Monotonicity-Based Reconstruction of Extreme Inclusions in Electrical Impedance Tomography
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Publication:5141939
DOI10.1137/19M1299219zbMath1455.35298arXiv1909.12110OpenAlexW3110876844MaRDI QIDQ5141939
Valentina Candiani, Henrik Garde, Nuutti Hyvönen, Jérémi Dardé
Publication date: 29 December 2020
Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1909.12110
perfectly conducting inclusionsmonotonicity principles for Neumann-to-Dirichlet boundary mapsperfectly insulating inclusions
Monotone operators and generalizations (47H05) Inverse problems for PDEs (35R30) PDEs with low regular coefficients and/or low regular data (35R05)
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Cites Work
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- Convergence and regularization for monotonicity-based shape reconstruction in electrical impedance tomography
- The regularized monotonicity method: detecting irregular indefinite inclusions
- The method of fundamental solutions for detection of cavities in EIT
- Localized potentials in electrical impedance tomography
- Superconductive and insulating inclusions for linear and non-linear conductivity equations
- Identification of small inhomogeneities of extreme conductivity by boundary measurements: A theorem on continuous dependence
- Recent progress on the factorization method for electrical impedance tomography
- Reconstruction of the support function for inclusion from boundary measurements
- Explicit Characterization of Inclusions in Electrical Impedance Tomography
- Conformal mapping for cavity inverse problem: an explicit reconstruction formula
- Exact Shape-Reconstruction by One-Step Linearization in Electrical Impedance Tomography
- Inverse problems and conformal mapping
- A regularization technique for the factorization method
- Direct Methods in the Theory of Elliptic Equations
- Electrical impedance tomography and Calderón's problem
- Determining conductivity by boundary measurements II. Interior results
- Size estimation of inclusion
- How to draw a picture of an unknown inclusion from boundary measurements. Two mathematical inversion algorithms
- The Inverse Conductivity Problem with One Measurement: Stability and Estimation of Size
- Numerical implementation of two noniterative methods for locating inclusions by impedance tomography
- Comparison of linear and non-linear monotonicity-based shape reconstruction using exact matrix characterizations
- Uniqueness and Lipschitz stability in electrical impedance tomography with finitely many electrodes
- Electrical impedance tomography
- A new non-iterative inversion method for electrical resistance tomography
- Complete Electrode Model of Electrical Impedance Tomography: Approximation Properties and Characterization of Inclusions
- Conductivity Imaging from One Interior Measurement in the Presence of Perfectly Conducting and Insulating Inclusions
- Reconstruction of piecewise constant layered conductivities in electrical impedance tomography
- On Regularity of the Logarithmic Forward Map of Electrical Impedance Tomography
- Enclosure method for the p -Laplace equation
- Monotonicity-Based Shape Reconstruction in Electrical Impedance Tomography
- Factorization method and irregular inclusions in electrical impedance tomography
- Nonlinear integral equations and the iterative solution for an inverse boundary value problem
- Sampling Methods