Convergence rates for total variation regularization of coefficient identification problems in elliptic equations. II

DOI10.1016/j.jmaa.2011.11.008zbMath1235.35099OpenAlexW1991496922MaRDI QIDQ662103

Tran Nhan Tam Quyen, Dinh Nho Hào

Publication date: 11 February 2012

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2011.11.008

zbMATH Keywords

convergence rateselliptic equationsill-posed problemsNeumann problemsource conditionstotal variation regularizationcoefficient identification

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Ill-posed problems for PDEs (35R25) Inverse problems for PDEs (35R30) Linear operators and ill-posed problems, regularization (47A52)

Related Items (18)

Direct method for solving the inverse coefficient problem ⋮ Convergence of proximal algorithms with stepsize controls for non-linear inverse problems and application to sparse non-negative matrix factorization ⋮ Convergence rate analysis of the coefficient identification problems in a Kuramoto–Sivashinsky equation ⋮ Sparsity regularization of the diffusion coefficient identification problem: well-posedness and convergence rates ⋮ Reconstructing conductivity coefficients based on sparsity regularization and measured data in electrical impedance tomography ⋮ Inverse problems with nonnegative and sparse solutions: algorithms and application to the phase retrieval problem ⋮ Convergence rates for nonlinear inverse problems of parameter identification using Bregman distances ⋮ Convergence analysis of an alternating direction method of multipliers for the identification of nonsmooth diffusion parameters with total variation ⋮ Descent gradient methods for nonsmooth minimization problems in ill-posed problems ⋮ Determining two coefficients in diffuse optical tomography with incomplete and noisy Cauchy data ⋮ Inverse problem for a class of nonlinear elliptic equations with entropy solution ⋮ Inverse coefficient problem for a second‐order elliptic equation with nonlocal boundary conditions ⋮ Finite element analysis for identifying the reaction coefficient in PDE from boundary observations ⋮ Finite element approximation of source term identification with TV-regularization ⋮ A Vectorized Regularization Method for Multivalued Parameters Identification ⋮ Numerical Study of Inverse Source Problem for Internal Degenerate Parabolic Equation ⋮ A total variation regularization method for an inverse problem of recovering an unknown diffusion coefficient in a parabolic equation ⋮ Finite element methods for coefficient identification in an elliptic equation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Convergence rates for Tikhonov regularization of a two-coefficient identification problem in an elliptic boundary value problem
• A piecewise constant level set method for elliptic inverse problems
• A variational method for numerical differentiation
• Level set and total variation regularization for elliptic inverse problems with discontinuous coefficients.
• Convergence rates for total variation regularization of coefficient identification problems in elliptic equations I
• Generalized Bregman distances and convergence rates for non-convex regularization methods
• Convergence rates for Tikhonov regularization of coefficient identification problems in Laplace-type equations
• Conditional Well-Posedness for an Elliptic Inverse Problem
• Identification of Discontinuous Parameters in Flow Equations
• Variational Analysis in Sobolev andBVSpaces
• Convergence rates for Tikhonov regularisation of non-linear ill-posed problems
• Convergence rates and source conditions for Tikhonov regularization with sparsity constraints
• An Abstract Framework for Elliptic Inverse Problems: Part 1. An Output Least-Squares Approach
• A variational method for parameter identification
• Identifiability and stability of a two-parameter estimation problem¹
• On the discretization and regularization of ill-posed problems with noncompact operators
• Numerical methods for elliptic inverse problems
• An Augmented Lagrangian Method for Identifying Discontinuous Parameters in Elliptic Systems
• Uniqueness for an Elliptic Inverse Problem
• Proximal Minimization Methods with Generalized Bregman Functions
• Regularization of linear least squares problems by total bounded variation
• The Output Least Squares Identifiability of the Diffusion Coefficient from an H¹–Observation in a 2–D Elliptic Equation
• Convergence rates of convex variational regularization
• Error estimates for non-quadratic regularization and the relation to enhancement
• Parameter identification for elliptic problems

This page was built for publication: Convergence rates for total variation regularization of coefficient identification problems in elliptic equations. II