| 引用本文: | 吴越,曾向荣,周典乐,等.图像恢复中的稳健交替方向乘子法.[J].国防科技大学学报,2018,40(2):112-118.[点击复制] |
| WU Yue,ZENG Xiangrong,ZHOU Dianle,et al.Image restoration via robust alternating direction method of multipliers[J].Journal of National University of Defense Technology,2018,40(2):112-118[点击复制] |
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| 图像恢复中的稳健交替方向乘子法 |
| 吴越, 曾向荣, 周典乐, 刘衍, 周家庆, 周经纶 |
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(国防科技大学 系统工程学院, 湖南 长沙 410073)
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| 摘要: |
| 交替方向乘子法在解决线性逆问题（包括图像恢复）中取得了良好的效果，但是其效果对惩罚参数的选择非常敏感，不利于具体的应用。提出基于惩罚参数自适应选择原理的稳健交替方向乘子法，对其优化条件和收敛性进行了详细分析。实验表明，在基于Parseval紧框架的图像恢复应用中，该算法不但对惩罚参数的选择表现出良好的稳健性，而且效果优于交替方向乘子法，并优于其他目前热门的算法。 |
| 关键词: 交替方向乘子法 图像恢复 压缩感知 紧框架 |
| DOI：10.11887/j.cn.201802018 |
| 投稿日期：2016-12-01 |
| 基金项目:国家自然科学基金资助项目（61602494）；国防科技大学科研计划资助项目（ZK16-03-16） |
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| Image restoration via robust alternating direction method of multipliers |
| WU Yue, ZENG Xiangrong, ZHOU Dianle, LIU Yan, ZHOU Jiaqing, ZHOU Jinglun |
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(College of Systems Engineering, National University of Defense Technology, Changsha 410073, China)
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| Abstract: |
| The ADMM (alternating direction method of multipliers) with appropriate parameters plays a successful role in solving linear inverse problems (including image restoration). But the results obtained by ADMM are sensitive to the choices of the penalty parameter, and this bad robustness brought some troubles in its applications. Based on a scheme of choosing the penalty parameter adaptively, a RADMM (robust ADMM) was proposed to tackle this shortcoming. Through analyzing optimization conditions and convergence of RADMM, we can conclude that the adaptive control of the penalty parameter provides good robustness, faster speed of convergence and better solution. And the experiments show that, in the application of image restoration based on the Parseval tight frame, the RADMM is robust to the choices of the penalty parameter, outperforms the ADMM, and is far superior to other alternative state-of-the-art methods. |
| Keywords: alternating direction method of multipliers image restoration compressed sensing tight frame |
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