Electrical impedance tomography: 3D reconstructions using scattering transforms

DOI10.1080/00036811.2011.598863zbMath1238.35183OpenAlexW2082384078WikidataQ58242481 ScholiaQ58242481MaRDI QIDQ2883310

Kim Knudsen, Per Christian Hansen, Fabrice Delbary

Publication date: 11 May 2012

Published in: Applicable Analysis (Search for Journal in Brave)

Full work available at URL: https://orbit.dtu.dk/en/publications/0ac80444-9165-48a2-8895-60e3c37c17a4

zbMATH Keywords

numerical solutionhyperinterpolationreconstruction algorithmelectrical impedance tomographyCalderón problemmoment method

Mathematics Subject Classification ID

Inverse problems for PDEs (35R30) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21) Inverse problems (including inverse scattering) in optics and electromagnetic theory (78A46)

Related Items (10)

Direct regularized reconstruction for the three-dimensional Calderón problem ⋮ The Born approximation in the three-dimensional Calderón problem. II: Numerical reconstruction in the radial case ⋮ The D-bar method for electrical impedance tomography—demystified ⋮ Hyperinterpolation for Spectral Wave Propagation Models in Three Dimensions ⋮ 3D electrical impedance tomography reconstructions from simulated electrode data using direct inversion \(\mathbf{t}^{\mathbf{exp}}\) and Calderón methods ⋮ Partial data inverse problem with 𝐿^{𝑛/2} potentials ⋮ The Born approximation in the three-dimensional Calderón problem ⋮ Edge-Enhancing Reconstruction Algorithm for Three-Dimensional Electrical Impedance Tomography ⋮ Numerical nonlinear complex geometrical optics algorithm for the 3D Calderón problem ⋮ A data-driven edge-preserving D-bar method for electrical impedance tomography

Cites Work

• A global uniqueness theorem for an inverse boundary value problem
• Direct electrical impedance tomography for nonsmooth conductivities
• Reconstructions from boundary measurements
• Complex geometrical optics solutions for Lipschitz conductivities.
• Uniqueness in the inverse conductivity problem for conductivities with \(3/2\) derivatives in \(L^p\), \(p>2n\)
• Polynomial interpolation and hyperinterpolation over general regions
• Global uniqueness for a two-dimensional inverse boundary value problem
• Regularized D-bar method for the inverse conductivity problem
• Calderón's inverse conductivity problem in the plane
• Explicit Characterization of Inclusions in Electrical Impedance Tomography
• Direct numerical reconstruction of conductivities in three dimensions using scattering transforms
• Towards a d-bar reconstruction method for three-dimensional EIT
• Nonlinear integral equations for the inverse electrical impedance problem
• 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
• Electrical impedance tomography
• D‐Bar Method for Electrical Impedance Tomography with Discontinuous Conductivities
• Non-linear integral equations for the complete electrode model in inverse impedance tomography
• Unnamed Item

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