Nonlinear Fourier analysis for discontinuous conductivities: computational results

DOI10.1016/j.jcp.2014.07.032zbMath1349.78047arXiv1310.7051OpenAlexW1974958647MaRDI QIDQ349516

Lassi Päivärinta, Juan Manuel Reyes, Samuli Siltanen, Kari Astala

Publication date: 5 December 2016

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1310.7051

zbMATH Keywords

inverse problemscattering transforminverse conductivity problemelectrical impedance tomographynonlinear Fourier transformBeltrami equationconductivity equationcomplex geometrical optics solution

Mathematics Subject Classification ID

Biomedical imaging and signal processing (92C55) Composite media; random media in optics and electromagnetic theory (78A48) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21)

Related Items (7)

Propagation and recovery of singularities in the inverse conductivity problem ⋮ A Hybrid Segmentation and D-Bar Method for Electrical Impedance Tomography ⋮ The D-bar method for electrical impedance tomography—demystified ⋮ An error embedded method based on generalized Chebyshev polynomials ⋮ Nachman’s reconstruction method for the Calderón problem with discontinuous conductivities ⋮ Unnamed Item ⋮ Numerical scattering for the defocusing Davey–Stewartson II equation for initial data with compact support

Cites Work

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• The Novikov-Veselov equation and the inverse scattering method. I: Analysis
• Direct electrical impedance tomography for nonsmooth conductivities
• Stability of the Calderón problem for less regular conductivities
• A boundary integral equation for Calderón's inverse conductivity problem
• Factorization method and inclusions of mixed type in an inverse elliptic boundary value problem
• Stability of Calderón's inverse conductivity problem in the plane for discontinuous conductivities
• Numerical solution method for the \(\overline\partial\)-equation in the plane
• Global uniqueness for a two-dimensional inverse boundary value problem
• Uniqueness in Calderón's problem with Lipschitz conductivities
• Regularized D-bar method for the inverse conductivity problem
• Application of the factorization method to the characterization of weak inclusions in electrical impedance tomography
• Calderón's inverse conductivity problem in the plane
• Explicit Characterization of Inclusions in Electrical Impedance Tomography
• Exceptional circles of radial potentials
• A direct reconstruction method for anisotropic electrical impedance tomography
• The Novikov–Veselov equation and the inverse scattering method: II. Computation
• The Novikov-Veselov Equation: Theory and Computation
• Numerical solution of the $\mathbb R$-linear Beltrami equation
• Reconstruction of Less Regular Conductivities in the Plane
• A direct D-bar reconstruction algorithm for recovering a complex conductivity in 2D
• The Factorization Method for Electrical Impedance Tomography in the Half-Space
• Reconstructing Discontinuities Using Complex Geometrical Optics Solutions
• The Factorization Method Applied to the Complete Electrode Model of Impedance Tomography
• Local detection of three-dimensional inclusions in electrical impedance tomography
• Detecting Inclusions in Electrical Impedance Tomography Without Reference Measurements
• Detection of Mines by Electric Measurements
• Electrical Impedance Tomography
• Uniqueness in the inverse conductivity problem for nonsmooth conductivities in two dimensions
• Direct Reconstructions of Conductivities from Boundary Measurements
• An implementation of the reconstruction algorithm of A Nachman for the 2D inverse conductivity problem
• Numerical implementation of two noniterative methods for locating inclusions by impedance tomography
• Numerical method for finding the convex hull of an inclusion in conductivity from boundary measurements
• Linear and Nonlinear Inverse Problems with Practical Applications
• Stable determination of conductivity by boundary measurements
• Electrical impedance tomography and Mittag-Leffler's function
• THE SOBOLEV NORM OF CHARACTERISTIC FUNCTIONS WITH APPLICATIONS TO THE CALDERON INVERSE PROBLEM
• D‐Bar Method for Electrical Impedance Tomography with Discontinuous Conductivities
• Probing for electrical inclusions with complex spherical waves
• Monotonicity-Based Shape Reconstruction in Electrical Impedance Tomography

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