Shape reconstruction of the multi-scale rough surface from multi-frequency phaseless data

Bao, Gang; Zhang, Lei

doi:10.1088/0266-5611/32/8/085002

Cited by 54 publications

(37 citation statements)

References 45 publications

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“…The mathematical analysis can be found in [10,11,18,22,32] and [13,20,23] on the well-posedness of the two-dimensional Helmholtz equation and the three-dimensional Maxwell equations, respectively. The inverse problems have also been considered mathematically and computationally for unbounded rough surfaces in [1,2,3,24].…”

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confidence: 99%

Inverse obstacle scattering for Maxwell’s equations in an unbounded structure

Wang

Zhang

2019

Inverse Problems

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This paper is concerned with analysis of electromagnetic wave scattering by an obstacle which is embedded in a two-layered lossy medium separated by an unbounded rough surface. Given a dipole point source, the direct problem is to determine the electromagnetic wave field for the given obstacle and unbounded rough surface; the inverse problem is to reconstruct simultaneously the obstacle and unbounded rough surface from the electromagnetic field measured on a plane surface above the obstacle. For the direct problem, a new boundary integral equation is proposed and its well-posedness is established. The analysis is based on the exponential decay of the dyadic Green function for Maxwell's equations in a lossy medium. For the inverse problem, the global uniqueness is proved and a local stability is discussed. A crucial step in the proof of the stability is to obtain the existence and characterization of the domain derivative of the electric field with respect to the shape of the obstacle and unbounded rough surface. , J j denote the electric field, the magnetic field, the electric current density, respectively, and ρ j = (iω) −1 ∇ · J j is the electric charge density. The external current source is assumed to be located in Ω 1 . The relation between the electric current density and the electric field is given bywhere J cs stands for the current source.

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Inverse obstacle scattering for Maxwell’s equations in an unbounded structure

Wang

Zhang

2019

Inverse Problems

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“…A continuation method [3] is developed to reconstruct the periodic grating profile from phaseless scattered data. In [2], a recursive linearization algorithm is proposed to image the multi-scale rough surface with tapered incident waves from measurements of the multi-frequency phaseless scattered data. In [24], an iterative method based on Rayleigh expansion is developed to solve the inverse diffraction grating problem with super-resolution by using phase or phaseless near-field data.…”

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confidence: 99%

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

Dong¹,

Zhang²,

Guo³

2019

Inverse Problems &Amp; Imaging

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In this paper, we consider the inverse problem of determining the location and the shape of a sound-soft obstacle from the modulus of the far-field data for a single incident plane wave. By adding a reference ball artificially to the inverse scattering system, we propose a system of nonlinear integral equations based iterative scheme to reconstruct both the location and the shape of the obstacle. The reference ball technique causes few extra computational costs, but breaks the translation invariance and brings information about the location of the obstacle. Several validating numerical examples are provided to illustrate the effectiveness and robustness of the proposed inversion algorithm.

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“…Our experimental data were collected for the case of the vertically propagated white light. To obtain data on an interval of frequencies, the light was filtered on six (6) wavelengths ranging from 0.420µm to 0.671µm. Following, e.g., [63], to measure the light intensity, we have used the detector array which is available in the camera of the Samsung Galaxy S3 mobile telephone unit.…”

Section: Introductionmentioning

confidence: 99%

A Numerical Method to Solve a Phaseless Coefficient Inverse Problem from a Single Measurement of Experimental Data

Klibanov¹,

Koshev²,

Nguyen³

et al. 2018

SIAM J. Imaging Sci.

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We propose in this paper a globally numerical method to solve a phaseless coefficient inverse problem: how to reconstruct the spatially distributed refractive index of scatterers from the intensity (modulus square) of the full complex valued wave field at an array of light detectors located on a measurement board. The propagation of the wave field is governed by the 3D Helmholtz equation. Our method consists of two stages. On the first stage, we use asymptotic analysis to obtain an upper estimate for the modulus of the scattered wave field. This estimate allows us to approximately reconstruct the wave field at the measurement board using an inversion formula. This reduces the phaseless inverse scattering problem to the phased one. At the second stage, we apply a recently developed globally convergent numerical method to reconstruct the desired refractive index from the total wave obtained at the first stage. Unlike the optimization approach, the two-stage method described above is global in the sense that it does not require a good initial guess of the true solution. We test our numerical method on both computationally simulated and experimental data. Although experimental data are noisy, our method produces quite accurate numerical results.

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Shape reconstruction of the multi-scale rough surface from multi-frequency phaseless data

Cited by 54 publications

References 45 publications

Inverse obstacle scattering for Maxwell’s equations in an unbounded structure

Inverse obstacle scattering for Maxwell’s equations in an unbounded structure

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

A Numerical Method to Solve a Phaseless Coefficient Inverse Problem from a Single Measurement of Experimental Data

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