Explicit Characterization of Inclusions in Electrical Impedance Tomography
From MaRDI portal
Publication:2719176
DOI10.1137/S003614100036656XzbMath0980.35170MaRDI QIDQ2719176
Publication date: 21 June 2001
Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)
electrical impedance tomographyNeumann-Dirichlet mapdipole singularitydipole-like indicator functions
Inverse problems for PDEs (35R30) PDEs with low regular coefficients and/or low regular data (35R05) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Boundary value and inverse problems for harmonic functions in higher dimensions (31B20) Boundary value and inverse problems for harmonic functions in two dimensions (31A25)
Related Items (42)
Electrical impedance tomography: 3D reconstructions using scattering transforms ⋮ Inverse Dirichlet problem and conformal mapping ⋮ Application of the factorization method to the characterization of weak inclusions in electrical impedance tomography ⋮ Higher-Order Quasi-Monte Carlo for Bayesian Shape Inversion ⋮ Nonlinear Fourier analysis for discontinuous conductivities: computational results ⋮ Comparison of linear and non-linear monotonicity-based shape reconstruction using exact matrix characterizations ⋮ Generalized linearization techniques in electrical impedance tomography ⋮ Mimicking relative continuum measurements by electrode data in two-dimensional electrical impedance tomography ⋮ Regularizing a linearized EIT reconstruction method using a sensitivity-based factorization method ⋮ A direct method for reconstructing inclusions and boundary conditions from electrostatic data ⋮ Convex backscattering support in electric impedance tomography ⋮ Incorporating knowledge on the measurement noise in electrical impedance tomography ⋮ Detecting stochastic inclusions in electrical impedance tomography ⋮ Shape Optimization for Free Boundary Problems – Analysis and Numerics ⋮ Electrical resistance tomography for locating inclusions using analytical boundary element integrals and their partial derivatives ⋮ Reconstruction of piecewise constant layered conductivities in electrical impedance tomography ⋮ A New Method for the Data Completion Problem and Application to Obstacle Detection ⋮ Monotonicity-Based Reconstruction of Extreme Inclusions in Electrical Impedance Tomography ⋮ New characterizations of solutions in inverse scattering theory ⋮ The regularized monotonicity method: detecting irregular indefinite inclusions ⋮ On imaging obstacles inside inhomogeneous media ⋮ The factorization method for cracks in electrical impedance tomography ⋮ The direct and inverse scattering problems for penetrable and impenetrable mixed obstacles ⋮ Convergence and regularization for monotonicity-based shape reconstruction in electrical impedance tomography ⋮ Numerical simulation and analysis of generalized difference method on triangular networks for electrical impedance tomography ⋮ Recent progress on the factorization method for electrical impedance tomography ⋮ Level set reconstruction of conductivity and permittivity from boundary electrical measurements using experimental data ⋮ The factorization method for real elliptic problems ⋮ Crack detection using electrostatic measurements ⋮ Electrical impedance tomography using level set representation and total variational regularization ⋮ Monotonicity in Inverse Medium Scattering on Unbounded Domains ⋮ Efficient treatment of stationary free boundary problems ⋮ Reconstruction of a grounded object in an electrostatic halfspace with an indicator function ⋮ Sampling Methods ⋮ On computation of test dipoles for factorization method ⋮ A shape calculus analysis for tracking type formulations in electrical impedance tomography ⋮ Monotonicity and local uniqueness for the Helmholtz equation ⋮ Construct Deep Neural Networks based on Direct Sampling Methods for Solving Electrical Impedance Tomography ⋮ Sampling and probe methods -- an algorithmical view ⋮ Inverse Obstacle Problem for the Non-Stationary Wave Equation with an Unknown Background ⋮ Identification of small inhomogeneities: Asymptotic factorization ⋮ Linear sampling methods for inverse boundary value problems in potential theory
This page was built for publication: Explicit Characterization of Inclusions in Electrical Impedance Tomography
