Necessary conditions for variational regularization schemes

DOI10.1088/0266-5611/29/7/075016zbMath1283.65055arXiv1204.0649OpenAlexW3105329799MaRDI QIDQ2861889

Nadja Worliczek, Dirk A. Lorenz

Publication date: 11 November 2013

Published in: Inverse Problems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1204.0649

zbMATH Keywords

stabilityconvergenceinverse problemIll-posed problemTikhonov regularizationKullback-Leibler divergencetopological spaceBregman distancediscrepancy functionalIvanov regularizationMorozov regularizationvariational regularizationa priori parameter choice

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Nonlinear ill-posed problems (47J06) Numerical solutions to equations with nonlinear operators (65J15) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Numerical solution to inverse problems in abstract spaces (65J22)

Related Items (15)

Quasi-solution of linear inverse problems in non-reflexive Banach spaces ⋮ Convergence and adaptive discretization of the IRGNM Tikhonov and the IRGNM Ivanov method under a tangential cone condition in Banach space ⋮ Computing quasisolutions of nonlinear inverse problems via efficient minimization of trust region problems ⋮ On convergence and convergence rates for Ivanov and Morozov regularization and application to some parameter identification problems in elliptic PDEs ⋮ An easily implementable algorithm for efficient projection onto the ordered weighted \(\ell_1\) norm ball ⋮ Tikhonov regularization with oversmoothing penalty for non-linear ill-posed problems in Hilbert scales ⋮ Minimization Based Formulations of Inverse Problems and Their Regularization ⋮ Denoising of image gradients and total generalized variation denoising ⋮ On the Use of ADMM for Imaging Inverse Problems: the Pros and Cons of Matrix Inversions ⋮ On the identification of the nonlinearity parameter in the Westervelt equation from boundary measurements ⋮ On ill-posedness concepts, stable solvability and saturation ⋮ Low Complexity Regularization of Linear Inverse Problems ⋮ Some application examples of minimization based formulations of inverse problems and their regularization ⋮ The Ivanov regularized Gauss-Newton method in Banach space with an a posteriori choice of the regularization radius ⋮ Generalized Modes in Bayesian Inverse Problems

This page was built for publication: Necessary conditions for variational regularization schemes