Efficient Algorithm for Isotropic and Anisotropic Total Variation Deblurring and Denoising
A new deblurring and denoising algorithm is proposed, for isotropic total variation-based image restoration. The algorithm consists of an efficient solver for the nonlinear system and an acceleration strategy for the outer iteration. For the nonlinear system, the split Bregman method is used to conv...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/797239 |
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| _version_ | 1832555562424860672 |
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| author | Yuying Shi Qianshun Chang |
| author_facet | Yuying Shi Qianshun Chang |
| author_sort | Yuying Shi |
| collection | DOAJ |
| description | A new deblurring and denoising algorithm is proposed, for isotropic total variation-based image restoration. The algorithm consists of an efficient solver for the nonlinear system and an acceleration strategy for the outer iteration. For the nonlinear system, the split Bregman method is used to convert it into linear system, and an algebraic multigrid method is applied to solve the linearized system. For the outer iteration, we have conducted formal convergence analysis to determine an auxiliary linear term that significantly stabilizes and accelerates the outer iteration. Numerical experiments demonstrate that our algorithm for deblurring and denoising problems is efficient. |
| format | Article |
| id | doaj-art-c5430189f09940b191e33ef61b15d41b |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-c5430189f09940b191e33ef61b15d41b2025-02-03T05:47:52ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/797239797239Efficient Algorithm for Isotropic and Anisotropic Total Variation Deblurring and DenoisingYuying Shi0Qianshun Chang1Department of Mathematics and Physics, North China Electric Power University, Beijing 102206, ChinaInstitute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, ChinaA new deblurring and denoising algorithm is proposed, for isotropic total variation-based image restoration. The algorithm consists of an efficient solver for the nonlinear system and an acceleration strategy for the outer iteration. For the nonlinear system, the split Bregman method is used to convert it into linear system, and an algebraic multigrid method is applied to solve the linearized system. For the outer iteration, we have conducted formal convergence analysis to determine an auxiliary linear term that significantly stabilizes and accelerates the outer iteration. Numerical experiments demonstrate that our algorithm for deblurring and denoising problems is efficient.http://dx.doi.org/10.1155/2013/797239 |
| spellingShingle | Yuying Shi Qianshun Chang Efficient Algorithm for Isotropic and Anisotropic Total Variation Deblurring and Denoising Journal of Applied Mathematics |
| title | Efficient Algorithm for Isotropic and Anisotropic Total Variation Deblurring and Denoising |
| title_full | Efficient Algorithm for Isotropic and Anisotropic Total Variation Deblurring and Denoising |
| title_fullStr | Efficient Algorithm for Isotropic and Anisotropic Total Variation Deblurring and Denoising |
| title_full_unstemmed | Efficient Algorithm for Isotropic and Anisotropic Total Variation Deblurring and Denoising |
| title_short | Efficient Algorithm for Isotropic and Anisotropic Total Variation Deblurring and Denoising |
| title_sort | efficient algorithm for isotropic and anisotropic total variation deblurring and denoising |
| url | http://dx.doi.org/10.1155/2013/797239 |
| work_keys_str_mv | AT yuyingshi efficientalgorithmforisotropicandanisotropictotalvariationdeblurringanddenoising AT qianshunchang efficientalgorithmforisotropicandanisotropictotalvariationdeblurringanddenoising |