Identification of Discontinuous Coefficients in Elliptic Problems Using Total Variation Regularization
From MaRDI portal
Publication:4442507
DOI10.1137/S1064827599326020zbMath1046.65090OpenAlexW2133619711WikidataQ57397354 ScholiaQ57397354MaRDI QIDQ4442507
Publication date: 20 January 2004
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1137/s1064827599326020
ellipticparameter estimationregularizationdiscontinuous coefficientsinverse problemsnumerical experimentsfilteringelliptic problemsleast squares methodnoise removaltotal variational norm
Boundary value problems for second-order elliptic equations (35J25) Inverse problems for PDEs (35R30) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) PDEs with low regular coefficients and/or low regular data (35R05) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21)
Related Items
On Geometric Inverse Problems in Time-Fractional Subdiffusion, On a level-set method for ill-posed problems with piecewise nonconstant coefficients, A parametric level set based collage method for an inverse problem in elliptic partial differential equations, Sparsity regularization of the diffusion coefficient identification problem: well-posedness and convergence rates, Parameter estimation with the multigrid-homotopy method for a nonlinear diffusion equation, Elliptic optimal control problems with \(L^1\)-control cost and applications for the placement of control devices, Domain decomposition methods for recovering Robin coefficients in elliptic and parabolic systems, Preconditioning PDE-constrained optimization with \(L^1\)-sparsity and control constraints, Identification of diffusion parameters in a non-linear convection–diffusion equation using adaptive homotopy perturbation method, Preconditioning for PDE-constrained optimization with total variation regularization, Convergence analysis of primal-dual based methods for total variation minimization with finite element approximation, A piecewise constant level set method for elliptic inverse problems, Bilevel Imaging Learning Problems as Mathematical Programs with Complementarity Constraints: Reformulation and Theory, Numerical reconstruction of a discontinuous diffusive coefficient in variable-order time-fractional subdiffusion, Identification of uncertainties in the shape of geophysical objects with level sets and the adjoint method, Unique continuation for the Lamé system using stabilized finite element methods, Equivalent a posteriori error estimates for elliptic optimal control problems with \(L^1\)-control cost, Variational method for multiple parameter identification in elliptic PDEs, Determining two coefficients in diffuse optical tomography with incomplete and noisy Cauchy data, Level set and total variation regularization for elliptic inverse problems with discontinuous coefficients., A method of determining the elastic properties of inhomogeneous solids, Estimation of piecewise constant coefficients of parabolic equations: applications to the detection of buried objects, Binary level set methods for topology and shape optimization of a two-density inhomogeneous drum, Nonstationary phase boundary estimation in electrical impedance tomography using unscented Kalman filter, Convergence rates for Tikhonov regularization of a two-coefficient identification problem in an elliptic boundary value problem, Adaptive finite element methods for the identification of distributed parameters in elliptic equation, Reconstruction of a permeability field with the wavelet multiscale-homotopy method for a nonlinear convection-diffusion equation, A nonlinear multigrid method for total variation minimization from image restoration, Equation error approach for elliptic inverse problems with an application to the identification of Lamé parameters, Estimation of a permeability field within the two-phase porous media flow using nonlinear multigrid method, Runge-Kutta type total variation regularization for nonlinear inverse problems, A first-order adjoint and a second-order hybrid method for an energy output least-squares elastography inverse problem of identifying tumor location, A fixed mesh method with immersed finite elements for solving interface inverse problems, Overlapping domain decomposition methods for linear inverse problems, A simple and feasible method for a class of large-scale \(l^1\)-problems, An improved noise removal model based on nonlinear fourth-order partial differential equations, The inverse medium problem in 1D PML-truncated heterogeneous semi-infinite domains, Variational piecewise constant level set methods for shape optimization of a two-density drum, Parameter estimation with the augmented Lagrangian method for a parabolic equation, Electrical impedance tomography using level set representation and total variational regularization, Identification of the reaction coefficient in time fractional diffusion equations, On the inverse problem of identifying Lamé coefficients in linear elasticity, Level-set approaches of L2-type for recovering shape and contrast in ill-posed problems, On the stabilization of singular identification problem of an unknown discontinuous diffusion parameter in elliptic equation, A variant of the level set method and applications to image segmentation, On the inverse problem of soil profile reconstruction: a comparison of time-domain approaches, Dual regularization in non-linear inverse scattering problems, A total variation regularization method for an inverse problem of recovering an unknown diffusion coefficient in a parabolic equation, A level set method to reconstruct the discontinuity of the conductivity in EIT, An ADMM-Newton-CNN numerical approach to a TV model for identifying discontinuous diffusion coefficients in elliptic equations: convex case with gradient observations, Finite element methods for coefficient identification in an elliptic equation, A New Energy Inversion for Parameter Identification in Saddle Point Problems with an Application to the Elasticity Imaging Inverse Problem of Predicting Tumor Location, A coupled complex boundary method for parameter identification in elliptic problems
