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Mathematical Problems in Engineering
Volume 2017, Article ID 3012910, 13 pages
Research Article

A Coordinate Descent Method for Total Variation Minimization

1Northeast Agricultural University, Harbin 150001, China
2Harbin Institute of Technology, Research Group for Computational Photography and Statistical Learning, School of Computer Science and Technology, Harbin 150001, China
3No. 211 Hospital of PLA, Harbin 150001, China
4Department of Computing, The Hong Kong Polytechnic University, Kowloon, Hong Kong

Correspondence should be addressed to Wangmeng Zuo; moc.liamg@ouzmwsc

Received 5 May 2017; Accepted 10 August 2017; Published 18 September 2017

Academic Editor: Gerardo Severino

Copyright © 2017 Hong Deng 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.


Total variation (TV) is a well-known image model with extensive applications in various images and vision tasks, for example, denoising, deblurring, superresolution, inpainting, and compressed sensing. In this paper, we systematically study the coordinate descent (CoD) method for solving general total variation (TV) minimization problems. Based on multidirectional gradients representation, the proposed CoD method provides a unified solution for both anisotropic and isotropic TV-based denoising (CoDenoise). With sequential sweeping and small random perturbations, CoDenoise is efficient in denoising and empirically converges to optimal solution. Moreover, CoDenoise also delivers new perspective on understanding recursive weighted median filtering. By incorporating with the Augmented Lagrangian Method (ALM), CoD was further extended to TV-based image deblurring (ALMCD). The results on denoising and deblurring validate the efficiency and effectiveness of the CoD-based methods.