Fixed-point algorithms for a TVL1 image restoration model

Jian Lu, Ke Qiao, Lixin Shen, Yuru Zou

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


In this paper, we study fixed point proximity algorithms for a TVL1 restoration model recovering blurred images with impulsive noise, and image inpainting. The model that minimizes the sum of a data fidelity term in the l1 -norm, a term in l2 -norm and total-variation regularization term is strictly convex. We obtain the solution of the model through finding a fixed point of a nonlinear mapping expressed in terms of the proximity operator of the l1-norm or the l2-norm, each of which is explicitly given. The non-expansivity of the mapping is also analysed theoretically. This formulation naturally leads to fixed-point algorithms for numerical treatment of the model. Numerical experiments demonstrate that the proposed algorithms perform favourably.

Original languageEnglish (US)
Pages (from-to)1829-1844
Number of pages16
JournalInternational Journal of Computer Mathematics
Issue number9
StatePublished - Sep 2 2018


  • 35A15
  • 49J40
  • 68U10
  • 94A08
  • Total variation
  • deblurring
  • impulsive noise
  • inpainting
  • proximity operator

ASJC Scopus subject areas

  • Computer Science Applications
  • Computational Theory and Mathematics
  • Applied Mathematics


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