A doubly sparse and low-patch-rank prior model for image restoration
•A unified doubly sparse and low-patch-rank prior model including two complementary sparse terms and one nuclear norm term.•A new low-patch-rank minimization model without total variation regularization.•An implementable three-block alternating minimization algorithm with global convergence and O(1/...
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| Veröffentlicht in: | Applied mathematical modelling Jg. 112; S. 786 - 799 |
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01.12.2022
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| Abstract | •A unified doubly sparse and low-patch-rank prior model including two complementary sparse terms and one nuclear norm term.•A new low-patch-rank minimization model without total variation regularization.•An implementable three-block alternating minimization algorithm with global convergence and O(1/k) convergence rate.•An extra sparse term under discrete cosine transform is able to improve the performance of the model on image restoration.
Image restoration is a core problem in computer vision and image processing. In this paper, we introduce a unified low-patch-rank minimization model, which possesses one nuclear norm regularization term promoting the low-patch-rankness, and two sparse regularization terms including the classical total variation (TV) norm and a general sparse term under certain transform such as discrete cosine transform. By setting balancing parameters, our unified model reduces to the classical TV-regularized low-patch-rank minimization model and yields a new non-TV-regularized low-patch-rank prior image restoration model. Due to the multi-block structure of the model, we introduce a three-block alternating minimization algorithm to find approximate solutions of the proposed models. A series of computational results on image inpainting and deblurring further show that our approaches are reliable to recover high-quality images from degraded ones. |
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| AbstractList | •A unified doubly sparse and low-patch-rank prior model including two complementary sparse terms and one nuclear norm term.•A new low-patch-rank minimization model without total variation regularization.•An implementable three-block alternating minimization algorithm with global convergence and O(1/k) convergence rate.•An extra sparse term under discrete cosine transform is able to improve the performance of the model on image restoration.
Image restoration is a core problem in computer vision and image processing. In this paper, we introduce a unified low-patch-rank minimization model, which possesses one nuclear norm regularization term promoting the low-patch-rankness, and two sparse regularization terms including the classical total variation (TV) norm and a general sparse term under certain transform such as discrete cosine transform. By setting balancing parameters, our unified model reduces to the classical TV-regularized low-patch-rank minimization model and yields a new non-TV-regularized low-patch-rank prior image restoration model. Due to the multi-block structure of the model, we introduce a three-block alternating minimization algorithm to find approximate solutions of the proposed models. A series of computational results on image inpainting and deblurring further show that our approaches are reliable to recover high-quality images from degraded ones. |
| Author | He, Hongjin Zhao, Lulu |
| Author_xml | – sequence: 1 givenname: Hongjin orcidid: 0000-0001-7672-4943 surname: He fullname: He, Hongjin email: hehongjin@nbu.edu.cn organization: School of Mathematics and Statistics, Ningbo University, Ningbo 315211, China – sequence: 2 givenname: Lulu surname: Zhao fullname: Zhao, Lulu email: zhllu01@163.com organization: School of Mathematics and Statistics, Fuzhou University, Fuzhou 350108, China |
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| Cites_doi | 10.1109/TIP.2003.819861 10.1016/j.jfranklin.2017.01.037 10.1007/s10589-015-9770-4 10.1109/TIP.2014.2299067 10.1109/JPROC.2009.2024776 10.1007/s10107-014-0826-5 10.1007/s10589-018-9994-1 10.1109/TIP.2017.2678798 10.1137/05064182X 10.1137/080738970 10.1137/110854989 10.1109/TIP.2005.859376 10.1007/s10107-016-1057-8 10.1007/s13675-015-0048-5 10.1016/j.image.2021.116308 10.1109/MSP.2013.2273004 10.1016/j.acha.2005.03.005 10.1137/110822347 10.1007/s00211-009-0222-x 10.1090/S0894-0347-2012-00740-1 10.1137/080725891 10.1137/130922793 10.1017/S096249291600009X 10.1007/s10444-015-9408-1 10.1007/s10444-017-9574-4 10.1016/0167-2789(92)90242-F 10.1007/s10851-014-0510-7 10.1109/TIP.2005.863057 10.1109/TIP.2013.2246520 |
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| Keywords | Total variation Image inpainting Image deblurring Low-patch-rank Alternating minimization algorithm Discrete cosine transform |
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| Snippet | •A unified doubly sparse and low-patch-rank prior model including two complementary sparse terms and one nuclear norm term.•A new low-patch-rank minimization... |
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| SubjectTerms | Alternating minimization algorithm Discrete cosine transform Image deblurring Image inpainting Low-patch-rank Total variation |
| Title | A doubly sparse and low-patch-rank prior model for image restoration |
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