New Robust PCA for Outliers and Heavy Sparse Noises’ Detection via Affine Transformation, the L∗,w and L2,1 Norms, and Spatial Weight Matrix in High-Dimensional Images: From the Perspective of Signal Processing
In this paper, we propose a novel robust algorithm for image recovery via affine transformations, the weighted nuclear, L∗,w, and the L2,1 norms. The new method considers the spatial weight matrix to account the correlated samples in the data, the L2,1 norm to tackle the dilemma of extreme values in...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2021/3047712 |
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| author | Peidong Liang Habte Tadesse Likassa Chentao Zhang Jielong Guo |
| author_facet | Peidong Liang Habte Tadesse Likassa Chentao Zhang Jielong Guo |
| author_sort | Peidong Liang |
| collection | DOAJ |
| description | In this paper, we propose a novel robust algorithm for image recovery via affine transformations, the weighted nuclear, L∗,w, and the L2,1 norms. The new method considers the spatial weight matrix to account the correlated samples in the data, the L2,1 norm to tackle the dilemma of extreme values in the high-dimensional images, and the L∗,w norm newly added to alleviate the potential effects of outliers and heavy sparse noises, enabling the new approach to be more resilient to outliers and large variations in the high-dimensional images in signal processing. The determination of the parameters is involved, and the affine transformations are cast as a convex optimization problem. To mitigate the computational complexity, alternating iteratively reweighted direction method of multipliers (ADMM) method is utilized to derive a new set of recursive equations to update the optimization variables and the affine transformations iteratively in a round-robin manner. The new algorithm is superior to the state-of-the-art works in terms of accuracy on various public databases. |
| format | Article |
| id | doaj-art-4098645d522c47d08ae9f491bef8bb77 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-4098645d522c47d08ae9f491bef8bb772025-02-03T07:23:29ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252021-01-01202110.1155/2021/30477123047712New Robust PCA for Outliers and Heavy Sparse Noises’ Detection via Affine Transformation, the L∗,w and L2,1 Norms, and Spatial Weight Matrix in High-Dimensional Images: From the Perspective of Signal ProcessingPeidong Liang0Habte Tadesse Likassa1Chentao Zhang2Jielong Guo3Fujian (Quanzhou)-HIT Research Institute of Engineering and Technology, Quanzhou 362000, ChinaDepartment of Statistics, College of Natural and Computational Sciences, Addis Ababa University, Addis Ababa, EthiopiaFujian (Quanzhou)-HIT Research Institute of Engineering and Technology, Quanzhou 362000, ChinaFujian Institute of Research on the Structure of Matter Fuzhou, Chinese Academy of Sciences, Fuzhou, ChinaIn this paper, we propose a novel robust algorithm for image recovery via affine transformations, the weighted nuclear, L∗,w, and the L2,1 norms. The new method considers the spatial weight matrix to account the correlated samples in the data, the L2,1 norm to tackle the dilemma of extreme values in the high-dimensional images, and the L∗,w norm newly added to alleviate the potential effects of outliers and heavy sparse noises, enabling the new approach to be more resilient to outliers and large variations in the high-dimensional images in signal processing. The determination of the parameters is involved, and the affine transformations are cast as a convex optimization problem. To mitigate the computational complexity, alternating iteratively reweighted direction method of multipliers (ADMM) method is utilized to derive a new set of recursive equations to update the optimization variables and the affine transformations iteratively in a round-robin manner. The new algorithm is superior to the state-of-the-art works in terms of accuracy on various public databases.http://dx.doi.org/10.1155/2021/3047712 |
| spellingShingle | Peidong Liang Habte Tadesse Likassa Chentao Zhang Jielong Guo New Robust PCA for Outliers and Heavy Sparse Noises’ Detection via Affine Transformation, the L∗,w and L2,1 Norms, and Spatial Weight Matrix in High-Dimensional Images: From the Perspective of Signal Processing International Journal of Mathematics and Mathematical Sciences |
| title | New Robust PCA for Outliers and Heavy Sparse Noises’ Detection via Affine Transformation, the L∗,w and L2,1 Norms, and Spatial Weight Matrix in High-Dimensional Images: From the Perspective of Signal Processing |
| title_full | New Robust PCA for Outliers and Heavy Sparse Noises’ Detection via Affine Transformation, the L∗,w and L2,1 Norms, and Spatial Weight Matrix in High-Dimensional Images: From the Perspective of Signal Processing |
| title_fullStr | New Robust PCA for Outliers and Heavy Sparse Noises’ Detection via Affine Transformation, the L∗,w and L2,1 Norms, and Spatial Weight Matrix in High-Dimensional Images: From the Perspective of Signal Processing |
| title_full_unstemmed | New Robust PCA for Outliers and Heavy Sparse Noises’ Detection via Affine Transformation, the L∗,w and L2,1 Norms, and Spatial Weight Matrix in High-Dimensional Images: From the Perspective of Signal Processing |
| title_short | New Robust PCA for Outliers and Heavy Sparse Noises’ Detection via Affine Transformation, the L∗,w and L2,1 Norms, and Spatial Weight Matrix in High-Dimensional Images: From the Perspective of Signal Processing |
| title_sort | new robust pca for outliers and heavy sparse noises detection via affine transformation the l∗ w and l2 1 norms and spatial weight matrix in high dimensional images from the perspective of signal processing |
| url | http://dx.doi.org/10.1155/2021/3047712 |
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