Quaternion Matrix Factorization for Low-Rank Quaternion Matrix Completion
The main aim of this paper is to study quaternion matrix factorization for low-rank quaternion matrix completion and its applications in color image processing. For the real-world color images, we proposed a novel model called low-rank quaternion matrix completion (LRQC), which adds total variation...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-05-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/9/2144 |
| _version_ | 1797602191739977728 |
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| author | Jiang-Feng Chen Qing-Wen Wang Guang-Jing Song Tao Li |
| author_facet | Jiang-Feng Chen Qing-Wen Wang Guang-Jing Song Tao Li |
| author_sort | Jiang-Feng Chen |
| collection | DOAJ |
| description | The main aim of this paper is to study quaternion matrix factorization for low-rank quaternion matrix completion and its applications in color image processing. For the real-world color images, we proposed a novel model called low-rank quaternion matrix completion (LRQC), which adds total variation and Tikhonov regularization to the factor quaternion matrices to preserve the spatial/temporal smoothness. Moreover, a proximal alternating minimization (PAM) algorithm was proposed to tackle the corresponding optimal problem. Numerical results on color images indicate the advantages of our method. |
| first_indexed | 2024-03-11T04:13:34Z |
| format | Article |
| id | doaj.art-cf66702097c64d53829043287d3e5f7c |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T04:13:34Z |
| publishDate | 2023-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-cf66702097c64d53829043287d3e5f7c2023-11-17T23:20:35ZengMDPI AGMathematics2227-73902023-05-01119214410.3390/math11092144Quaternion Matrix Factorization for Low-Rank Quaternion Matrix CompletionJiang-Feng Chen0Qing-Wen Wang1Guang-Jing Song2Tao Li3Department of Mathematics, Shanghai University, Shanghai 200444, ChinaDepartment of Mathematics, Shanghai University, Shanghai 200444, ChinaSchool of Mathematics and Information Sciences, Weifang University, Weifang 261061, ChinaKey Laboratory of Engineering Modeling and Statistical Computation of Hainan Province, Department of Mathematics, Hainan University, Haikou 570228, ChinaThe main aim of this paper is to study quaternion matrix factorization for low-rank quaternion matrix completion and its applications in color image processing. For the real-world color images, we proposed a novel model called low-rank quaternion matrix completion (LRQC), which adds total variation and Tikhonov regularization to the factor quaternion matrices to preserve the spatial/temporal smoothness. Moreover, a proximal alternating minimization (PAM) algorithm was proposed to tackle the corresponding optimal problem. Numerical results on color images indicate the advantages of our method.https://www.mdpi.com/2227-7390/11/9/2144low-rank quaternion matrix factorizationquaternion matrix completionproximal alternating minimizationcolor image restoration |
| spellingShingle | Jiang-Feng Chen Qing-Wen Wang Guang-Jing Song Tao Li Quaternion Matrix Factorization for Low-Rank Quaternion Matrix Completion Mathematics low-rank quaternion matrix factorization quaternion matrix completion proximal alternating minimization color image restoration |
| title | Quaternion Matrix Factorization for Low-Rank Quaternion Matrix Completion |
| title_full | Quaternion Matrix Factorization for Low-Rank Quaternion Matrix Completion |
| title_fullStr | Quaternion Matrix Factorization for Low-Rank Quaternion Matrix Completion |
| title_full_unstemmed | Quaternion Matrix Factorization for Low-Rank Quaternion Matrix Completion |
| title_short | Quaternion Matrix Factorization for Low-Rank Quaternion Matrix Completion |
| title_sort | quaternion matrix factorization for low rank quaternion matrix completion |
| topic | low-rank quaternion matrix factorization quaternion matrix completion proximal alternating minimization color image restoration |
| url | https://www.mdpi.com/2227-7390/11/9/2144 |
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