Low-Rank Approximation via Generalized Reweighted Iterative Nuclear and Frobenius Norms

The low-rank approximation problem has recently attracted wide concern due to its excellent performance in realworld applications such as image restoration, traffic monitoring, and face recognition. Compared with the classic nuclear norm, the Schatten-p norm is stated to be a closer approximation to...

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Bibliographic Details
Published in:IEEE transactions on image processing Vol. 29; pp. 2244 - 2257
Main Authors: Huang, Yan, Liao, Guisheng, Xiang, Yijian, Zhang, Lei, Li, Jie, Nehorai, Arye
Format: Journal Article
Language:English
Published: United States IEEE 01.01.2020
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Approximation
Approximation algorithms
Face recognition
generalized iterative reweighted Frobenius norm (GIRFN)
generalized iterative reweighted nuclear norm (GIRNN)
Image decomposition
Image restoration
Iterative algorithms
Iterative methods
Low-rank approximation problem
matrix completion (MC)
Matrix decomposition
Matrix methods
Minimization
Norms
Object recognition
Optimization
Principal component analysis
Principal components analysis
robust principal component analysis (RPCA)
Robustness (mathematics)
Sparse matrices
ISSN:1057-7149, 1941-0042, 1941-0042
Online Access:Get full text
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Summary:The low-rank approximation problem has recently attracted wide concern due to its excellent performance in realworld applications such as image restoration, traffic monitoring, and face recognition. Compared with the classic nuclear norm, the Schatten-p norm is stated to be a closer approximation to restrain the singular values for practical applications in the real world. However, Schatten-p norm minimization is a challenging non-convex, non-smooth, and non-Lipschitz problem. In this paper, inspired by the reweighted ℓ 1 and ℓ 2 norm for compressive sensing, the generalized iterative reweighted nuclear norm (GIRNN) and the generalized iterative reweighted Frobenius norm (GIRFN) algorithms are proposed to approximate Schatten-p norm minimization. By involving the proposed algorithms, the problem becomes more tractable and the closed solutions are derived from the iteratively reweighted subproblems. In addition, we prove that both proposed algorithms converge at a linear rate to a bounded optimum. Numerical experiments for the practical matrix completion (MC), robust principal component analysis (RPCA), and image decomposition problems are illustrated to validate the superior performance of both algorithms over some common state-of-the-art methods.
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ISSN:1057-7149
1941-0042
1941-0042
DOI:10.1109/TIP.2019.2949383