The Linearized Inverse Problem in Multifrequency Electrical Impedance Tomography
From MaRDI portal
Publication:3179614
DOI10.1137/16M1061564zbMath1381.94006arXiv1602.04312OpenAlexW2278879664MaRDI QIDQ3179614
Wenlong Zhang, Giovanni S. Alberti, Jin-Keun Seo, Bangti Jin, Habib Ammari
Publication date: 19 December 2016
Published in: SIAM Journal on Imaging Sciences (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1602.04312
regularizationreconstructiongroup sparsitylinearized inverse problemimperfectly known boundarymultifrequency electrical impedance tomography
Ill-posedness and regularization problems in numerical linear algebra (65F22) Boundary value problems for second-order elliptic equations (35J25) Biomedical imaging and signal processing (92C55) Inverse problems for PDEs (35R30) Image processing (compression, reconstruction, etc.) in information and communication theory (94A08) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21) Inverse problems in optimal control (49N45)
Related Items
Discretization and convergence of the EIT optimal control problem in Sobolev spaces with dominating mixed smoothness, Convexification of restricted Dirichlet-to-Neumann map, Imaging Anisotropic Conductivities from Current Densities, Polynomial Collocation for Handling an Inaccurately Known Measurement Configuration in Electrical Impedance Tomography, The Influence of Surface Deformations on the Forward Magnetoencephalographic Problem, A new non-iterative reconstruction method for the electrical impedance tomography problem, Identification of an inclusion in multifrequency electric impedance tomography, Convexification of electrical impedance tomography with restricted Dirichlet-to-Neumann map data, Mathematical Framework for Abdominal Electrical Impedance Tomography to Assess Fatness, Numerical determination of anomalies in multifrequency electrical impedance tomography, Adaptive reconstruction for electrical impedance tomography with a piecewise constant conductivity, Sensitivity analysis for 3D Maxwell's equations and its use in the resolution of an inverse medium problem at fixed frequency, Geophysical imaging of subsurface structures with least squares estimates, Optoacoustic image reconstruction: the full inverse problem with variable bases, Linearized reconstruction for diffuse optical spectroscopic imaging
Cites Work
- Unnamed Item
- Spectroscopic imaging of a dilute cell suspension
- Expectation propagation for nonlinear inverse problems -- with an application to electrical impedance tomography
- Regularization methods in Banach spaces.
- A mathematical and numerical framework for magnetoacoustic tomography with magnetic induction
- An introduction to mathematics of emerging biomedical imaging
- Variational methods in imaging
- An accurate formula for the reconstruction of conductivity inhomogeneities.
- Electrical impedance tomography using level set representation and total variational regularization
- Reconstruction of small inhomogeneities from boundary measurements
- A mathematical and numerical framework for ultrasonically-induced Lorentz force electrical impedance tomography
- Inverse Problems
- A reconstruction algorithm for electrical impedance tomography based on sparsity regularization
- A direct sampling method for electrical impedance tomography
- [https://portal.mardi4nfdi.de/wiki/Publication:2971324 Discrete approximation and regularisation for the inverse conductivity problem]
- Discretization of variational regularization in Banach spaces
- Spectral Condition Numbers of Orthogonal Projections and Full Rank Linear Least Squares Residuals
- Magnetic Resonance Electrical Impedance Tomography (MREIT)
- Newton regularizations for impedance tomography: a numerical study
- The MUSIC algorithm for impedance tomography of small inclusions from discrete data
- An anisotropic inverse boundary value problem
- Electrical Impedance Tomography by Elastic Deformation
- Impedance-Acoustic Tomography
- Elastic-net regularization: error estimates and active set methods
- Detecting Inclusions in Electrical Impedance Tomography Without Reference Measurements
- Existence and Uniqueness for Electrode Models for Electric Current Computed Tomography
- Enhanced Electrical Impedance Tomographyviathe Mumford–Shah Functional
- An implementation of the reconstruction algorithm of A Nachman for the 2D inverse conductivity problem
- Statistical inversion and Monte Carlo sampling methods in electrical impedance tomography
- An iterative thresholding algorithm for linear inverse problems with a sparsity constraint
- A real time algorithm for the location search of discontinuous conductivities with one measurement
- Electrical impedance tomography
- T-Scan Electrical Impedance Imaging System for Anomaly Detection
- Frechet derivatives in inverse obstacle scattering
- An analysis of electrical impedance tomography with applications to Tikhonov regularization
- Mathematical Modeling of Mechanical Vibration-Assisted Conductivity Imaging
- Reconstructing small perturbations in electrical admittivity at low frequencies
- An analysis of finite element approximation in electrical impedance tomography
- The Inverse Conductivity Problem with an Imperfectly Known Boundary
- Inverse acoustic and electromagnetic scattering theory
