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

Yan Huang, Guisheng Liao, Yijian Xiang, Lei Zhang, Jie Li, Arye Nehorai

Research output: Contribution to journalArticlepeer-review

25 Scopus citations

Abstract

The low-rank approximation problem has recently attracted wide concern due to its excellent performance in real-world 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 ell _{1}$ and ell _{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.

Original languageEnglish
Article number8887531
Pages (from-to)2244-2257
Number of pages14
JournalIEEE Transactions on Image Processing
Volume29
DOIs
StatePublished - 2020

Keywords

  • Low-rank approximation problem
  • generalized iterative reweighted Frobenius norm (GIRFN)
  • generalized iterative reweighted nuclear norm (GIRNN)
  • image decomposition
  • matrix completion (MC)
  • robust principal component analysis (RPCA)

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