A new iterative method for a class of linear system arising from image restoration problems
In this paper, by utilizing the matrix properties arising from the image restoration model, a new iterative method for solving the corresponding augmented linear system is proposed. Theoretical results about the convergence properties and computational advantage of the new method are studied in deta...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2021-11-01
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| Series: | Results in Applied Mathematics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2590037421000534 |
| _version_ | 1828948181142994944 |
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| author | Li-Dan Liao Rui-Xia Li Xiang Wang |
| author_facet | Li-Dan Liao Rui-Xia Li Xiang Wang |
| author_sort | Li-Dan Liao |
| collection | DOAJ |
| description | In this paper, by utilizing the matrix properties arising from the image restoration model, a new iterative method for solving the corresponding augmented linear system is proposed. Theoretical results about the convergence properties and computational advantage of the new method are studied in detail, showing that it just involves a matrix–vector product, which can be implemented by fast Fourier transform (FFT) or discrete Cosine transform (DCT) algorithms and can save much computation cost. Numerical experiments are provided, further confirm that our theoretical results is reliable and our method is feasible and effective. |
| first_indexed | 2024-12-14T05:42:17Z |
| format | Article |
| id | doaj.art-061ef15f6f104384b08872e76ccef61e |
| institution | Directory Open Access Journal |
| issn | 2590-0374 |
| language | English |
| last_indexed | 2024-12-14T05:42:17Z |
| publishDate | 2021-11-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Applied Mathematics |
| spelling | doaj.art-061ef15f6f104384b08872e76ccef61e2022-12-21T23:14:58ZengElsevierResults in Applied Mathematics2590-03742021-11-0112100221A new iterative method for a class of linear system arising from image restoration problemsLi-Dan Liao0Rui-Xia Li1Xiang Wang2Department of Mathematics, Nanchang University, Nanchang 330031, PR ChinaSchool of Mathematics and Data Science, Shaanxi University of Science and Technology, Xi’an 710021, PR China; Corresponding author.Department of Mathematics, Nanchang University, Nanchang 330031, PR ChinaIn this paper, by utilizing the matrix properties arising from the image restoration model, a new iterative method for solving the corresponding augmented linear system is proposed. Theoretical results about the convergence properties and computational advantage of the new method are studied in detail, showing that it just involves a matrix–vector product, which can be implemented by fast Fourier transform (FFT) or discrete Cosine transform (DCT) algorithms and can save much computation cost. Numerical experiments are provided, further confirm that our theoretical results is reliable and our method is feasible and effective.http://www.sciencedirect.com/science/article/pii/S2590037421000534Image restorationBoundary conditionsIterative methodConvergenceSpectral properties |
| spellingShingle | Li-Dan Liao Rui-Xia Li Xiang Wang A new iterative method for a class of linear system arising from image restoration problems Results in Applied Mathematics Image restoration Boundary conditions Iterative method Convergence Spectral properties |
| title | A new iterative method for a class of linear system arising from image restoration problems |
| title_full | A new iterative method for a class of linear system arising from image restoration problems |
| title_fullStr | A new iterative method for a class of linear system arising from image restoration problems |
| title_full_unstemmed | A new iterative method for a class of linear system arising from image restoration problems |
| title_short | A new iterative method for a class of linear system arising from image restoration problems |
| title_sort | new iterative method for a class of linear system arising from image restoration problems |
| topic | Image restoration Boundary conditions Iterative method Convergence Spectral properties |
| url | http://www.sciencedirect.com/science/article/pii/S2590037421000534 |
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