Efficient estimation of regularization parameters via downsampling and the singular value expansion, downsampling regularization parameter estimation

DOI10.1007/s10543-016-0637-6zbMath1367.65061arXiv1311.0398OpenAlexW3121632954MaRDI QIDQ2359760

Yang Wang, Michael Horst, Douglas Cochran, Rosemary A. Renaut, Jakob K. Hansen

Publication date: 22 June 2017

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1311.0398

zbMATH Keywords

Galerkin methodnumerical resultssingular value decompositionTikhonov regularizationdiscrepancy principlegeneralized cross validationill-posed integral equationill-posed inverse problemsingular value expansionregularization parameter estimation

Mathematics Subject Classification ID

Numerical solutions to overdetermined systems, pseudoinverses (65F20) Ill-posedness and regularization problems in numerical linear algebra (65F22) Numerical methods for integral equations (65R20) Numerical methods for ill-posed problems for integral equations (65R30) Fredholm integral equations (45B05) Numerical methods for inverse problems for integral equations (65R32)

Related Items (4)

Determination of regularization parameter via solving a multi-objective optimization problem ⋮ Unbiased predictive risk estimation of the Tikhonov regularization parameter: convergence with increasing rank approximations of the singular value decomposition ⋮ Joint inversion of compact operators ⋮ An efficient Gauss-Newton algorithm for solving regularized total least squares problems

Uses Software

• LSQR
• Regularization tools
• UTV

Cites Work

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• Tikhonov regularization based on generalized Krylov subspace methods
• A weighted-GCV method for Lanczos-hybrid regularization
• Noise propagation in regularizing iterations for image deblurring
• Iterative regularization with minimum-residual methods
• Computation of the singular value expansion
• Functional partial canonical correlation
• Discontinuous parameter estimates with least squares estimators
• Regularization parameter estimation for large-scale Tikhonov regularization using a priori information
• The regularizing effect of the Golub-Kahan iterative bidiagonalization and revealing the noise level in the data
• Embedded techniques for choosing the parameter in Tikhonov regularization
• Windowed Spectral Regularization of Inverse Problems
• Deblurring Images
• A Newton root-finding algorithm for estimating the regularization parameter for solving ill-conditioned least squares problems
• Generalized Cross-Validation as a Method for Choosing a Good Ridge Parameter
• LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
• Multi-Parameter Regularization Methods for High-Resolution Image Reconstruction With Displacement Errors
• Computational Methods for Inverse Problems
• Linear integral equations
• An introduction to the mathematical theory of inverse problems

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