A new non-iterative reconstruction method for the electrical impedance tomography problem

DOI10.1088/1361-6420/aa54e4zbMath1362.65119OpenAlexW2566589064MaRDI QIDQ2977547

A. D. Ferreira, Antonio André Novotny

Publication date: 18 April 2017

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

Full work available at URL: https://doi.org/10.1088/1361-6420/aa54e4

zbMATH Keywords

algorithminverse problemoverdetermined boundary value problemnumerical experimenttopological asymptotic expansiontopological derivativesdetection of corrosion in structuresdetection of tumorslocalization of mineral depositsnew reconstruction algorithm

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Biomedical imaging and signal processing (92C55) Inverse problems in geophysics (86A22) Inverse problems for PDEs (35R30) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21)

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Investigation of a non-iterative technique based on topological derivatives for fast localization of small conductivity inclusions ⋮ Inverse acoustic scattering using high-order small-inclusion expansion of misfit function ⋮ Topological derivatives of shape functionals. part III: second-order method and applications ⋮ Enhancing electrical impedance tomography reconstruction using learned half-quadratic splitting networks with Anderson acceleration ⋮ Reconstruction of the source term in a time-fractional diffusion equation from partial domain measurement ⋮ Pollution sources reconstruction based on the topological derivative method ⋮ On the Kohn–Vogelius formulation for solving an inverse source problem ⋮ Noniterative Reconstruction Method for an Inverse Potential Problem Modeled by a Modified Helmholtz Equation ⋮ Topological derivative-based technique for imaging thin inhomogeneities with few incident directions ⋮ Singular geometry perturbation based method for shape-topology optimization in unsteady Stokes flow ⋮ Imaging of mass distributions from partial domain measurement ⋮ A noniterative reconstruction method for solving a time-fractional inverse source problem from partial boundary measurements

Cites Work

• Mathematical and statistical methods for multistatic imaging
• Second-order topological expansion for electrical impedance tomography
• Higher-order topological sensitivity for 2-D potential problems. Application to fast identification of inclusions
• Identification of small inhomogeneities of extreme conductivity by boundary measurements: A theorem on continuous dependence
• Reconstruction of small inhomogeneities from boundary measurements
• Topological derivatives in shape optimization
• Stability and Resolution Analysis for a Topological Derivative Based Imaging Functional
• A new one‐shot pointwise source reconstruction method
• The Linearized Inverse Problem in Multifrequency Electrical Impedance Tomography
• Thin cylindrical conductivity inclusions in a three-dimensional domain: a polarization tensor and unique determination from boundary data
• Relaxation of a variational method for impedance computed tomography
• Identification of conductivity imperfections of small diameter by boundary measurements. Continuous dependence and computational reconstruction
• A general representation formula for boundary voltage perturbations caused by internal conductivity inhomogeneities of low volume fraction
• A Fast Local Level Set Method for Inverse Gravimetry
• Reconstruction of the potential from partial Cauchy data for the Schroedinger equation
• Cloaking via change of variables in electric impedance tomography
• A new reconstruction method for the inverse source problem from partial boundary measurements

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