Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

On the total variation dictionary model

Language

English

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. © 2010 IEEE.

Keywords

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

Publication Date

2010

Source Publication Title

IEEE Transactions on Image Processing

Volume

19

Issue

3

Start Page

821

End Page

825

Publisher

Institute of Electrical and Electronics Engineers

DOI

10.1109/TIP.2009.2034701

Link to Publisher's Edition

http://dx.doi.org/10.1109/TIP.2009.2034701

ISSN (print)

10577149

ISSN (electronic)

19410042

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