Efficient preconditioning strategies for accelerating GMRES in block-structured nonlinear systems for image deblurring.
We propose an efficient preconditioning strategy to accelerate the convergence of Krylov subspace methods, specifically for solving complex nonlinear systems with a block five-by-five structure, commonly found in cell-centered finite difference discretizations for image deblurring using mean curvatu...
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| Format: | Article |
| Language: | English |
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Public Library of Science (PLoS)
2025-01-01
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| Series: | PLoS ONE |
| Online Access: | https://doi.org/10.1371/journal.pone.0322146 |
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| _version_ | 1839647553653571584 |
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| author | Rizwan Khalid Shahbaz Ahmad Mohamed Medani Yahia Said Iftikhar Ali |
| author_facet | Rizwan Khalid Shahbaz Ahmad Mohamed Medani Yahia Said Iftikhar Ali |
| author_sort | Rizwan Khalid |
| collection | DOAJ |
| description | We propose an efficient preconditioning strategy to accelerate the convergence of Krylov subspace methods, specifically for solving complex nonlinear systems with a block five-by-five structure, commonly found in cell-centered finite difference discretizations for image deblurring using mean curvature techniques. Our method introduces two innovative preconditioned matrices, analyzed spectrally to show a favorable eigenvalue distribution that accelerates convergence in the Generalized Minimal Residual (GMRES) method. This technique significantly improves image quality, as measured by peak signal-to-noise ratio (PSNR), and demonstrates faster convergence compared to traditional GMRES, requiring minimal CPU time and few iterations for exceptional deblurring performance. The preconditioned matrices' eigenvalues cluster around 1, indicating a beneficial spectral distribution. The source code is available at https://github.com/shahbaz1982/Precondition-Matrix. |
| format | Article |
| id | doaj-art-a5b44b5e9e5c47c892e91f58b76d5bb7 |
| institution | Matheson Library |
| issn | 1932-6203 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Public Library of Science (PLoS) |
| record_format | Article |
| series | PLoS ONE |
| spelling | doaj-art-a5b44b5e9e5c47c892e91f58b76d5bb72025-06-30T05:31:57ZengPublic Library of Science (PLoS)PLoS ONE1932-62032025-01-01206e032214610.1371/journal.pone.0322146Efficient preconditioning strategies for accelerating GMRES in block-structured nonlinear systems for image deblurring.Rizwan KhalidShahbaz AhmadMohamed MedaniYahia SaidIftikhar AliWe propose an efficient preconditioning strategy to accelerate the convergence of Krylov subspace methods, specifically for solving complex nonlinear systems with a block five-by-five structure, commonly found in cell-centered finite difference discretizations for image deblurring using mean curvature techniques. Our method introduces two innovative preconditioned matrices, analyzed spectrally to show a favorable eigenvalue distribution that accelerates convergence in the Generalized Minimal Residual (GMRES) method. This technique significantly improves image quality, as measured by peak signal-to-noise ratio (PSNR), and demonstrates faster convergence compared to traditional GMRES, requiring minimal CPU time and few iterations for exceptional deblurring performance. The preconditioned matrices' eigenvalues cluster around 1, indicating a beneficial spectral distribution. The source code is available at https://github.com/shahbaz1982/Precondition-Matrix.https://doi.org/10.1371/journal.pone.0322146 |
| spellingShingle | Rizwan Khalid Shahbaz Ahmad Mohamed Medani Yahia Said Iftikhar Ali Efficient preconditioning strategies for accelerating GMRES in block-structured nonlinear systems for image deblurring. PLoS ONE |
| title | Efficient preconditioning strategies for accelerating GMRES in block-structured nonlinear systems for image deblurring. |
| title_full | Efficient preconditioning strategies for accelerating GMRES in block-structured nonlinear systems for image deblurring. |
| title_fullStr | Efficient preconditioning strategies for accelerating GMRES in block-structured nonlinear systems for image deblurring. |
| title_full_unstemmed | Efficient preconditioning strategies for accelerating GMRES in block-structured nonlinear systems for image deblurring. |
| title_short | Efficient preconditioning strategies for accelerating GMRES in block-structured nonlinear systems for image deblurring. |
| title_sort | efficient preconditioning strategies for accelerating gmres in block structured nonlinear systems for image deblurring |
| url | https://doi.org/10.1371/journal.pone.0322146 |
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