Circuits, Systems, and Signal Processing

, Volume 38, Issue 1, pp 218–241 | Cite as

An Effective Weighted Hybrid Regularizing Approach for Image Noise Reduction

  • Md. Robiul Islam
  • Chen XuEmail author
  • Rana Aamir Raza
  • Yu Han


Digital images are mostly noised due to transmission and capturing disturbances. Hence, denoising becomes a notable issue because of the necessity of removing noise before its use in any application. In denoising, the important challenge is to remove the noise while protecting true information and avoiding undesirable modification in the images. The performance of classical denoising methods including convex total variation or some nonconvex regularizers is not effective enough. Thus, it is still an ongoing research toward better denoising result. Since edge preservation is a tricky issue during denoising process, designing an appropriate regularizer for a given fidelity is a mostly crucial matter in real-world problems. Therefore, we attempt to design a robust smoothing term in energy functional so that it can reduce the possibility of discontinuity and distortion of image edge details. In this work, we introduce a new denoising technique that inherits the benefits of both convex and nonconvex regularizers. The proposed method encompasses with a novel weighted hybrid regularizer in variational framework to ensure a better trade-off between the noise removal and image edge preservation. A new algorithm based on Chambolle’s method and iteratively reweighting method is proposed to solve the model efficiently. The numerical results ensure that the proposed hybrid denoising approach can perform better than the classical convex, nonconvex regularizer-based denoising and some other methods.


Image denoising Total variation Euler Lagrange equation Nonconvex regularizer Dual projection 



This work was supported in part by the National Natural Science Foundation of China under Grants 61402290, 61472257, 61772343 and 61379030; in part by the Foundation for Distinguished Young Talents in Higher Education of Guangdong, China, under Grant 2014KQNCX134; in part by the Natural Science Foundation of Guangdong, China, under Grant 1714050003822; and in part by the Science Foundation of Shenzhen Science Technology and Innovation Commission, China, under Grant JCYJ20160331114526190.


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Md. Robiul Islam
    • 1
  • Chen Xu
    • 2
    Email author
  • Rana Aamir Raza
    • 1
  • Yu Han
    • 2
  1. 1.College of Computer Science and Software EngineeringShenzhen UniversityShenzhenChina
  2. 2.College of Mathematics and Computational ScienceShenzhen UniversityShenzhenChina

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