An iterative method for Tikhonov regularization with a general linear regularization operator

DOI10.1216/JIE-2010-22-3-465zbMath1210.65092OpenAlexW2059130945MaRDI QIDQ616671

Michiel E. Hochstenbach, Lothar Reichel

Publication date: 12 January 2011

Published in: Journal of Integral Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1216/jie-2010-22-3-465

zbMATH Keywords

numerical examplesimage processingintegral equationsiterative methodTikhonov regularizationdiscrepancy principleGolub-Kahan bidiagonalizationgeneral regularization operatorill-posed linear least squares problem

Mathematics Subject Classification ID

Numerical solutions to overdetermined systems, pseudoinverses (65F20) Ill-posedness and regularization problems in numerical linear algebra (65F22) Computing methodologies for image processing (68U10) Iterative numerical methods for linear systems (65F10) Numerical methods for ill-posed problems for integral equations (65R30) Fredholm integral equations (45B05)

Related Items (26)

Projected nonstationary iterated Tikhonov regularization ⋮ On the choice of solution subspace for nonstationary iterated Tikhonov regularization ⋮ A new framework for multi-parameter regularization ⋮ A Generalized Krylov Subspace Method for $\ell_p$-$\ell_q$ Minimization ⋮ Direct Implementation of Tikhonov Regularization for the First Kind Integral Equation ⋮ Golub-Kahan vs. Monte Carlo: a comparison of bidiagonlization and a randomized SVD method for the solution of linear discrete ill-posed problems ⋮ On the choice of subspace for large-scale Tikhonov regularization problems in general form ⋮ Inverse subspace problems with applications ⋮ Embedded techniques for choosing the parameter in Tikhonov regularization ⋮ Learning regularization parameters for general-form Tikhonov ⋮ A GCV based Arnoldi-Tikhonov regularization method ⋮ A Golub-Kahan-type reduction method for matrix pairs ⋮ Variable projection methods for separable nonlinear inverse problems with general-form Tikhonov regularization ⋮ A projection method for general form linear least-squares problems ⋮ Tikhonov regularization via flexible Arnoldi reduction ⋮ A majorization-minimization Golub-Kahan bidiagonalization method for \(\ell_2-\ell_q\) mimimization with applications in image restorization ⋮ Generalized Hybrid Iterative Methods for Large-Scale Bayesian Inverse Problems ⋮ Relaxed Regularization for Linear Inverse Problems ⋮ A class of parameter choice rules for stationary iterated weighted Tikhonov regularization scheme ⋮ Optimization of structural similarity in mathematical imaging ⋮ Relaxed Regularization for Linear Inverse Problems ⋮ Hybrid projection methods for large-scale inverse problems with mixed Gaussian priors ⋮ Square regularization matrices for large linear discrete ill-posed problems ⋮ A modified Tikhonov regularization method ⋮ Simple and efficient determination of the Tikhonov regularization parameter chosen by the generalized discrepancy principle for discrete ill-posed problems ⋮ Multidirectional subspace expansion for one-parameter and multiparameter Tikhonov regularization

Uses Software

• Regularization tools

Cites Work

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