Zhang, Zhenwei, Chen, Ke 
ORCID: 0000-0002-6093-6623, Tang, Ke and Duan, Yuping
(2023)
Fast Multi-grid Methods for Minimizing Curvature Energies.
IEEE Transactions on Image Processing, 32.
p. 1.
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Duan_YP_Juan_final_07-03-2023download.pdf - Author Accepted Manuscript Download (7MB) | Preview |
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 1024×1024 within 40s, while the ALM method [1] requires around 200s.
| Item Type: | Article |
|---|---|
| Additional Information: | (c) 2023 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works. |
| Uncontrolled Keywords: | Minimization, Computational modeling, Image restoration, Image reconstruction, Convergence, Surface treatment, Surface reconstruction, Mean curvature, gaussian curvature, multi-grid method, domain decomposition method, image denoising, image reconstruction |
| Divisions: | Faculty of Science and Engineering > School of Physical Sciences |
| Depositing User: | Symplectic Admin |
| Date Deposited: | 13 Mar 2023 08:36 |
| Last Modified: | 20 Apr 2023 06:25 |
| DOI: | 10.1109/tip.2023.3251024 |
| Related URLs: | |
| URI: | https://livrepository.liverpool.ac.uk/id/eprint/3168937 |
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