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New Robust PCA for Outliers and Heavy Sparse Noises' Detection via Affine Transformation, the Lā,w and L2,1 Norms, and Spatial Weight Matrix in High-Dimensional Images: From the Perspective of Signal Processing.
- Source :
-
International Journal of Mathematics & Mathematical Sciences . 9/28/2021, p1-9. 9p. - Publication Year :
- 2021
-
Abstract
- In this paper, we propose a novel robust algorithm for image recovery via affine transformations, the weighted nuclear, L ā , w , and the L 2,1 norms. The new method considers the spatial weight matrix to account the correlated samples in the data, the L 2,1 norm to tackle the dilemma of extreme values in the high-dimensional images, and the L ā , 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 01611712
- Database :
- Academic Search Index
- Journal :
- International Journal of Mathematics & Mathematical Sciences
- Publication Type :
- Academic Journal
- Accession number :
- 152680914
- Full Text :
- https://doi.org/10.1155/2021/3047712