Estimation of the Regularization Parameter in Linear Discrete Ill-Posed Problems Using the Picard parameter. We present a new approach for determining the regularization parameter for general-form Tikhonov regularization of linear ill-posed problems. In our approach the regularization parameter is found by approximately minimizing the distance between the unknown noiseless data and the data reconstructed from the regularized solution. We obtain the approximation of this distance by employing the Picard parameter to separate the noise from the data in the coordinate system of the generalized SVD. The Picard parameter is found using a simple and reliable algorithm based on successive estimations of the noise variance from the Fourier coefficients of the data. Numerical examples demonstrate the accuracy and efficiency of our method. A MATLAB-based implementation of the proposed algorithms can be found at this https URL: PicardREG: A MATALB package for solving discrete linear ill-posed problems with general-form Tikhonov regularization using the Picard parameter developed by Eitan Levin and Alexander Meltzer. This package supplements the manuscript titled “Estimation of the regularization parameter in linear discrete ill-posed problems using the Picard parameter.
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References in zbMATH (referenced in 5 articles )
Showing results 1 to 5 of 5.
- Zare, Hossein; Hajarian, Masoud: An efficient Gauss-Newton algorithm for solving regularized total least squares problems (2022)
- Benvenuto, Federico; Jin, Bangti: A parameter choice rule for Tikhonov regularization based on predictive risk (2020)
- Zare, Hossein; Hajarian, Masoud: Determination of regularization parameter via solving a multi-objective optimization problem (2020)
- Renaut, Rosemary A.; Helmstetter, Anthony W.; Vatankhah, Saeed: Unbiased predictive risk estimation of the Tikhonov regularization parameter: convergence with increasing rank approximations of the singular value decomposition (2019)
- Levin, Eitan; Meltzer, Alexander Y.: Estimation of the regularization parameter in linear discrete ill-posed problems using the Picard parameter (2017)