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A Coordinate Descent Method for Total Variation Minimization

Author

Listed:
  • Hong Deng
  • Dongwei Ren
  • Gang Xiao
  • David Zhang
  • Wangmeng Zuo

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.

Suggested Citation

  • Hong Deng & Dongwei Ren & Gang Xiao & David Zhang & Wangmeng Zuo, 2017. "A Coordinate Descent Method for Total Variation Minimization," Mathematical Problems in Engineering, Hindawi, vol. 2017, pages 1-13, September.
    • Handle: RePEc:hin:jnlmpe:3012910
    DOI: 10.1155/2017/3012910
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