Abstract
This paper presents some preconditioning techniques that enhance the performance of iterative regularization methods applied to image deblurring problems determined by a wide variety of point spread functions (PSFs) and boundary conditions. We first consider the anti-identity preconditioner, which symmetrizes the coefficient matrix associated to problems with zero boundary conditions, allowing the use of MINRES as a regularization method. When considering more sophisticated boundary conditions and strongly nonsymmetric PSFs, we show that the anti-identity preconditioner improves the performance of GMRES. We then consider both stationary and iteration-dependent regularizing circulant preconditioners that, applied in connection with the anti-identity matrix and both standard and flexible Krylov subspaces, speed up the iterations. A theoretical result about the clustering of the eigenvalues of the preconditioned matrices is proved in a special case. Extensive numerical experiments show the effectiveness of the new preconditioning techniques, including when the deblurring of sparse images is considered.
Original language | English |
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Pages (from-to) | 157-178 |
Number of pages | 22 |
Journal | Electronic Transactions on Numerical Analysis |
Volume | 59 |
Early online date | 5 Oct 2023 |
DOIs | |
Publication status | Published - 31 Dec 2023 |
Bibliographical note
Acknowledgments. The work of the first and second authors was partially supported by the Gruppo Nazionale per il Calcolo Scientifico (GNCS).Funding
Acknowledgments. The work of the first and second authors was partially supported by the Gruppo Nazionale per il Calcolo Scientifico (GNCS).
Funders | Funder number |
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Gruppo Nazionale per il Calcolo Scientifico |
Keywords
- Krylov subspace methods
- Toeplitz matrices
- inverse problems
- preconditioning
- regularization
ASJC Scopus subject areas
- Analysis
- Applied Mathematics