Cross-validation and other criteria for estimating the regularizing parameter
- 1 January 1991
- conference paper
- Published by Institute of Electrical and Electronics Engineers (IEEE)
- No. 15206149,p. 3021-3024 vol.4
- https://doi.org/10.1109/icassp.1991.151039
Abstract
The application of regularization to ill-conditioned problems necessitates the choice of a regularizing parameter which trades fidelity to the data for smoothness of the solution. Methods based on the properties of the residuals and on the generalized cross-validation have been proposed for estimating the regularizing parameter. Alternative methods to compute the regularizing parameter are proposed. The resulting values of the regularizing parameter are compared with the values obtained from the above-mentioned methods. Furthermore, it is shown that under certain conditions all the above-mentioned methods result in the same value for the regularizing parameter. Experimental results are presented which verify theoretical results.Keywords
This publication has 11 references indexed in Scilit:
- Optimal estimation of the regularization parameter and stabilizing functional for regularized image restorationOptical Engineering, 1990
- Spline Models for Observational DataPublished by Society for Industrial & Applied Mathematics (SIAM) ,1990
- Image reconstruction and restoration: overview of common estimation structures and problemsIEEE Transactions on Acoustics, Speech, and Signal Processing, 1989
- Iterative Image Restoration AlgorithmsOptical Engineering, 1989
- Optimal estimation of contour properties by cross-validated regularizationPublished by Institute of Electrical and Electronics Engineers (IEEE) ,1989
- Bayesian Confidence Intervals for Smoothing SplinesJournal of the American Statistical Association, 1988
- Generalized Cross-Validation as a Method for Choosing a Good Ridge ParameterTechnometrics, 1979
- Smoothing noisy data with spline functionsNumerische Mathematik, 1978
- Practical Approximate Solutions to Linear Operator Equations When the Data are NoisySIAM Journal on Numerical Analysis, 1977
- The Application of Constrained Least Squares Estimation to Image Restoration by Digital ComputerIEEE Transactions on Computers, 1973