中文版 | English
Title

Fast Multi-Grid Methods for Minimizing Curvature Energies

Author
Publication Years
2023
DOI
Source Title
ISSN
1941-0042
EISSN
1941-0042
Volume32Pages:1716-1731
Abstract
The geometric high-order regularization methods such as mean curvature and Gaussian curvature, have been intensively studied during the last decades due to their abilities in preserving geometric properties including image edges, corners, and contrast. However, the dilemma between restoration quality and computational efficiency is an essential roadblock for high-order methods. In this paper, we propose fast multi-grid algorithms for minimizing both mean curvature and Gaussian curvature energy functionals without sacrificing accuracy for efficiency. Unlike the existing approaches based on operator splitting and the Augmented Lagrangian method (ALM), no artificial parameters are introduced in our formulation, which guarantees the robustness of the proposed algorithm. Meanwhile, we adopt the domain decomposition method to promote parallel computing and use the fine-to-coarse structure to accelerate convergence. Numerical experiments are presented on image denoising, CT, and MRI reconstruction problems to demonstrate the superiority of our method in preserving geometric structures and fine details. The proposed method is also shown effective in dealing with large-scale image processing problems by recovering an image of size $1024\times 1024$ within 40s, while the ALM-based method requires around 200s.
Keywords
URL[Source Record]
Indexed By
Language
English
SUSTech Authorship
Others
Funding Project
National Natural Science Foundation of China (NSFC)["12071345","11701418"]
WOS Research Area
Computer Science ; Engineering
WOS Subject
Computer Science, Artificial Intelligence ; Engineering, Electrical & Electronic
WOS Accession No
WOS:000947305800004
Publisher
Data Source
IEEE
PDF urlhttps://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10061442
Citation statistics
Cited Times [WOS]:0
Document TypeJournal Article
Identifierhttp://kc.sustech.edu.cn/handle/2SGJ60CL/501516
DepartmentResearch Institute of Trustworthy Autonomous Systems
工学院_计算机科学与工程系
Affiliation
1.Center for Applied Mathematics, Tianjin University, Tianjin, China
2.Department of Mathematical Sciences, Liverpool Centre of Mathematics for Healthcare and Centre for Mathematical Imaging Techniques, University of Liverpool, Liverpool, U.K.
3.Department of Computer Science and Engineering, Guangdong Key Laboratory of Brain-Inspired Intelligent Computation, Research Institute of Trustworthy Autonomous Systems, Southern University of Science and Technology, Shenzhen, China
Recommended Citation
GB/T 7714
Zhenwei Zhang,Ke Chen,Ke Tang,et al. Fast Multi-Grid Methods for Minimizing Curvature Energies[J]. IEEE Transactions on Image Processing,2023,32:1716-1731.
APA
Zhenwei Zhang,Ke Chen,Ke Tang,&Yuping Duan.(2023).Fast Multi-Grid Methods for Minimizing Curvature Energies.IEEE Transactions on Image Processing,32,1716-1731.
MLA
Zhenwei Zhang,et al."Fast Multi-Grid Methods for Minimizing Curvature Energies".IEEE Transactions on Image Processing 32(2023):1716-1731.
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