Towards a d-bar reconstruction method for three-dimensional EIT

DOI10.1515/156939406777571102zbMath1111.35108OpenAlexW1988172910MaRDI QIDQ3431316

Kim Knudsen, Samuli Siltanen, Horia D. Cornean

Publication date: 10 April 2007

Published in: Journal of Inverse and Ill-posed Problems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/156939406777571102

zbMATH Keywords

boundary integral equationscattering transforminverse conductivity problemelectrical impedance tomography\(\overline\partial\)-methodexponentially growing solutionscomplex frequency method

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Inverse problems for PDEs (35R30) Inverse scattering problems in quantum theory (81U40) (overlinepartial)-Neumann problems and formal complexes in context of PDEs (35N15)

Related Items (11)

Electrical impedance tomography: 3D reconstructions using scattering transforms ⋮ Direct regularized reconstruction for the three-dimensional Calderón problem ⋮ Distinguishability Revisited: Depth Dependent Bounds on Reconstruction Quality in Electrical Impedance Tomography ⋮ The D-bar method for electrical impedance tomography—demystified ⋮ Reconstruction of piecewise constant layered conductivities in electrical impedance tomography ⋮ 3D electrical impedance tomography reconstructions from simulated electrode data using direct inversion \(\mathbf{t}^{\mathbf{exp}}\) and Calderón methods ⋮ Electrical Impedance Tomography ⋮ Dirichlet-to-Neumann semigroup acts as a magnifying glass ⋮ Partial data inverse problem with 𝐿^{𝑛/2} potentials ⋮ 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

• An \(n\)-dimensional Borg-Levinson theorem
• Surface gradients and continuity properties for some integral operators in classical scattering theory
• A Multidimensional Inverse-Scattering Method
• A Problem in Electrical Prospection and a n-Dimensional Borg-Levinson Theorem
• Electrical Impedance Tomography
• Stable determination of conductivity by boundary measurements
• Global Uniqueness in the Impedance-Imaging Problem for Less Regular Conductivities

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