Color Image Recovery Using Generalized Matrix Completion over Higher-Order Finite Dimensional Algebra
To improve the accuracy of color image completion with missing entries, we present a recovery method based on generalized higher-order scalars. We extend the traditional second-order matrix model to a more comprehensive higher-order matrix equivalent, called the “t-matrix” model, which incorporates...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-10-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/12/10/954 |
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| author | Liang Liao Zhuang Guo Qi Gao Yan Wang Fajun Yu Qifeng Zhao Stephen John Maybank Zhoufeng Liu Chunlei Li Lun Li |
| author_facet | Liang Liao Zhuang Guo Qi Gao Yan Wang Fajun Yu Qifeng Zhao Stephen John Maybank Zhoufeng Liu Chunlei Li Lun Li |
| author_sort | Liang Liao |
| collection | DOAJ |
| description | To improve the accuracy of color image completion with missing entries, we present a recovery method based on generalized higher-order scalars. We extend the traditional second-order matrix model to a more comprehensive higher-order matrix equivalent, called the “t-matrix” model, which incorporates a pixel neighborhood expansion strategy to characterize the local pixel constraints. This “t-matrix” model is then used to extend some commonly used matrix and tensor completion algorithms to their higher-order versions. We perform extensive experiments on various algorithms using simulated data and publicly available images. The results show that our generalized matrix completion model and the corresponding algorithm compare favorably with their lower-order tensor and conventional matrix counterparts. |
| first_indexed | 2024-03-10T21:26:54Z |
| format | Article |
| id | doaj.art-e7f0c19eb3ce4d008172a18a95ad54a2 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-10T21:26:54Z |
| publishDate | 2023-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-e7f0c19eb3ce4d008172a18a95ad54a22023-11-19T15:38:25ZengMDPI AGAxioms2075-16802023-10-01121095410.3390/axioms12100954Color Image Recovery Using Generalized Matrix Completion over Higher-Order Finite Dimensional AlgebraLiang Liao0Zhuang Guo1Qi Gao2Yan Wang3Fajun Yu4Qifeng Zhao5Stephen John Maybank6Zhoufeng Liu7Chunlei Li8Lun Li9School of Electronics and Information, Zhongyuan University of Technology, Zhengzhou 451191, ChinaSchool of Electronics and Information, Zhongyuan University of Technology, Zhengzhou 451191, ChinaSchool of Electronics and Information, Zhongyuan University of Technology, Zhengzhou 451191, ChinaSchool of Electronics and Information, Zhongyuan University of Technology, Zhengzhou 451191, ChinaSchool of Electronics and Information, Zhongyuan University of Technology, Zhengzhou 451191, ChinaSchool of Electronics and Information, Zhongyuan University of Technology, Zhengzhou 451191, ChinaBirkbeck College, University of London, London WC1E 7HY, UKSchool of Electronics and Information, Zhongyuan University of Technology, Zhengzhou 451191, ChinaSchool of Electronics and Information, Zhongyuan University of Technology, Zhengzhou 451191, ChinaSchool of Information Engineering, Zhengzhou University, Zhengzhou 450001, ChinaTo improve the accuracy of color image completion with missing entries, we present a recovery method based on generalized higher-order scalars. We extend the traditional second-order matrix model to a more comprehensive higher-order matrix equivalent, called the “t-matrix” model, which incorporates a pixel neighborhood expansion strategy to characterize the local pixel constraints. This “t-matrix” model is then used to extend some commonly used matrix and tensor completion algorithms to their higher-order versions. We perform extensive experiments on various algorithms using simulated data and publicly available images. The results show that our generalized matrix completion model and the corresponding algorithm compare favorably with their lower-order tensor and conventional matrix counterparts.https://www.mdpi.com/2075-1680/12/10/954higher-order tensor completionpixel neighborhood strategygeneralized matrix modellow rankfinite-dimensional algebraconvex optimization |
| spellingShingle | Liang Liao Zhuang Guo Qi Gao Yan Wang Fajun Yu Qifeng Zhao Stephen John Maybank Zhoufeng Liu Chunlei Li Lun Li Color Image Recovery Using Generalized Matrix Completion over Higher-Order Finite Dimensional Algebra Axioms higher-order tensor completion pixel neighborhood strategy generalized matrix model low rank finite-dimensional algebra convex optimization |
| title | Color Image Recovery Using Generalized Matrix Completion over Higher-Order Finite Dimensional Algebra |
| title_full | Color Image Recovery Using Generalized Matrix Completion over Higher-Order Finite Dimensional Algebra |
| title_fullStr | Color Image Recovery Using Generalized Matrix Completion over Higher-Order Finite Dimensional Algebra |
| title_full_unstemmed | Color Image Recovery Using Generalized Matrix Completion over Higher-Order Finite Dimensional Algebra |
| title_short | Color Image Recovery Using Generalized Matrix Completion over Higher-Order Finite Dimensional Algebra |
| title_sort | color image recovery using generalized matrix completion over higher order finite dimensional algebra |
| topic | higher-order tensor completion pixel neighborhood strategy generalized matrix model low rank finite-dimensional algebra convex optimization |
| url | https://www.mdpi.com/2075-1680/12/10/954 |
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