Low Rank Prior and Total Variation Regularization for Image Deblurring

Liyan Ma, Li Xu, Tieyong ZENG*

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

52 Citations (Scopus)


The similar image patches should have similar underlying structures. Thus the matrix constructed from stacking the similar patches together has low rank. Based on this fact, the nuclear norm minimization, which is the convex relaxation of low rank minimization, leads to good denoising results. Recently, the weighted nuclear norm minimization has been applied to image denoising. This approach presents state-of-the-art result for image denoising. In this paper, we further study the weighted nuclear norm minimization problem for general image recovery task. For the weights being in arbitrary order, we prove that such minimization problem has a unique global optimal solution in the closed form. Incorporating this idea with the celebrated total variation regularization, we then investigate the image deblurring problem. Numerical experimental results illustratively clearly that the proposed algorithms achieve competitive performance.

Original languageEnglish
Pages (from-to)1336-1357
Number of pages22
JournalJournal of Scientific Computing
Issue number3
Publication statusPublished - 1 Mar 2017

Scopus Subject Areas

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • Engineering(all)
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Image deblurring
  • Low rank
  • Nuclear norm
  • Variational method


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