Two-Step Approach for the Restoration of Images Corrupted by Multiplicative Noise

Yu Mei Huang, De Yong Lu, Tieyong Zeng*

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

29 Citations (Scopus)
32 Downloads (Pure)


The restoration of images corrupted by blurring and multiplicative noise is a challenging problem in applied mathematics that has attracted much attention in recent years. In this article, we propose a two-step approach to solve the problem of restoring images degraded by multiplicative noise and blurring, where the multiplicative noise is first reduced by nonlocal filters and then a convex variational model is adopted to obtain the final restored images. The variational model of the second step is composed of an L1-L 2 data-fidelity term and a total variation regularization term. The alternating direction method (ADM) is utilized to solve this variational problem, and we also prove that the ADM algorithm converges at least linearly. Experimental results show that the proposed two-step approach performs better than the existing methods for restoring images with multiplicative noise and blurring, both in the quality of the restored images and the convergence speed of the algorithms.

Original languageEnglish
Pages (from-to)A2856-A2873
Number of pages18
JournalSIAM Journal on Scientific Computing
Issue number6
Publication statusPublished - 5 Dec 2013

Scopus Subject Areas

  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Alternating direction method
  • Deblurring
  • Image restoration
  • Multiplicative noise
  • Total variation
  • Variational method


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