Tikhonov regularization is commonly used for the solution of linear discrete ill-posed problems with error-contaminated data. A regularization parameter, that determines the quality of the computed solution, has to be chosen. One of the most popular approaches to choosing this parameter is to minimize the Generalized Cross Validation (GCV) function. We will present two fairly inexpensive ways to determine upper and lower bounds for the numerator and denominator of the GCV function for large matrices.

This presentation is part of Minisymposium “MS34 - Numerical Linear Algebra techniques for Image Restoration and Reconstruction (2 parts)”
organized by: Caterina Fenu (University of Cagliari) , Marco Donatelli (University of Insubria) .

Authors:

Caterina Fenu (University of Cagliari)

Giuseppe Rodriguez (University of Cagliari)

Lothar Reichel (Kent State University)

Hassane Sadok (Université du Littoral Côte d'Opale)

Keywords:

inverse problems, numerical linear algebra