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Fast Linearized Augmented Lagrangian Method for Euler's Elastica Model

Part of: Partial differential equations, initial value and time-dependent initial-boundary value problems Communication, information

Published online by Cambridge University Press:  20 February 2017

Jun Zhang ,
Rongliang Chen ,
Chengzhi Deng  and
Shengqian Wang
Jun Zhang*
Affiliation:
Jiangxi Province Key Laboratory of Water Information Cooperative Sensing and Intelligent Processing, Nanchang Institute of Technology, Nanchang 330099, Jiangxi, China College of Science, Nanchang Institute of Technology, Nanchang 330099, Jiangxi, China
Rongliang Chen*
Affiliation:
Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen 518055, P. R. China
Chengzhi Deng*
Affiliation:
Jiangxi Province Key Laboratory of Water Information Cooperative Sensing and Intelligent Processing, Nanchang Institute of Technology, Nanchang 330099, Jiangxi, China
Shengqian Wang*
Affiliation:
Jiangxi Province Key Laboratory of Water Information Cooperative Sensing and Intelligent Processing, Nanchang Institute of Technology, Nanchang 330099, Jiangxi, China
*
*Corresponding author. Email addresses:junzhang0805@126.com (J. Zhang), rl.chen@siat.ac.cn (R.-L. Chen), dengcz@nit.edu.cn (C.-Z. Deng), sqwang113@263.net (S.-Q. Wang)
*Corresponding author. Email addresses:junzhang0805@126.com (J. Zhang), rl.chen@siat.ac.cn (R.-L. Chen), dengcz@nit.edu.cn (C.-Z. Deng), sqwang113@263.net (S.-Q. Wang)
*Corresponding author. Email addresses:junzhang0805@126.com (J. Zhang), rl.chen@siat.ac.cn (R.-L. Chen), dengcz@nit.edu.cn (C.-Z. Deng), sqwang113@263.net (S.-Q. Wang)
*Corresponding author. Email addresses:junzhang0805@126.com (J. Zhang), rl.chen@siat.ac.cn (R.-L. Chen), dengcz@nit.edu.cn (C.-Z. Deng), sqwang113@263.net (S.-Q. Wang)
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Abstract

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.

Keywords

Image denoisingEuler's elastica modellinearized augmented Lagrangian methodshrink operatorclosed form solution

MSC classification

Secondary: 65M55: Multigrid methods; domain decomposition 68U10: Image processing 94A08: Image processing (compression, reconstruction, etc.)
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 10 , Issue 1 , February 2017 , pp. 98 - 115
Copyright
Copyright © Global-Science Press 2017 

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