Fast multi-grid methods for minimizing curvature energies

Zhang, Zhenwei and Chen, Ke and Tang, Ke and Duan, Yuping (2023) Fast multi-grid methods for minimizing curvature energies. IEEE Transactions on Image Processing, 32. pp. 1716-1731. ISSN 1057-7149 (https://doi.org/10.1109/TIP.2023.3251024)

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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-based method requires around 200s.

ORCID iDs

Zhang, Zhenwei, Chen, Ke ORCID logoORCID: https://orcid.org/0000-0002-6093-6623, Tang, Ke and Duan, Yuping;
  • Item type:Article
    ID code:87009
    Dates:
    Date
    Event
    9 March 2023
    Published
    15 February 2023
    Accepted
    3 April 2022
    Submitted
    Notes:Copyright © 2023 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, 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 component of this work in other works.
    Subjects:Science > Mathematics > Electronic computers. Computer science
    Department:Faculty of Science > Mathematics and Statistics
    Depositing user: Pure Administrator
    Date deposited:19 Oct 2023 15:02
    Last modified:11 Nov 2024 14:07
    URI:https://strathprints.strath.ac.uk/id/eprint/87009
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