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Volume 11, Issue 2
A Restricted Linearised Augmented Lagrangian Method for Euler's Elastica Model

Yinghui Zhang, Xiaojuan Deng, Xing Zhao & Hongwei Li

DOI: 10.4208/eajam.200520.191020

East Asian J. Appl. Math., 11 (2021), pp. 276-300.

Published online: 2021-02

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  • Abstract

A simple cutting-off strategy for the augmented Lagrangian formulation for minimising the Euler's elastica energy is introduced. It is connected to a discovered internal inconsistency of the model and helps to decouple the tricky dependence between auxiliary splitting variables, thus fixing the problem mentioned. Numerical experiments show that the method converges much faster than conventional algorithms, provides a better parameter-tuning and ensures the higher quality of image restorations.

  • Keywords

Euler's elastica, augmented Lagrangian, image denoising.

  • AMS Subject Headings

65M55, 68U10, 94A08

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-11-276, author = {Zhang , YinghuiDeng , XiaojuanZhao , Xing and Li , Hongwei}, title = {A Restricted Linearised Augmented Lagrangian Method for Euler's Elastica Model}, journal = {East Asian Journal on Applied Mathematics}, year = {2021}, volume = {11}, number = {2}, pages = {276--300}, abstract = {

A simple cutting-off strategy for the augmented Lagrangian formulation for minimising the Euler's elastica energy is introduced. It is connected to a discovered internal inconsistency of the model and helps to decouple the tricky dependence between auxiliary splitting variables, thus fixing the problem mentioned. Numerical experiments show that the method converges much faster than conventional algorithms, provides a better parameter-tuning and ensures the higher quality of image restorations.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.200520.191020}, url = {http://global-sci.org/intro/article_detail/eajam/18635.html} }
TY - JOUR T1 - A Restricted Linearised Augmented Lagrangian Method for Euler's Elastica Model AU - Zhang , Yinghui AU - Deng , Xiaojuan AU - Zhao , Xing AU - Li , Hongwei JO - East Asian Journal on Applied Mathematics VL - 2 SP - 276 EP - 300 PY - 2021 DA - 2021/02 SN - 11 DO - http://doi.org/10.4208/eajam.200520.191020 UR - https://global-sci.org/intro/article_detail/eajam/18635.html KW - Euler's elastica, augmented Lagrangian, image denoising. AB -

A simple cutting-off strategy for the augmented Lagrangian formulation for minimising the Euler's elastica energy is introduced. It is connected to a discovered internal inconsistency of the model and helps to decouple the tricky dependence between auxiliary splitting variables, thus fixing the problem mentioned. Numerical experiments show that the method converges much faster than conventional algorithms, provides a better parameter-tuning and ensures the higher quality of image restorations.

Zhang , YinghuiDeng , XiaojuanZhao , Xing and Li , Hongwei. (2021). A Restricted Linearised Augmented Lagrangian Method for Euler's Elastica Model. East Asian Journal on Applied Mathematics. 11 (2). 276-300. doi:10.4208/eajam.200520.191020
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