Comparison of parameter choices in regularization algorithms in case of different information about noise level

DOI10.1007/s10092-010-0027-4zbMath1216.65063OpenAlexW2012016993MaRDI QIDQ535347

Reimo Palm, Toomas Raus, Uno Hämarik

Publication date: 11 May 2011

Published in: Calcolo (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10092-010-0027-4

zbMATH Keywords

regularizationHilbert spacenumerical experimentsdiscrepancy principleill-posed problemregularization parameter choiceLandweber methodnumerical comparisonTikhonov methodnoise levelBrezinski-Rodriguez-Seatzu ruleextrapolated Tikhonov methodHanke-Raus rulequasioptimality criterion

Mathematics Subject Classification ID

Numerical solutions to equations with linear operators (65J10) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Linear operators and ill-posed problems, regularization (47A52)

Related Items (12)

Semi-heuristic parameter choice rules for Tikhonov regularisation with operator perturbations ⋮ Heuristic Parameter Choice in Tikhonov Method from Minimizers of the Quasi-Optimality Function ⋮ Adaptivity and Oracle Inequalities in Linear Statistical Inverse Problems: A (Numerical) Survey ⋮ Estimating Solution Smoothness and Data Noise with Tikhonov Regularization ⋮ The quasi-optimality criterion in the linear functional strategy ⋮ A numerical comparison of some heuristic stopping rules for nonlinear Landweber iteration ⋮ A family of rules for parameter choice in Tikhonov regularization of ill-posed problems with inexact noise level ⋮ Approximation of the Tikhonov regularization parameter through Aitken's extrapolation ⋮ Heuristic Parameter Choice Rules for Tikhonov Regularization with Weakly Bounded Noise ⋮ Unnamed Item ⋮ A simplified L-curve method as error estimator ⋮ Monotonicity of error of regularized solution and its use for parameter choice

Uses Software

• Regularization tools
• ErresTools

Cites Work

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• Comparing parameter choice methods for regularization of ill-posed problems
• On the convergence of the quasioptimality criterion for (iterated) Tikhonov regularization
• Error estimates for linear systems with applications to regularization
• Nonstationary iterated Tikhonov regularization
• Extrapolation techniques for ill-conditioned linear systems
• Regularization tools: A Matlab package for analysis and solution of discrete ill-posed problems
• Multi-parameter regularization techniques for ill-conditioned linear systems
• The discrepancy principle for a class of regularization methods
• On Minimization Strategies for Choice of the Regularization Parameter in Ill-Posed Problems
• On the choice of the regularization parameter in ill-posed problems with approximately given noise level of data
• The quasi-optimality criterion for classical inverse problems
• The convergence of a new heuristic parameter selection criterion for general regularization methods
• EXTRAPOLATION OF TIKHONOV REGULARIZATION METHOD
• ON RULES FOR STOPPING THE CONJUGATE GRADIENT TYPE METHODS IN ILL‐POSED PROBLEMS
• Recent results on the quasi-optimality principle
• Analysis of Discrete Ill-Posed Problems by Means of the L-Curve
• Practical Approximate Solutions to Linear Operator Equations When the Data are Noisy
• A General Heuristic for Choosing the Regularization Parameter in Ill-Posed Problems
• The use of monotonicity for choosing the regularization parameter in ill-posed problems
• NEW RULE FOR CHOICE OF THE REGULARIZATION PARAMETER IN (ITERATED) TIKHONOV METHOD
• Heuristic Parameter-Choice Rules for Convex Variational Regularization Based on Error Estimates
• Use of extrapolation in regularization methods

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