On the total variation dictionary model

Tieyong ZENG*, Kwok Po NG

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

23 Citations (Scopus)


The goal of this paper is to provide a theoretical study of a total variation (TV) dictionary model. Based on the properties of convex analysis and bounded variation functions, the existence of solutions of the TV dictionary model is proved. We then show that the dual form of the model can be given by the minimization of the sum of the l1-norm of the dual solution and the Bregman distance between the curvature of the primal solution and the subdifferential of TV norm of the dual solution. This theoretical result suggests that the dictionary must represent sparsely the curvatures of solution image in order to obtain a better denoising performance.

Original languageEnglish
Article number5288597
Pages (from-to)821-825
Number of pages5
JournalIEEE Transactions on Image Processing
Issue number3
Publication statusPublished - Mar 2010

Scopus Subject Areas

  • Software
  • Computer Graphics and Computer-Aided Design

User-Defined Keywords

  • Curvature
  • Dictionary
  • Dual problem
  • Sparse representation
  • Total variation


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