![Cover Image for System.Linq.Enumerable+EnumerablePartition`1[System.Char]](https://coverimages.igi-global.com/images/search-article.png)
Symmetrization techniques in image deblurring
OAI: oai:purehost.bath.ac.uk:publications/42aa7dc6-6ce3-42b3-adb3-6ed2d6cc6049 • DOI: https://doi.org/10.1553/etna_vol59s157
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.