Signal, Image and Video Processing

, Volume 8, Issue 1, pp 39–47 | Cite as

Image decomposition using adaptive second-order total generalized variation

  • Jianlou XuEmail author
  • Xiangchu Feng
  • Yan Hao
  • Yu Han
Original Paper


This paper proposes a new model for image decomposition which separates an image into a cartoon, consisting only of geometric objects, and an oscillatory component, consisting of textures or noise. The proposed model is given in a variational formulation with adaptive second-order total generalized variation (TGV). The adaptive behavior preserves the key features such as object boundaries and textures while avoiding staircasing effect. To speed up the computation, the split Bregman method is used to solve the proposed model. Experimental results and comparisons demonstrate the proposed model is more effective for image decomposition than the methods of the state-of-the-art image decomposition models.


Image decomposition Cartoon Texture TGV  Split Bregman Staircasing effect 



This work is supported by the National Science Foundation of China (No. 60872138, 61105011, 61271294). Meanwhile, the authors also thank Editor-in-Chief Prof. Murat Kunt and anonymous reviewers for their constructive comments that greatly improve this paper.


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Copyright information

© Springer-Verlag London 2012

Authors and Affiliations

  1. 1.School of SciencesXidian UniversityXi’anPeople’s Republic of China
  2. 2.School of Mathematics and StatisticsHenan University of Science and TechnologyLuoyangPeople’s Republic of China

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