A Semismooth Newton Method for Nonlinear Parameter Identification Problems with Impulsive Noise

DOI10.1137/110826187zbMath1250.65134OpenAlexW2002178240MaRDI QIDQ2912280

Christian Clason, Bangti Jin

Publication date: 14 September 2012

Published in: SIAM Journal on Imaging Sciences (Search for Journal in Brave)

Full work available at URL: http://unipub.uni-graz.at/doi/doi:10.1137/110826187

zbMATH Keywords

convergencenumerical examplesinverse problemsparameter identificationregularization parameterimpulsive noiseelliptic differential equationnoise modelsemismooth Newton method\(L^1\) data fitting

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Inverse problems for PDEs (35R30) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21)

Related Items (33)

A posteriori error estimates for an optimal control problem with a bilinear state equation ⋮ Generalized inexact Newton regularization for nonlinear ill-posed problems in Banach spaces ⋮ A non-convex denoising model for impulse and Gaussian noise mixture removing using bi-level parameter identification ⋮ Expectation propagation for nonlinear inverse problems -- with an application to electrical impedance tomography ⋮ A proximal iteratively regularized Gauss-Newton method for nonlinear inverse problems ⋮ An optimal control approach for determining the source term in fractional diffusion equation by different cost functionals ⋮ Inexact Newton regularization combined with gradient methods in Banach spaces ⋮ A fast two-point gradient algorithm based on sequential subspace optimization method for nonlinear ill-posed problems ⋮ A Fast Averaged Kaczmarz Iteration with Convex Penalty for Inverse Problems in Hilbert Spaces ⋮ Simplified Levenberg–Marquardt method in Banach spaces for nonlinear ill-posed operator equations ⋮ A projected homotopy perturbation method for nonlinear inverse problems in Banach spaces ⋮ Heuristic rule for inexact Newton-Landweber iteration with convex penalty terms of nonlinear: ill-posed problems ⋮ Mixed gradient-Tikhonov methods for solving nonlinear ill-posed problems in Banach spaces ⋮ A Fast Data-Driven Iteratively Regularized Method with Convex Penalty for Solving Ill-Posed Problems ⋮ A primal-dual approach for the Robin inverse problem in a nonlinear elliptic equation: the case of the \(L^1 - L^2\) cost functional ⋮ An automatic \(L_1\)-based regularization method for the analysis of FFC dispersion profiles with quadrupolar peaks ⋮ An alternative extrapolation scheme of PDHGM for saddle point problem with nonlinear function ⋮ Inverse problem for a class of nonlinear elliptic equations with entropy solution ⋮ Uniqueness, Lipschitz Stability, and Reconstruction for the Inverse Optical Tomography Problem ⋮ Stability of saddle points via explicit coderivatives of pointwise subdifferentials ⋮ \(L^1\) penalization of volumetric dose objectives in optimal control of PDEs ⋮ Convergence Rates for Exponentially Ill-Posed Inverse Problems with Impulsive Noise ⋮ Simultaneous recovery of the temperature and species concentration from integral equation model ⋮ An accelerated homotopy perturbation iteration for nonlinear ill-posed problems in Banach spaces with uniformly convex penalty ⋮ Fast subspace optimization method for nonlinear inverse problems in Banach spaces with uniformly convex penalty terms ⋮ A denoising model adapted for impulse and Gaussian noises using a constrained-PDE ⋮ A Vectorized Regularization Method for Multivalued Parameters Identification ⋮ An iteration regularization method with general convex penalty for nonlinear inverse problems in Banach spaces ⋮ A projective two-point gradient Kaczmarz iteration for nonlinear ill-posed problems ⋮ Error estimates for variational regularization of inverse problems with general noise models for data and operator ⋮ Enhanced choice of the parameters in an iteratively regularized Newton-Landweber iteration in Banach space ⋮ Low rank matrix recovery with adversarial sparse noise* ⋮ Primal-Dual Extragradient Methods for Nonlinear Nonsmooth PDE-Constrained Optimization

Uses Software

• FTVd

This page was built for publication: A Semismooth Newton Method for Nonlinear Parameter Identification Problems with Impulsive Noise