Near-Optimal Spectral Filtering and Error Estimation for Solving Ill-Posed Problems

DOI10.1137/15M1019581zbMath1329.65084OpenAlexW2210031132MaRDI QIDQ3457834

Dianne P. O'Leary, Viktoria Taroudaki

Publication date: 18 December 2015

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/15m1019581

zbMATH Keywords

inverse problemregularizationsingular value decompositionspectral filtererror estimateTikhonov regularizationill-posed problemdeconvolutionparameter selectionuncertainty quantificationtruncated SVDTikhonov filterspline filterHeaviside filterKronecker approximationtruncated singular component method

Mathematics Subject Classification ID

Numerical solutions to overdetermined systems, pseudoinverses (65F20) Ill-posedness and regularization problems in numerical linear algebra (65F22)

Related Items

Near-Optimal Spectral Filtering and Error Estimation for Solving Ill-Posed Problems ⋮ Learning regularization parameters for general-form Tikhonov ⋮ Learning spectral windowing parameters for regularization using unbiased predictive risk and generalized cross validation techniques for multiple data sets ⋮ Estimation of the Regularization Parameter in Linear Discrete Ill-Posed Problems Using the Picard Parameter ⋮ Unbiased predictive risk estimation of the Tikhonov regularization parameter: convergence with increasing rank approximations of the singular value decomposition

Cites Work

• Unnamed Item
• Nonlinear total variation based noise removal algorithms
• A new Tikhonov regularization method
• The discrete Picard condition for discrete ill-posed problems
• Near-Optimal Parameters for Tikhonov and Other Regularization Methods
• Deblurring Images
• Near-Optimal Spectral Filtering and Error Estimation for Solving Ill-Posed Problems
• Generalized Cross-Validation as a Method for Choosing a Good Ridge Parameter
• Restoring Images Degraded by Spatially Variant Blur
• A Test for Normality of Observations and Regression Residuals
• A Framework for Regularization via Operator Approximation
• A Numerical Method for Solving Fredholm Integral Equations of the First Kind Using Singular Values
• An omnibus test of normality for moderate and large size samples
• A NEW MEASURE OF RANK CORRELATION
• The Kolmogorov-Smirnov Test for Goodness of Fit
• Nonparametric Tests Against Trend