Newton regularizations for impedance tomography: convergence by local injectivity
From MaRDI portal
Publication:3549277
DOI10.1088/0266-5611/24/6/065009zbMath1152.35516OpenAlexW2005782434WikidataQ60707579 ScholiaQ60707579MaRDI QIDQ3549277
Andreas Rieder, Armin Lechleiter
Publication date: 22 December 2008
Published in: Inverse Problems (Search for Journal in Brave)
Full work available at URL: https://semanticscholar.org/paper/c2cf54aa025ba4f824235cae95c83ebce6b64e62
Error bounds for boundary value problems involving PDEs (65N15) Inverse problems for PDEs (35R30) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20)
Related Items (41)
On global normal linear approximations for nonlinear Bayesian inverse problems ⋮ Discretization and convergence of the EIT optimal control problem in Sobolev spaces with dominating mixed smoothness ⋮ Interpolation of missing electrode data in electrical impedance tomography ⋮ A Bernstein–von-Mises theorem for the Calderón problem with piecewise constant conductivities ⋮ Towards a general convergence theory for inexact Newton regularizations ⋮ On the tangential cone condition for electrical impedance tomography ⋮ A Hybrid Segmentation and D-Bar Method for Electrical Impedance Tomography ⋮ Direct regularized reconstruction for the three-dimensional Calderón problem ⋮ Generalized linearization techniques in electrical impedance tomography ⋮ Series reversion in Calderón’s problem ⋮ Range-relaxed strategy applied to the Levenberg–Marquardt method with uniformly convex penalization term in Banach spaces ⋮ The Calderón Problem with Finitely Many Unknowns is Equivalent to Convex Semidefinite Optimization ⋮ Enhancing residual-based techniques with shape reconstruction features in electrical impedance tomography ⋮ Mixed gradient-Tikhonov methods for solving nonlinear ill-posed problems in Banach spaces ⋮ On a Dynamic Variant of the Iteratively Regularized Gauss–Newton Method with Sequential Data ⋮ On the iterative regularization of non-linear illposed problems in \(L^{\infty}\) ⋮ Series reversion for electrical impedance tomography with modeling errors * ⋮ Linear Functional Strategy and the Approximate Inverse for Nonlinear Ill-Posed Problems ⋮ A high order discontinuous Galerkin method for the recovery of the conductivity in electrical impedance tomography ⋮ Tangential Cone Condition for the Full Waveform Forward Operator in the Viscoelastic Regime: The Nonlocal Case ⋮ A range-relaxed criteria for choosing the Lagrange multipliers in the Levenberg-Marquardt-Kaczmarz method for solving systems of non-linear ill-posed equations: application to EIT-CEM with real data ⋮ Determining two coefficients in diffuse optical tomography with incomplete and noisy Cauchy data ⋮ On the \(hp\)-adaptive solution of complete electrode model forward problems of electrical impedance tomography ⋮ Modified forward and inverse Born series for the Calderon and diffuse-wave problems ⋮ Uniqueness and Lipschitz stability in electrical impedance tomography with finitely many electrodes ⋮ An inverse boundary value problem for the p -Laplacian: a linearization approach ⋮ Non-convex ℓp regularization for sparse reconstruction of electrical impedance tomography ⋮ Lipschitz stability estimate and reconstruction of Lamé parameters in linear elasticity ⋮ Variational source condition for ill-posed backward nonlinear Maxwell’s equations ⋮ On a Family of Gradient-Type Projection Methods for Nonlinear Ill-Posed Problems ⋮ Convergence and regularization for monotonicity-based shape reconstruction in electrical impedance tomography ⋮ How to solve inverse scattering problems without knowing the source term: a three-step strategy ⋮ On projective Landweber–Kaczmarz methods for solving systems of nonlinear ill-posed equations ⋮ Lamé Parameter Estimation from Static Displacement Field Measurements in the Framework of Nonlinear Inverse Problems ⋮ Levenberg-Marquardt algorithm for acousto-electric tomography based on the complete electrode model ⋮ The Tangential Cone Condition for Some Coefficient Identification Model Problems in Parabolic PDEs ⋮ Infinite-dimensional inverse problems with finite measurements ⋮ Variational Source Conditions in $L^p$-spaces ⋮ Tangential cone condition and Lipschitz stability for the full waveform forward operator in the acoustic regime ⋮ Joint estimation of Robin coefficient and domain boundary for the Poisson problem ⋮ Local recovery of a piecewise constant anisotropic conductivity in EIT on domains with exposed corners
This page was built for publication: Newton regularizations for impedance tomography: convergence by local injectivity
