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Mathematical Problems in Engineering
Volume 2015, Article ID 815132, 11 pages
Research Article

A New Fast Algorithm for Constrained Four-Directional Total Variation Image Denoising Problem

1LIST, Key Laboratory of Computer Network and Information Integration, Southeast University, Ministry of Education, Nanjing 210096, China
2INSERM U1099, 35000 Rennes, France
3LTSI, Université de Rennes I, 35000 Rennes, France
4Centre de Recherche en Information Médicale Sino-Français (CRIBs), 35000 Rennes, France

Received 1 August 2014; Revised 26 September 2014; Accepted 2 October 2014

Academic Editor: Jian Guo Zhou

Copyright © 2015 Fan Liao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A new four-directional total variation (4-TV) model, applicable to isotropic and anisotropic TV functions, is proposed for image denoising. A dual based fast gradient projection algorithm for the constrained 4-TV image denoising problem is also reported which combines the well-known gradient projection and the fast gradient projection methods. Experimental results show that this model provides in most cases a better signal to noise ratio when compared to previous models like the reference TV, the total generalized variation, and the nonlocal total variation.