The Application of the Accelerated Proximal Gradient Descent Algorithm for the Solution of the Weighted Schatten-p Norm in Sparse Noise Extraction

In this study, we introduce the weighted Schatten-p norm optimization robust principal component analysis model, transforming the nuclear norm into a combination of the Schatten-p norm and the weighted nuclear norm for enhanced flexibility. We adapt the model for compatibility with the Accelerated P...

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Bibliographic Details
Published in:Circuits, systems, and signal processing Vol. 43; no. 8; pp. 5169 - 5190
Main Authors: Wang, Jiajun, Chen, Jing, Zhu, Quanmin
Format: Journal Article
Language:English
Published: New York Springer US 01.08.2024
Springer Nature B.V
Subjects:
Algorithms
Approximation
Circuits and Systems
Convex analysis
Dimensional analysis
Electrical Engineering
Electronics and Microelectronics
Engineering
Image enhancement
Instrumentation
Lagrange multiplier
Machine learning
Methods
Noise
Optimization
Parameter identification
Principal components analysis
Signal processing
Signal,Image and Speech Processing
RPCA
Accelerated proximal gradient descent algorithm
Weighted nuclear norm
Schatten-p norm
Sparse noise
Low-rank matrix recovery
ISSN:0278-081X, 1531-5878
Online Access:Get full text
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Summary:In this study, we introduce the weighted Schatten-p norm optimization robust principal component analysis model, transforming the nuclear norm into a combination of the Schatten-p norm and the weighted nuclear norm for enhanced flexibility. We adapt the model for compatibility with the Accelerated Proximal gradient descent algorithm (APG) and use APG to solve this new model. In the experimental section, we analyze the algorithm’s adaptability under various conditions through multi-dimensional variation analysis on generated data. Additionally, we assess its practical effectiveness by testing on noisy images for restoration, establishing the proposed method as the most advanced algorithm in terms of performance.
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ISSN:0278-081X
1531-5878
DOI:10.1007/s00034-024-02697-z