Signal, Image and Video Processing

, Volume 13, Issue 1, pp 179–187 | Cite as

Low-rank constraint with sparse representation for image restoration under multiplicative noise

  • Lixia Chen
  • Pingfang Zhu
  • Xuewen WangEmail author
Original Paper


In this paper, a novel model is proposed to remove multiplicative noise via sparse representation and low-rank constraint. We first translate multiplicative noise into additive one by a logarithmic transform and introduce a regularization with nonlocal similarity and low-rank constraint to capture the essential features. To solve the proposed model, it is divided into three subproblems, and the alternative optimization method is employed. After the denoising image in the log-domain was available, the recovered image is obtained by an exponential function and a bias correction. Compared with the state-of-the-art methods, the proposed algorithm achieves better denoising results both in terms of objective metrics and visual effects.


Multiplicative noise removal Dictionary learning Low-rank constraint Nonlocal similarity 



This project is partially supported by the National Natural Science Foundation of China (61362021, 61661017, 61662014), Guangxi Natural Science Foundation (2016GXNSFAA-380043, 2013GXNSFDA019030), Guangxi Higher Education Undergraduate Teaching Reform Project (2017JGB230) and Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation (LDAC201704).


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Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematics and Computing Science, Guangxi Colleges and Universities Key Laboratory of Data Analysis and ComputationGuilin University of Electronic TechnologyGuilinChina
  2. 2.School of Computer Science and Information SecurityGuilin University of Electronic TechnologyGuilinChina

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