Enhancing residual-based techniques with shape reconstruction features in electrical impedance tomography

DOI10.1088/0266-5611/32/12/125002zbMath1362.35333arXiv1511.07079OpenAlexW2179941141WikidataQ59895852 ScholiaQ59895852MaRDI QIDQ2957530

Bastian Harrach, Mach Nguyet Minh

Publication date: 26 January 2017

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

Full work available at URL: https://arxiv.org/abs/1511.07079

zbMATH Keywords

global convergencelinearized equationelectrical impedance tomographyshape reconstructionminimizing residual

Mathematics Subject Classification ID

Inverse problems for PDEs (35R30) Second-order elliptic equations (35J15)

Related Items (26)

Discretization and convergence of the EIT optimal control problem in Sobolev spaces with dominating mixed smoothness ⋮ Monotonicity-based regularization for shape reconstruction in linear elasticity ⋮ Monotonicity-Based Regularization for Phantom Experiment Data in Electrical Impedance Tomography ⋮ Monotonicity-based inversion of fractional semilinear elliptic equations with power type nonlinearities ⋮ Convexification of restricted Dirichlet-to-Neumann map ⋮ Simultaneous recovery of piecewise analytic coefficients in a semilinear elliptic equation ⋮ Monotonicity in inverse obstacle scattering on unbounded domains ⋮ Monotonicity and Enclosure Methods for the $p$-Laplace Equation ⋮ Monotonicity in inverse scattering for Maxwell's equations ⋮ A shape optimization approach for electrical impedance tomography with point measurements ⋮ Uniqueness and Lipschitz stability in electrical impedance tomography with finitely many electrodes ⋮ Convexification of electrical impedance tomography with restricted Dirichlet-to-Neumann map data ⋮ Global Uniqueness and Lipschitz-Stability for the Inverse Robin Transmission Problem ⋮ The regularized monotonicity method: detecting irregular indefinite inclusions ⋮ Monotonicity-based electrical impedance tomography for lung imaging ⋮ Lipschitz stability estimate and reconstruction of Lamé parameters in linear elasticity ⋮ Uniqueness, stability and global convergence for a discrete inverse elliptic Robin transmission problem ⋮ On Localizing and Concentrating Electromagnetic Fields ⋮ Monotonicity in Inverse Medium Scattering on Unbounded Domains ⋮ 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 ⋮ Monotonicity and local uniqueness for the Helmholtz equation ⋮ The monotonicity principle for magnetic induction tomography ⋮ Shape reconstruction in linear elasticity: standard and linearized monotonicity method ⋮ Monotonicity Principle in tomography of nonlinear conducting materials ^*

Uses Software

• CVX

Cites Work

• Unnamed Item
• Convergence and regularization for monotonicity-based shape reconstruction in electrical impedance tomography
• A global uniqueness theorem for an inverse boundary value problem
• Localized potentials in electrical impedance tomography
• Inequalities for the Schatten p-Norm. IV
• Global uniqueness for a two-dimensional inverse boundary value problem
• Recent progress on the factorization method for electrical impedance tomography
• On an inverse boundary value problem
• Sparsity reconstruction in electrical impedance tomography: an experimental evaluation
• Calderón's inverse conductivity problem in the plane
• Reconstruction of the Refractive Index from Experimental Backscattering Data Using a Globally Convergent Inverse Method
• A reconstruction algorithm for electrical impedance tomography based on sparsity regularization
• Exact Shape-Reconstruction by One-Step Linearization in Electrical Impedance Tomography
• Graph Implementations for Nonsmooth Convex Programs
• Monotonicity based imaging methods for elliptic and parabolic inverse problems
• Newton regularizations for impedance tomography: convergence by local injectivity
• Determining conductivity by boundary measurements
• Monotonicity-based electrical impedance tomography for lung imaging
• Linear and Nonlinear Inverse Problems with Practical Applications
• A new non-iterative inversion method for electrical resistance tomography
• Sampling Methods
• Sparsity regularization for parameter identification problems
• Monotonicity-Based Shape Reconstruction in Electrical Impedance Tomography
• Factorization method and irregular inclusions in electrical impedance tomography
• An introduction to the mathematical theory of inverse problems

This page was built for publication: Enhancing residual-based techniques with shape reconstruction features in electrical impedance tomography