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

Zhifang Liu (), Yuping Duan (), Chunlin Wu () and Xue-Cheng Tai ()
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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)

Chapter 13 in Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging, 2023, pp 503-549 from Springer

Abstract: 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.

Keywords: Variable splitting; Augmented lagrangian method; Total variation; Image restoration; Box constraint (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/978-3-030-98661-2_84

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