New Robust Principal Component Analysis for Joint Image Alignment and Recovery via Affine Transformations, Frobenius and L2,1 Norms
This paper proposes an effective and robust method for image alignment and recovery on a set of linearly correlated data via Frobenius and L2,1 norms. The most popular and successful approach is to model the robust PCA problem as a low-rank matrix recovery problem in the presence of sparse corruptio...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2020/8136384 |
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| author | Habte Tadesse Likassa |
| author_facet | Habte Tadesse Likassa |
| author_sort | Habte Tadesse Likassa |
| collection | DOAJ |
| description | This paper proposes an effective and robust method for image alignment and recovery on a set of linearly correlated data via Frobenius and L2,1 norms. The most popular and successful approach is to model the robust PCA problem as a low-rank matrix recovery problem in the presence of sparse corruption. The existing algorithms still lack in dealing with the potential impact of outliers and heavy sparse noises for image alignment and recovery. Thus, the new algorithm tackles the potential impact of outliers and heavy sparse noises via using novel ideas of affine transformations and Frobenius and L2,1 norms. To attain this, affine transformations and Frobenius and L2,1 norms are incorporated in the decomposition process. As such, the new algorithm is more resilient to errors, outliers, and occlusions. To solve the convex optimization involved, an alternating iterative process is also considered to alleviate the complexity. Conducted simulations on the recovery of face images and handwritten digits demonstrate the effectiveness of the new approach compared with the main state-of-the-art works. |
| format | Article |
| id | doaj-art-717687107ac34cf1adbeaebe1ff012d6 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-717687107ac34cf1adbeaebe1ff012d62025-02-03T06:46:37ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252020-01-01202010.1155/2020/81363848136384New Robust Principal Component Analysis for Joint Image Alignment and Recovery via Affine Transformations, Frobenius and L2,1 NormsHabte Tadesse Likassa0Department of Statistics, Ambo University, Ambo, EthiopiaThis paper proposes an effective and robust method for image alignment and recovery on a set of linearly correlated data via Frobenius and L2,1 norms. The most popular and successful approach is to model the robust PCA problem as a low-rank matrix recovery problem in the presence of sparse corruption. The existing algorithms still lack in dealing with the potential impact of outliers and heavy sparse noises for image alignment and recovery. Thus, the new algorithm tackles the potential impact of outliers and heavy sparse noises via using novel ideas of affine transformations and Frobenius and L2,1 norms. To attain this, affine transformations and Frobenius and L2,1 norms are incorporated in the decomposition process. As such, the new algorithm is more resilient to errors, outliers, and occlusions. To solve the convex optimization involved, an alternating iterative process is also considered to alleviate the complexity. Conducted simulations on the recovery of face images and handwritten digits demonstrate the effectiveness of the new approach compared with the main state-of-the-art works.http://dx.doi.org/10.1155/2020/8136384 |
| spellingShingle | Habte Tadesse Likassa New Robust Principal Component Analysis for Joint Image Alignment and Recovery via Affine Transformations, Frobenius and L2,1 Norms International Journal of Mathematics and Mathematical Sciences |
| title | New Robust Principal Component Analysis for Joint Image Alignment and Recovery via Affine Transformations, Frobenius and L2,1 Norms |
| title_full | New Robust Principal Component Analysis for Joint Image Alignment and Recovery via Affine Transformations, Frobenius and L2,1 Norms |
| title_fullStr | New Robust Principal Component Analysis for Joint Image Alignment and Recovery via Affine Transformations, Frobenius and L2,1 Norms |
| title_full_unstemmed | New Robust Principal Component Analysis for Joint Image Alignment and Recovery via Affine Transformations, Frobenius and L2,1 Norms |
| title_short | New Robust Principal Component Analysis for Joint Image Alignment and Recovery via Affine Transformations, Frobenius and L2,1 Norms |
| title_sort | new robust principal component analysis for joint image alignment and recovery via affine transformations frobenius and l2 1 norms |
| url | http://dx.doi.org/10.1155/2020/8136384 |
| work_keys_str_mv | AT habtetadesselikassa newrobustprincipalcomponentanalysisforjointimagealignmentandrecoveryviaaffinetransformationsfrobeniusandl21norms |