基于$L_{1/2}/L_2$正则化的图像盲去模糊方法

doi:10.3969/j.issn.1005-3085.2015.05.004

工程数学学报 ›› 2015, Vol. 32 ›› Issue (5): 659-666.doi: 10.3969/j.issn.1005-3085.2015.05.004

基于$L_{1/2}/L_2$正则化的图像盲去模糊方法

靖稳峰¹, 赵仁省¹, 李智敏², 宋伟², 郑琰²

1- 西安交通大学数学与统计学院，西安 710049
2- 国网河南省电力公司郑州供电公司，郑州 450000

收稿日期:2014-12-26 接受日期:2015-01-14 出版日期:2015-10-15 发布日期:2015-12-15
基金资助:
国家973计划项目 (2013CB329406HZ)；国网河南省电力公司2012科技项目 (521710120002).

Blind Deblurring Based on an $L_{1/2}/L_2$ Regularization

JING Wen-feng¹, ZHAO Ren-xing¹, LI Zhi-min², SONG Wei², ZHENG Yan²

1- School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049
2- State Grid Henan Electric Power Company Zhengzhou Power Supply Company, Zhengzhou 450000

Received:2014-12-26 Accepted:2015-01-14 Online:2015-10-15 Published:2015-12-15
Supported by:
The National Basic Research Program of China (973 Program) (2013CB329406HZ); the Technical Project of State Grid Henan Electric Power Company (521710120002).

摘要/Abstract

摘要： 图像去模糊是图像识别和视频分析的基础性工作．在实际应用中，多数情形是模糊核未知的盲去模糊问题．盲去模糊问题是一个病态问题，通常需建立某种正则化模型求解．已有的图像去模糊正则化模型难以恢复模糊图像的细节，本文提出了一种基于$L_{1/2}/L_2$的正则化模型，并设计了求解该模型的交替投影迭代算法．数值实验表明，所提出的模型和算法能够更好地恢复模糊图像的细微结构，并且计算效率高，对参数的鲁棒性强．

关键词: 图像去模糊, 盲去模糊, 正则化模型, 交替投影迭代

Abstract:

Image deblurring is the basic work for image recognition and video analysis. In real-world applications, most image deblurring problems are ones of blind image deblurring. The problems are ill-posed and need to be solved by regularization methods. Since the existing regularization models for image deblurring are difficult to restore image details, we propose a novel blind deblurring model based on $L_{1/2}/L_2$ regularization and an alternating projection iteration algorithm to solve it. Experimental results demonstrate that the proposed model and algorithm have very good restoration on the detailed structure of original deblurred images, and have high computational efficiency and fine robustness to parameters as well.

Key words: image deblurring, blind deblurring, regularization model, alternating projection iteration

中图分类号:

TP391

靖稳峰, 赵仁省, 李智敏, 宋伟, 郑琰. 基于$L_{1/2}/L_2$正则化的图像盲去模糊方法[J]. 工程数学学报, 2015, 32(5): 659-666.

JING Wen-feng, ZHAO Ren-xing, LI Zhi-min, SONG Wei, ZHENG Yan. Blind Deblurring Based on an $L_{1/2}/L_2$ Regularization[J]. Chinese Journal of Engineering Mathematics, 2015, 32(5): 659-666.

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基于$L_{1/2}/L_2$正则化的图像盲去模糊方法

Blind Deblurring Based on an $L_{1/2}/L_2$ Regularization

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