Transactions of Nanjing University of Aeronautics & Astronautics
Arnoldi Projection Fractional Tikhonov for Large Scale Ill-Posed Problems
- Article
- Figures
- Metrics
- Preview PDF
- Reference
- Related
- Cited by
- Materials
Abstract:
It is well known that Tikhonov regularization in standard form may determine approximate solutions that are too smooth for ill-posed problems, so fractional Tikhonov methods have been introduced to remedy this shortcoming. And Tikhonov regularization for large-scale linear ill-posed problems is commonly implemented by determining a partial Arnoldi decomposition of the given matrix. In this paper, we propose a new method to compute an approximate solution of large scale linear discrete ill-posed problems which applies projection fractional Tikhonov regularization in Krylov subspace via Arnoldi process. The projection fractional Tikhonov regularization combines the fractional matrices and orthogonal projection operators. A suitable value of the regularization parameter is determined by the discrepancy principle. Numerical examples with application to image restoration are carried out to examine that the performance of the method.
Keywords:
Project Supported:
This work was supported by the National Natural Science Foundations of China (Nos.11571171 and 61473148).
Clc Number:
CHINA AERO-SCIENCES
Mobile website
