Image decomposition combining a total variational filter and a Tikhonov quadratic filter

  • Yan Hao
  • Jianlou Xu
  • Jian Bai
  • Yu Han


In this paper, we propose a new variational model for image decomposition which separates an image into a cartoon, consisting only of geometric objects and an oscillatory component, consisting of texture or noise. In the new model, the \(\hbox {H}^{-1}\)-norm is considered as the data fitting term and the regularization term is composed of a total variational filter and a Tikhonov quadratic filter. These two filters can be automatically selected by a soft threshold function. When the pixels belong to the cartoon area, the total variational filter is adopted, which can preserve the geometric structures of image such as the edges, well. When the pixels belong to texture region, the Tikhonov quadratic filter is chosen,which can extract the texture of image well. To solve the proposed model effectively, the split Bregman method is employed. Experimental results demonstrate that the proposed model and algorithm can obtain better decomposition results than those of classical models.


Total variation Image decomposition Split Bregman Image denoising 



This work is supported by the National Natural Science Fund of China (No: 61301229, 61105011) and the doctoral research fund of Henan University of Science and Technology (No: 09001708, 09001751). In addition, we would like to thank the Associate Editor and anonymous reviewers for their constructive comments that greatly improve this paper.


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsHenan University of Science and TechnologyLuoyangChina
  2. 2.School of SciencesXidian UniversityXi’anChina
  3. 3.College of Mathematic and Computational ScienceShenzhen UniversityShenzhen China

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