Monotonicity in inverse scattering for Maxwell's equations

DOI10.3934/ipi.2022032OpenAlexW4285132693MaRDI QIDQ2697351

Annalena Albicker, Roland Griesmaier

Publication date: 18 April 2023

Published in: Inverse Problems and Imaging (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/ipi.2022032

zbMATH Keywords

Maxwell's equationsinhomogeneous mediuminverse scatteringmonotonicity principlesfar field operator

Mathematics Subject Classification ID

Inverse problems for PDEs (35R30) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21) Inverse problems (including inverse scattering) in optics and electromagnetic theory (78A46) Maxwell equations (35Q61)

Related Items (2)

Imaging of nonlinear materials via the Monotonicity Principle ⋮ Monotonicity-based shape reconstruction for an inverse scattering problem in a waveguide

Cites Work

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• Convergence and regularization for monotonicity-based shape reconstruction in electrical impedance tomography
• Spherical harmonics and approximations on the unit sphere. An introduction
• The regularized monotonicity method: detecting irregular indefinite inclusions
• The mathematical theory of time-harmonic Maxwell's equations. Expansion-, integral-, and variational methods
• Localized potentials in electrical impedance tomography
• The factorization method for obstacles with a-priori separated sound-soft and sound-hard parts
• Monotonicity and local uniqueness for the Helmholtz equation
• An integral equation for Maxwell's equations in a layered medium with an application to the factorization method
• The factorization and monotonicity method for the defect in an open periodic waveguide
• On the regularity of characteristic functions
• Difference Factorizations and Monotonicity in Inverse Medium Scattering for Contrasts with Fixed Sign on the Boundary
• Inverse Scattering Theory and Transmission Eigenvalues
• Enhancing residual-based techniques with shape reconstruction features in electrical impedance tomography
• The Linear Sampling Method in Inverse Electromagnetic Scattering
• The factorization method for EIT in the case of mixed inclusions
• Regularity theorems for Maxwell's equations
• Size estimation of inclusion
• The Inverse Conductivity Problem with One Measurement: Stability and Estimation of Size
• The linear sampling method for solving the electromagnetic inverse medium problem
• Monotonicity-Based Regularization for Phantom Experiment Data in Electrical Impedance Tomography
• Comparison of linear and non-linear monotonicity-based shape reconstruction using exact matrix characterizations
• Uncertainty principles for inverse source problems for electromagnetic and elastic waves
• Detecting stochastic inclusions in electrical impedance tomography
• Monotonicity based imaging method for time-domain eddy current problems
• Monotonicity and Enclosure Methods for the $p$-Laplace Equation
• ON UNIQUENESS FOR TIME HARMONIC ANISOTROPIC MAXWELL'S EQUATIONS WITH PIECEWISE REGULAR COEFFICIENTS
• On Localizing and Concentrating Electromagnetic Fields
• Monotonicity in Inverse Medium Scattering on Unbounded Domains
• Finite Element Methods for Maxwell's Equations
• Obstacle visualization via the factorization method for the mixed boundary value problem
• A new non-iterative inversion method for electrical resistance tomography
• Remarks on the factorization and monotonicity method for inverse acoustic scatterings
• Erratum: Monotonicity in Inverse Medium Scattering on Unbounded Domains
• The monotonicity principle for magnetic induction tomography
• Monotonicity in inverse obstacle scattering on unbounded domains
• Monotonicity-Based Reconstruction of Extreme Inclusions in Electrical Impedance Tomography
• Monotonicity-Based Inversion of the Fractional Schrödinger Equation II. General Potentials and Stability
• Dimension Bounds in Monotonicity Methods for the Helmholtz Equation
• Monotonicity-based Inversion of the Fractional Schrödinger Equation I. Positive Potentials
• Inverse Acoustic and Electromagnetic Scattering Theory
• Inside–outside duality with artificial backgrounds
• Inside-Outside Duality and the Determination of Electromagnetic Interior Transmission Eigenvalues
• Solving Boundary Integral Problems with BEM++
• Monotonicity-Based Shape Reconstruction in Electrical Impedance Tomography
• The inside–outside duality for scattering problems by inhomogeneous media
• The factorization method for Maxwell's equations
• Qualitative Indicator Functions for Imaging Crack Networks Using Acoustic Waves
• Monotonicity Principle in tomography of nonlinear conducting materials ^*

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