Comparison of linear and non-linear monotonicity-based shape reconstruction using exact matrix characterizations

DOI10.1080/17415977.2017.1290088zbMath1391.35417arXiv1602.04053OpenAlexW3102443514MaRDI QIDQ4563440

Henrik Garde

Publication date: 1 June 2018

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

Full work available at URL: https://arxiv.org/abs/1602.04053

zbMATH Keywords

ill-posed problemelectrical impedance tomographyinverse boundary value problemmonotonicity methoddirect reconstruction

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) Biomedical imaging and signal processing (92C55) Inverse problems for PDEs (35R30) PDEs with low regular coefficients and/or low regular data (35R05) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21)

Related Items (13)

Monotonicity-based shape reconstruction for an inverse scattering problem in a waveguide ⋮ Monotonicity in inverse obstacle scattering on unbounded domains ⋮ Monotonicity in inverse scattering for Maxwell's equations ⋮ Reconstruction of piecewise constant layered conductivities in electrical impedance tomography ⋮ Global Uniqueness and Lipschitz-Stability for the Inverse Robin Transmission Problem ⋮ Monotonicity-Based Reconstruction of Extreme Inclusions in Electrical Impedance Tomography ⋮ The regularized monotonicity method: detecting irregular indefinite inclusions ⋮ 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 ⋮ Monotonicity and local uniqueness for the Helmholtz equation ⋮ Monotonicity Principle in tomography of nonlinear conducting materials ^*

Uses Software

• gmpy2

Cites Work

• Convergence and regularization for monotonicity-based shape reconstruction in electrical impedance tomography
• A global uniqueness theorem for an inverse boundary value problem
• Multidimensional inverse spectral problem for the equation \(-\Delta \psi -(v(x)-Eu(x))\psi =0\)
• Reconstructions from boundary measurements
• Matrices with multiple symmetry properties: applications of centro-Hermitian and per-Hermitian matrices
• Perturbation theory for linear operators.
• Global uniqueness for a two-dimensional inverse boundary value problem
• Uniqueness in Calderón's problem with Lipschitz conductivities
• Calderón's inverse conductivity problem in the plane
• Reconstruction of the support function for inclusion from boundary measurements
• Explicit Characterization of Inclusions in Electrical Impedance Tomography
• Exponential instability in an inverse problem for the Schrödinger equation
• Monotonicity based imaging methods for elliptic and parabolic inverse problems
• The Factorization Method Applied to the Complete Electrode Model of Impedance Tomography
• Spectral Approximation for Compact Operators
• How to draw a picture of an unknown inclusion from boundary measurements. Two mathematical inversion algorithms
• Numerical implementation of two noniterative methods for locating inclusions by impedance tomography
• Stable determination of conductivity by boundary measurements
• A new non-iterative inversion method for electrical resistance tomography
• Distinguishability Revisited: Depth Dependent Bounds on Reconstruction Quality in Electrical Impedance Tomography
• Monotonicity-Based Shape Reconstruction in Electrical Impedance Tomography

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