the inverse problem. The computation schemes proposed in this paper are relatively simple and easy to implement. Several numerical examples are presented to show the effectiveness of the proposed methods. ARTICLE HISTORY

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Section: Downloaded By [University Of Bath] At 05:40 21 June 2016mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Time domain scattering and inverse scattering problems in a locally perturbed half-plane

Chen

Guo

2016

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“…Here, we present a multi-frequency hybrid technique to reconstruct unknown object images with enhanced resolution. Although some approaches related to multi-frequency LSM have been studied [36,37], the hybrid method presented in this paper will provide a more feasible and efficient way to reconstruct targets with complex geometries than the previous works. On top of this, polarization diversity is introduced into the hybrid method to improve the reconstruction stability with respect to variances of regularization parameters.…”

Section: Introductionmentioning

confidence: 99%

Frequency and Polarization-Diversified Linear Sampling Methods for Microwave Tomography and Remote Sensing Using Electromagnetic Metamaterials

et al. 2017

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Metamaterial leaky wave antennas (MTM-LWAs), one kind of frequency scanning antennas, exhibit frequency-space mapping characteristics that can be utilized to obtain a sufficient field of view (FOV) and reconstruct shapes in both remote sensing and microwave imaging. In this article, we utilize MTM-LWAs to conduct a spectrally encoded three-dimensional (3D) microwave tomography and remote sensing that can reconstruct conductive targets with various dimensions. In this novel imaging technique, we employ the linear sampling method (LSM) as a powerful and fast reconstruction approach. Unlike the traditional LSM using only one single frequency to illuminate a fixed direction, the proposed method utilizes a frequency scanning MTM antenna array able to accomplish frequency-space mapping over the targeted 3D background that includes unknown objects. In addition, a novel technique based on a frequency and polarization hybrid method is proposed to improve the shape reconstruction resolution and stability in ill-posed inverse problems. Both simulation and experimental results demonstrate the unique advantages of the proposed LSM using MTM-LWAs with frequency and polarization diversity as an efficient 3D remote sensing and tomography scheme.

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“…We can combine a quadrature method and a collocation method based on trigonometric interpolation to achieve this. [34] Then we obtain a matrix equation like Ah y = b y from the discretization of operator Equation (26). In order to Downloaded by [University of Nebraska, Lincoln] at 05:51 30 December 2015…”

Section: A Remark On Numerical Solution To Our Inverse Problemmentioning

confidence: 99%

“…Recently, the linear sampling method in the time domain has been developed to solve inverse scattering problems for recovering penetrable or impenetrable obstacles. [24][25][26] A drawback of the frequency domain linear sampling method is the large amount of data required for the implementation and failure for small aperture data-sets. To a certain extent, by going to time domain, the limitation can be alleviated.…”

Section: Introductionmentioning

confidence: 99%

The direct and inverse problem for an inclusion within a heat-conducting layered medium

Guo

Yan

Zhou

2015

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This paper is concerned with the problem of heat conduction from an inclusion in a heat transfer layered medium. Making use of the boundary integral equation method, the well-posedness of the forward problem is established by the Fredholm theory. Then an inverse boundary value problem, i.e. identifying the inclusion from the measurements of the temperature and heat flux on the accessible exterior boundary of the medium is considered in the framework of the linear sampling method. Based on a careful analysis of the Dirichlet-to-Neumann map, the mathematical fundamentals of the linear sampling method for reconstructing the inclusion are proved rigorously. ARTICLE HISTORY

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Toward a time domain approach to the linear sampling method

Cited by 46 publications

References 14 publications

Time domain scattering and inverse scattering problems in a locally perturbed half-plane

Time domain scattering and inverse scattering problems in a locally perturbed half-plane

Frequency and Polarization-Diversified Linear Sampling Methods for Microwave Tomography and Remote Sensing Using Electromagnetic Metamaterials

The direct and inverse problem for an inclusion within a heat-conducting layered medium

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