Volume 10, Issue 1
Fast Linearized Augmented Lagrangian Method for Euler's Elastica Model

Jun Zhang, Rongliang Chen, Chengzhi Deng & Shengqian Wang

Numer. Math. Theor. Meth. Appl., 10 (2017), pp. 98-115.

Published online: 2017-10

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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. 

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@Article{NMTMA-10-98, author = {}, title = {Fast Linearized Augmented Lagrangian Method for Euler's Elastica Model}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2017}, volume = {10}, number = {1}, pages = {98--115}, 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. 

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2017.m1611}, url = {http://global-sci.org/intro/article_detail/nmtma/12338.html} }
TY - JOUR T1 - Fast Linearized Augmented Lagrangian Method for Euler's Elastica Model JO - Numerical Mathematics: Theory, Methods and Applications VL - 1 SP - 98 EP - 115 PY - 2017 DA - 2017/10 SN - 10 DO - http://doi.org/10.4208/nmtma.2017.m1611 UR - https://global-sci.org/intro/article_detail/nmtma/12338.html KW - AB -

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. 

Jun Zhang, Rongliang Chen, Chengzhi Deng & Shengqian Wang. (2020). Fast Linearized Augmented Lagrangian Method for Euler's Elastica Model. Numerical Mathematics: Theory, Methods and Applications. 10 (1). 98-115. doi:10.4208/nmtma.2017.m1611
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