Multidimensional Systems and Signal Processing

, Volume 30, Issue 1, pp 503–527 | Cite as

Image denoising using combined higher order non-convex total variation with overlapping group sparsity

  • Tarmizi AdamEmail author
  • Raveendran ParamesranEmail author


It is widely known that the total variation image restoration suffers from the stair casing artifacts which results in blocky restored images. In this paper, we address this problem by proposing a combined non-convex higher order total variation with overlapping group sparse regularizer. The hybrid scheme of both the overlapping group sparse and the non-convex higher order total variation for blocky artifact removal is complementary. The overlapping group sparse term tends to smoothen out blockiness in the restored image more globally, while the non-convex higher order term tends to smoothen parts that are more local to texture while preserving sharp edges. To solve the proposed image restoration model, we develop an iteratively re-weighted \(\ell _1\) based alternating direction method of multipliers algorithm to deal with the constraints and subproblems. In this study, the images are degraded with different levels of Gaussian noise. A comparative analysis of the proposed method with the overlapping group sparse total variation, the Lysaker, Lundervold and Tai model, the total generalized variation and the non-convex higher order total variation, was carried out for image denoising. The results in terms of peak signal-to-noise ratio and structure similarity index measure show that the proposed method gave better performance than the compared algorithms.


Alternating direction method Total variation Denoising Non-convex Overlapping group sparsity 



We would like to thank the anonymous reviewers for their valuable suggestions for improving this paper. We would also like to thank Dr. Jun Liu of University of Electronic Science and Technology of China for generously sharing the codes for OGSTV with us.


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

Authors and Affiliations

  1. 1.Department of Electrical Engineering, Faculty of EngineeringUniversity of MalayaKuala LumpurMalaysia

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