Fast Linearized Augmented Lagrangian Method for Euler's Elastica Model

被引:31
|
作者
Zhang, Jun [1 ,2 ]
Chen, Rongliang [3 ]
Deng, Chengzhi [1 ]
Wang, Shengqian [1 ]
机构
[1] Nanchang Inst Technol, Jiangxi Prov Key Lab Water Informat Cooperat Sens, Nanchang 330099, Jiangxi, Peoples R China
[2] Nanchang Inst Technol, Coll Sci, Nanchang 330099, Jiangxi, Peoples R China
[3] Chinese Acad Sci, Shenzhen Inst Adv Technol, Shenzhen 518055, Peoples R China
关键词
Image denoising; Euler's elastica model; linearized augmented Lagrangian method; shrink operator; closed form solution; TOTAL VARIATION MINIMIZATION; SPLIT BREGMAN ITERATION; FAST ALGORITHM; DUAL METHODS; IMAGES; ROF;
D O I
10.4208/nmtma.2017.m1611
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Recently, many variational models involving high order derivatives have been widely used in image processing, because they can reduce staircase effects during noise elimination. However, it is very challenging to construct efficient algorithms to obtain the minimizers of original high order functionals. In this paper, we propose a new linearized augmented Lagrangian method for Euler's elastica image denoising model. We detail the procedures of finding the saddle-points of the augmented Lagrangian functional. Instead of solving associated linear systems by FFT or linear iterative methods (e. g., the Gauss-Seidel method), we adopt a linearized strategy to get an iteration sequence so as to reduce computational cost. In addition, we give some simple complexity analysis for the proposed method. Experimental results with comparison to the previous method are supplied to demonstrate the efficiency of the proposed method, and indicate that such a linearized augmented Lagrangian method is more suitable to deal with large-sized images.
引用
收藏
页码:98 / 115
页数:18
相关论文
共 50 条
  • [1] A Fast Augmented Lagrangian Method for Euler's Elastica Model
    Duan, Yuping
    Wang, Yu
    Tai, Xue-Cheng
    Hahn, Jooyoung
    [J]. SCALE SPACE AND VARIATIONAL METHODS IN COMPUTER VISION, 2012, 6667 : 144 - +
  • [2] A Fast Augmented Lagrangian Method for Euler's Elastica Models
    Duan, Yuping
    Wang, Yu
    Hahn, Jooyoung
    [J]. NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS, 2013, 6 (01) : 47 - 71
  • [3] A Fast Algorithm for Euler's Elastica Model Using Augmented Lagrangian Method
    Tai, Xue-Cheng
    Hahn, Jooyoung
    Chung, Ginmo Jason
    [J]. SIAM JOURNAL ON IMAGING SCIENCES, 2011, 4 (01): : 313 - 344
  • [4] A Restricted Linearised Augmented Lagrangian Method for Euler's Elastica Model
    Zhang, Yinghui
    Deng, Xiaojuan
    Zhao, Xing
    Li, Hongwei
    [J]. EAST ASIAN JOURNAL ON APPLIED MATHEMATICS, 2021, 11 (02) : 276 - 300
  • [5] AUGMENTED LAGRANGIAN METHOD FOR AN EULER'S ELASTICA BASED SEGMENTATION MODEL THAT PROMOTES CONVEX CONTOURS
    Bae, Egil
    Tai, Xue-Cheng
    Zhu, Wei
    [J]. INVERSE PROBLEMS AND IMAGING, 2017, 11 (01) : 1 - 23
  • [6] Fast Coordinate Descent Augmented Lagrangian Methods for linearized MPC
    Ghinea, Liliana Maria
    Lupu, Daniela
    Barbu, Marian
    Necoara, Ion
    [J]. CONTROL ENGINEERING AND APPLIED INFORMATICS, 2023, 25 (01): : 49 - 58
  • [7] A Stochastic Linearized Augmented Lagrangian Method for Decentralized Bilevel Optimization
    Lu, Songtao
    Zeng, Siliang
    Cui, Xiaodong
    Squillante, Mark S.
    Horesh, Lior
    Kingsbury, Brian
    Liu, Jia
    Hong, Mingyi
    [J]. ADVANCES IN NEURAL INFORMATION PROCESSING SYSTEMS 35, NEURIPS 2022, 2022,
  • [8] A Penalty Relaxation Method for Image Processing Using Euler's Elastica Model
    He, Fang
    Wang, Xiao
    Chen, Xiaojun
    [J]. SIAM JOURNAL ON IMAGING SCIENCES, 2021, 14 (01): : 389 - 417
  • [9] A Fast Linearised Augmented Lagrangian Method for a Mean Curvature Based Model
    Zhang, Jun
    Deng, Chengzhi
    Shi, Yuying
    Wang, Shengqian
    Zhu, Yonggui
    [J]. EAST ASIAN JOURNAL ON APPLIED MATHEMATICS, 2018, 8 (03) : 463 - 476
  • [10] Fast X-Ray CT Image Reconstruction Using a Linearized Augmented Lagrangian Method With Ordered Subsets
    Nien, Hung
    Fessler, Jeffrey A.
    [J]. IEEE TRANSACTIONS ON MEDICAL IMAGING, 2015, 34 (02) : 388 - 399