Sampling methods for reconstructing the geometry of a local perturbation in unknown periodic layers

DOI10.1016/j.camwa.2017.07.015zbMath1398.35225OpenAlexW2744315984MaRDI QIDQ1672638

Houssem Haddar, Thi-Phong Nguyen

Publication date: 11 September 2018

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://hal.inria.fr/hal-01645674/file/InversePb.pdf

zbMATH Keywords

factorization methodlinear sampling methodinverse scattering problemsperiodic layersFloquet-Bloch transform

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) Periodic solutions to PDEs (35B10) Scattering theory for PDEs (35P25) Diffraction, scattering (78A45) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Composite media; random media in optics and electromagnetic theory (78A48) Inverse problems (including inverse scattering) in optics and electromagnetic theory (78A46)

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Cites Work

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• Identifying defects in an unknown background using differential measurements
• Inverse scattering of elastic waves by periodic structures: uniqueness under the third or fourth kind boundary conditions
• Qualitative methods in inverse scattering theory. An introduction
• The factorization method is independent of transmission eigenvalues
• The factorization method applied to cracks with impedance boundary conditions
• A complete factorization method for scattering by periodic surfaces
• Inverse Scattering Theory and Transmission Eigenvalues
• Numerical analysis of the factorization method for EIT with a piecewise constant uncertain background
• Reconstruction of obstacles embedded in waveguides
• Factorization Method for Electromagnetic Inverse Scattering from Biperiodic Structures
• Discreteness of Transmission Eigenvalues via Upper Triangular Compact Operators
• On the identification of defects in a periodic waveguide from far field data
• The factorization method in inverse elastic scattering from penetrable bodies
• The Factorization Method for Electrical Impedance Tomography in the Half-Space
• The Factorization Method Applied to the Complete Electrode Model of Impedance Tomography
• MUSIC for Extended Scatterers as an Instance of the Factorization Method
• Characterization of the shape of a scattering obstacle using the spectral data of the far field operator
• Factorization of the far-field operator for the inhomogeneous medium case and an application in inverse scattering theory
• A simple method using Morozov's discrepancy principle for solving inverse scattering problems
• The factorization method in inverse scattering from periodic structures
• On the use of the linear sampling method to identify cracks in elastic waveguides
• On the existence of transmission eigenvalues in an inhomogeneous medium
• A sampling method for the inverse transmission problem for periodic media
• Transmission eigenvalues
• The factorization method for inverse elastic scattering from periodic structures
• A generalized formulation of the linear sampling method with exact characterization of targets in terms of farfield measurements
• Factorization method and irregular inclusions in electrical impedance tomography
• Inverse acoustic and electromagnetic scattering theory

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