A Coordinate Descent Method for Total Variation Minimization. (18th September 2017)

• Record Type: Journal Article
• Authors: Deng, Hong; Ren, Dongwei; Xiao, Gang; Zhang, David; Zuo, Wangmeng
• Other Names: Severino Gerardo Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2017(2017)
• Publication Date: 2017-09-18
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2017/3012910
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : 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.