On the total variation dictionary model

Tieyong Zeng; Michael K. Ng

doi:10.1109/TIP.2009.2034701

On the total variation dictionary model

Tieyong Zeng^*, Michael K. Ng

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

23 Citations (Scopus)

Abstract

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 language	English
Article number	5288597
Pages (from-to)	821-825
Number of pages	5
Journal	IEEE Transactions on Image Processing
Volume	19
Issue number	3
DOIs	https://doi.org/10.1109/TIP.2009.2034701
Publication status	Published - 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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10.1109/TIP.2009.2034701

Cite this

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abstract = "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.",

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author = "Tieyong Zeng and Ng, {Michael K.}",

note = "Funding Information: Manuscript received May 06, 2009; revised September 21, 2009. First published October 16, 2009; current version published February 18, 2010. This work was supported in part by RGC 203109, RGC 201508, the FRGs of Hong Kong Baptist University, and the PROCORE—France/Hong Kong Joint Research Scheme sponsored by the Research Grant Council of Hong Kong and the Consulate General of France in Hong Kong F-HK05/08T. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Eric Kolaczyk.",

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AB - 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.

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On the total variation dictionary model

Abstract

Scopus Subject Areas

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