Symmetrization techniques in image deblurring

Marco Donatelli, Paola Ferrari, Silvia Gazzola

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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 languageEnglish
Pages (from-to)157-178
Number of pages22
JournalElectronic Transactions on Numerical Analysis
Volume59
Early online date5 Oct 2023
DOIs
Publication statusPublished - 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).

FundersFunder number
Gruppo Nazionale per il Calcolo Scientifico

    Keywords

    • Krylov subspace methods
    • Toeplitz matrices
    • inverse problems
    • preconditioning
    • regularization

    ASJC Scopus subject areas

    • Analysis
    • Applied Mathematics

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