Multiplicative noise removal in imaging: An exp-model and its fixed-point proximity algorithm

Jian Lu, Lixin Shen, Chen Xu, Yuesheng Xu

Research output: Contribution to journalArticlepeer-review

42 Scopus citations


We propose a variational model for restoration of images corrupted by multiplicative noise. The proposed model formulated in the logarithm transform domain of the desirable images consists of a data fitting term, a quadratic term, and a total variation regularizer. The data fitting term results directly from the presence of the multiplicative noise and the quadratic term reflects the statistics of the noise. We show that the proposed model is strictly convex under a mild condition. The solution of the model is then characterized in terms of the fixed-point of a nonlinear map described by the proximity operator of a function involved in the model. Based on the characterization, we present a fixed-point proximity algorithm for solving the model and analyze its convergence. Our numerical results indicate that the proposed model compares favorably to several existing state-of-the-art models with better results in terms of the peak signal-to-noise ratio of the denoised images and the CPU time consumed.

Original languageEnglish (US)
Pages (from-to)518-539
Number of pages22
JournalApplied and Computational Harmonic Analysis
Issue number2
StatePublished - Sep 1 2016


  • Exp-model
  • Fixed-point proximity algorithm
  • Multiplicative noise

ASJC Scopus subject areas

  • Applied Mathematics


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