Performance of relaxed iterative methods for image deblurring problems
In this paper, we consider performance of relaxation iterative methods for four types of image deblurring problems with different regularization terms. We first study how to apply relaxation iterative methods efficiently to the Tikhonov regularization problems, and then we propose how to find good p...
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| Format: | Article |
| Language: | English |
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SAGE Publishing
2019-07-01
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| Series: | Journal of Algorithms & Computational Technology |
| Online Access: | https://doi.org/10.1177/1748302619861732 |
| _version_ | 1828758463242567680 |
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| author | Jae H Yun |
| author_facet | Jae H Yun |
| author_sort | Jae H Yun |
| collection | DOAJ |
| description | In this paper, we consider performance of relaxation iterative methods for four types of image deblurring problems with different regularization terms. We first study how to apply relaxation iterative methods efficiently to the Tikhonov regularization problems, and then we propose how to find good preconditioners and near optimal relaxation parameters which are essential factors for fast convergence rate and computational efficiency of relaxation iterative methods. We next study efficient applications of relaxation iterative methods to Split Bregman method and the fixed point method for solving the L1-norm or total variation regularization problems. Lastly, we provide numerical experiments for four types of image deblurring problems to evaluate the efficiency of relaxation iterative methods by comparing their performances with those of Krylov subspace iterative methods. Numerical experiments show that the proposed techniques for finding preconditioners and near optimal relaxation parameters of relaxation iterative methods work well for image deblurring problems. For the L1-norm and total variation regularization problems, Split Bregman and fixed point methods using relaxation iterative methods perform quite well in terms of both peak signal to noise ratio values and execution time as compared with those using Krylov subspace methods. |
| first_indexed | 2024-12-11T00:42:22Z |
| format | Article |
| id | doaj.art-b6b567a5244c48df81d3f554028e3e92 |
| institution | Directory Open Access Journal |
| issn | 1748-3026 |
| language | English |
| last_indexed | 2024-12-11T00:42:22Z |
| publishDate | 2019-07-01 |
| publisher | SAGE Publishing |
| record_format | Article |
| series | Journal of Algorithms & Computational Technology |
| spelling | doaj.art-b6b567a5244c48df81d3f554028e3e922022-12-22T01:26:52ZengSAGE PublishingJournal of Algorithms & Computational Technology1748-30262019-07-011310.1177/1748302619861732Performance of relaxed iterative methods for image deblurring problemsJae H YunIn this paper, we consider performance of relaxation iterative methods for four types of image deblurring problems with different regularization terms. We first study how to apply relaxation iterative methods efficiently to the Tikhonov regularization problems, and then we propose how to find good preconditioners and near optimal relaxation parameters which are essential factors for fast convergence rate and computational efficiency of relaxation iterative methods. We next study efficient applications of relaxation iterative methods to Split Bregman method and the fixed point method for solving the L1-norm or total variation regularization problems. Lastly, we provide numerical experiments for four types of image deblurring problems to evaluate the efficiency of relaxation iterative methods by comparing their performances with those of Krylov subspace iterative methods. Numerical experiments show that the proposed techniques for finding preconditioners and near optimal relaxation parameters of relaxation iterative methods work well for image deblurring problems. For the L1-norm and total variation regularization problems, Split Bregman and fixed point methods using relaxation iterative methods perform quite well in terms of both peak signal to noise ratio values and execution time as compared with those using Krylov subspace methods.https://doi.org/10.1177/1748302619861732 |
| spellingShingle | Jae H Yun Performance of relaxed iterative methods for image deblurring problems Journal of Algorithms & Computational Technology |
| title | Performance of relaxed iterative methods for image deblurring problems |
| title_full | Performance of relaxed iterative methods for image deblurring problems |
| title_fullStr | Performance of relaxed iterative methods for image deblurring problems |
| title_full_unstemmed | Performance of relaxed iterative methods for image deblurring problems |
| title_short | Performance of relaxed iterative methods for image deblurring problems |
| title_sort | performance of relaxed iterative methods for image deblurring problems |
| url | https://doi.org/10.1177/1748302619861732 |
| work_keys_str_mv | AT jaehyun performanceofrelaxediterativemethodsforimagedeblurringproblems |