Fast Multi-Grid Methods for Minimizing Curvature Energies

Zhenwei Zhang1; Ke Chen2; Ke Tang3; Yuping Duan1

2023

10.1109/TIP.2023.3251024

IEEE Transactions on Image Processing   Impact Factor & Quartile

1941-0042

1941-0042

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.

Mean curvature gaussian curvature multi-grid method domain decomposition method image denoising image reconstruction

SCI

English

Others

National Natural Science Foundation of China (NSFC)["12071345","11701418"]

Computer Science ; Engineering

Computer Science, Artificial Intelligence ; Engineering, Electrical & Electronic

WOS:000947305800004

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC

ENGINEERING

IEEE

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

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.

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.

Zhenwei Zhang,et al."Fast Multi-Grid Methods for Minimizing Curvature Energies".IEEE Transactions on Image Processing 32(2023):1716-1731.