A GCV based Arnoldi-Tikhonov regularization method

2013/03/31 by Paolo Novati, Novati, Paolo, Maria Rosaria Russo +1
Engineering · Mathematics · #Advanced Image Fusion Techniques #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in inverse problems #Statistical and numerical algorithms

paper · pdf · doi:10.48550/arxiv.1304.0148

openalex publication_date 2013/03/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For the solution of linear discrete ill-posed problems, in this paper we consider the Arnoldi-Tikhonov method coupled with the Generalized Cross Validation for the computation of the regularization parameter at each iteration. We study the convergence behavior of the Arnoldi method and its properties for the approximation of the (generalized) singular values, under the hypothesis that Picard condition is satisfied. Numerical experiments on classical test problems and on image restoration are presented.

Citations

• Generalized Cross-Validation as a Method for Choosing a Good Ridge Parameter
• The discrete picard condition for discrete ill-posed problems

Related

• Embedded techniques for choosing the parameter in Tikhonov regularization
• Convergence analysis and parameter estimation for the iterated Arnoldi-Tikhonov method
• Arnoldi decomposition, GMRES, and preconditioning for linear discrete\n ill-posed problems
• Preconditioning linear systems via matrix function evaluation
• Improved parameter selection strategy for the iterated Arnoldi-Tikhonov method