面向单幅图像去雨的非相干字典学习及其稀疏表示研究

doi:10.11959/j.issn.1000-436x.2017149

通信学报 ›› 2017, Vol. 38 ›› Issue (7): 28-35.doi: 10.11959/j.issn.1000-436x.2017149

面向单幅图像去雨的非相干字典学习及其稀疏表示研究

汤红忠^1,^2,³,王翔^1,³,张小刚²,李骁^1,³,毛丽珍^1,³

¹ 湘潭大学信息工程学院，湖南湘潭 411105
² 湖南大学电气与信息工程学院，湖南长沙 410082
³ 湘潭大学控制工程研究所，湖南湘潭 411105

修回日期:2017-04-08 出版日期:2017-07-01 发布日期:2017-08-25
作者简介:汤红忠（1979-），女，湖南衡山人，湖南大学博士生，湘潭大学副教授，主要研究方向为图像处理与模式识别、字典学习及稀疏表示。|王翔（1991-），男，湖南衡阳人，湘潭大学硕士生，主要研究方向为图像处理与模式识别。|张小刚（1972-），男，河南汝南人，湖南大学教授、博士生导师，主要研究方向为工业过程控制与模式识别。|李骁（1993-），男，湖南临湘人，湘潭大学硕士生，主要研究方向为图像处理与模式识别。|毛丽珍（1994-），女，湖南岳阳人，湘潭大学硕士生，主要研究方向为图像处理与模式识别。
基金资助:
国家自然科学基金资助项目(61573299);国家自然科学基金资助项目(61673162);国家自然科学基金资助项目(61672216);国家自然科学基金资助项目(61602397);湖南省自然科学基金资助项目(2017JJ3315);湖南省自然科学基金资助项目(2017JJ2251);湖南省自然科学基金资助项目(2016JJ3125)

Incoherent dictionary learning and sparse representation for single-image rain removal

Hong-zhong TANG^1,^2,³,Xiang WANG^1,³,Xiao-gang ZHANG²,Xiao LI^1,³,Li-zhen MAO^1,³

¹ College of Information Engineering,Xiangtan University,Xiangtan 411105,China
² College of Electrical and Information Engineering,Hunan University,Changsha 410082,China
³ Institute of Control Engineering,Xiangtan University,Xiangtan 411105,China

Revised:2017-04-08 Online:2017-07-01 Published:2017-08-25
Supported by:
The National Natural Science Foundation of China(61573299);The National Natural Science Foundation of China(61673162);The National Natural Science Foundation of China(61672216);The National Natural Science Foundation of China(61602397);The Natural Science Foundation of Hunan Province(2017JJ3315);The Natural Science Foundation of Hunan Province(2017JJ2251);The Natural Science Foundation of Hunan Province(2016JJ3125)

摘要/Abstract

摘要：

提出一种非相干字典学习及稀疏表示方法，并将其应用于单幅图像去雨。该方法在字典学习阶段，为降低有雨原子与无雨原子间的相似性，引入字典的非相干性，构建新的目标函数，不仅可以保证有雨字典与无雨字典的可分性，而且学习的非相干字典具有类似于紧框架的性质，可以逼近等角紧框架。通过有雨字典与无雨字典对高频图像的稀疏表示，能够更好地分离出高频图像中的有雨分量与无雨分量，将高频无雨分量与低频图像融合实现图像去雨。采用合成雨图与真实雨图对算法进行验证，实验结果表明，算法所学习的非相干字典具有较好的稀疏表示性能，去雨后的图像雨线残留较少，边缘细节保持较好，视觉效果更为清晰自然。

关键词: 非相干字典, 字典学习, 稀疏表示, 单幅图像去雨

Abstract:

The incoherent dictionary learning and sparse representation algorithm was present and it was applied to single-image rain removal.The incoherence of the dictionary was introduced to design a new objective function in the dictionary learning,which addressed the problem of reducing the similarity between rain atoms and non-rain atoms.The divisibility of rain dictionary and non-rain dictionary could be ensured.Furthermore,the learned dictionary had similar properties to the tight frame and approximates the equiangular tight frame.The high frequency in the rain image could be decomposed into a rain component and a non-rain component by performing sparse coding based learned incoherent dictionary,then the non-rain component in the high frequency and the low frequency were fused to remove rain.Experimental results demonstrate that the learned incoherent dictionary has better performance of sparse representation.The recovered rain-free image has less residual rain,and preserves effectively the edges and details.So the visual effect of recovered image is more sharpness and natural.

Key words: incoherent dictionary, dictionary learning, sparse representation, single-image rain removal

中图分类号:

TP391.4

汤红忠,王翔,张小刚,李骁,毛丽珍. 面向单幅图像去雨的非相干字典学习及其稀疏表示研究[J]. 通信学报, 2017, 38(7): 28-35.

Hong-zhong TANG,Xiang WANG,Xiao-gang ZHANG,Xiao LI,Li-zhen MAO. Incoherent dictionary learning and sparse representation for single-image rain removal[J]. Journal on Communications, 2017, 38(7): 28-35.

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参考文献 20

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比较对象	图像1	图像2	图像3	图像4	图像5	图像6	平均值
标准图像	1	1	1	1	1	1	1
合成有雨图像	0.755	0.600	0.525	0.712	0.688	0.708	0.665
文献[8]算法去雨图像	0.726	0.762	0.669	0.748	0.695	0.802	0.734
文献[9]算法去雨图像	0.775	0.765	0.539	0.584	0.675	0.722	0.677
文献[10]算法去雨图像	0.752	0.805	0.635	0.821	0.700	0.741	0.742
本文算法去雨图像	0.811	0.812	0.689	0.821	0.760	0.805	0.783

比较对象	图像1	图像2	图像3	图像4	图像5	图像6	平均值
标准图像	∞	∞	∞	∞	∞	∞	∞
合成有雨图像	23.86	20.40	19.08	23.31	19.89	22.67	21.54
文献[8]算法去雨图像	24.70	25.63	19.20	25.37	22.30	21.77	23.16
文献[9]算法去雨图像	25.56	25.51	19.55	22.76	25.37	21.06	23.30
文献[10]算法去雨图像	24.55	26.14	26.70	28.71	19.50	23.10	24.78
本文算法去雨图像	26.53	26.21	25.37	26.57	19.82	24.90	24.90

图像尺寸（M×N）	文献[8]算法运行时间/s	文献[9]算法运行时间/s	文献[10]算法运行时间/s	本文算法运行时间/s
558×374	153.16	144.34	382.39	122.75
317×450	128.11	114.97	149.35	77.03
317×317	76.83	78.54	104.75	30.87

面向单幅图像去雨的非相干字典学习及其稀疏表示研究

Incoherent dictionary learning and sparse representation for single-image rain removal

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