An eigenvalue method using multiple frequency data for inverse scattering problems

Sun, Jiguang

doi:10.1088/0266-5611/28/2/025012

Cited by 32 publications

(40 citation statements)

References 27 publications

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“…In addition, in order to improve the image quality obtained from LSM, recently, the hybridization combining LSM and quantitative methods was proposed to solve inverse scattering problems [32][33][34][35]. Here, we present a multi-frequency hybrid technique to reconstruct unknown object images with enhanced resolution.…”

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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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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“…In literature [16] and [17], this behavior was called an "eigenvalue problem" while corresponding β and frequencies were called eigenvalue and resonant frequencies [28], respectively. Fig.…”

Section: A Pecmentioning

confidence: 99%

“…In order to pursue this task, it is required to know the characteristic nature of LSM for reconstructing the dielectric and PEC objects. In [16] and [17], the behavior of LSM for these objects is discussed as a function of operating frequency. However, the behavior with respect to the properties of objects (i.e., dimension and permittivity) has not been reported.…”

Section: Introductionmentioning

confidence: 99%

Shape Reconstruction of Mixed Boundary Objects by Linear Sampling Method

Erramshetty

Bhattacharya

2015

IEEE Trans. Antennas Propagat.

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Geometric reconstruction of dielectric objects in the presence of a perfect electric conducting (PEC) object is investigated with the application of linear sampling method (LSM). The scattered fields from the cylindrical objects of circular cross sections are represented as a multipole expansion, and a numerical analysis is carried out to explore the behavior and limitations of LSM. By considering various numerical examples, the imaging capabilities of LSM for mixed cases (both dielectric and PEC objects) are studied in terms of frequency of operation and permittivity of dielectric objects. To overcome the drawbacks of standard LSM indicator, a modified LSM indicator based on a multifrequency approach is introduced. Apart from the synthetic data, the analysis is also validated by the experimental data provided by the Fresnel Institute.Index Terms-Linear sampling method (LSM), mixed boundary problem, multipole expansion, reconstruction.

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“…Only minor changes are necessary in the subsequent iterations. Multiple frequency data are used to obtain a better reconstruction (see, e.g., [2,16,19]). …”

Section: Introductionmentioning

confidence: 99%

The Reconstruction of Obstacles in a Waveguide Using Finite Elements

Sun¹

2018

JCM

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This paper concerns the reconstruction of a penetrable obstacle embedded in a waveguide using the scattered data due to point sources, which is formulated as an optimization problem. We propose a fast reconstruction method based on a carefully designed finite element scheme for the direct scattering problem. The method has several merits: 1) the linear sampling method is used to quickly obtain a good initial guess; 2) finite Fourier series are used to approximate the boundary of the obstacle, which is decoupled from the boundary used by the finite element method; and 3) the mesh is fixed and hence the stiffness matrix, mass matrix, and right hand side are assembled once and only minor changes are made at each iteration. The effectiveness of the proposed method is demonstrated by numerical examples.Mathematics subject classification: 78A46, 65M32, 65M60.

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An eigenvalue method using multiple frequency data for inverse scattering problems

Cited by 32 publications

References 27 publications

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

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

Shape Reconstruction of Mixed Boundary Objects by Linear Sampling Method

The Reconstruction of Obstacles in a Waveguide Using Finite Elements

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