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On Variable Splitting and Augmented Lagrangian Method for Total Variation-Related Image Restoration Models

In: Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging

Author

Listed:
  • Zhifang Liu

    (Tianjin Normal University, School of Mathematical Sciences)

  • Yuping Duan

    (Tianjin University, Center for Applied Mathematics)

  • Chunlin Wu

    (Nankai University, School of Mathematical Sciences)

  • Xue-Cheng Tai

    (Hong Kong Center for Cerebro-cardiovascular Health Engineering (COCHE))

Abstract

Variable splitting and augmented Lagrangian method are widely used in image processing. This chapter briefly reviews its applications for solving the total variation (TV) related image restoration problems. Due to the nonsmoothness of TV, related models and variants are nonsmooth convex or nonconvex minimization problems. Variable splitting and augmented Lagrangian method can benefit from the separable structure and efficient subsolvers, and has convergence guarantee in convex cases. We present this approach for a number of TV minimization models including TV-L2, TV-L1, TV with nonquadratic fidelity term, multichannel TV, high-order TV, and curvature minimization models.

Suggested Citation

  • Zhifang Liu & Yuping Duan & Chunlin Wu & Xue-Cheng Tai, 2023. "On Variable Splitting and Augmented Lagrangian Method for Total Variation-Related Image Restoration Models," Springer Books, in: Ke Chen & Carola-Bibiane Schönlieb & Xue-Cheng Tai & Laurent Younes (ed.), Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging, chapter 13, pages 503-549, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-98661-2_84
    DOI: 10.1007/978-3-030-98661-2_84
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