L1范数约束的非局部均值正则图像去模糊模型

doi:10.13190/j.jbupt.2017-101

北京邮电大学学报 ›› 2018, Vol. 41 ›› Issue (1): 81-87.doi: 10.13190/j.jbupt.2017-101

L₁范数约束的非局部均值正则图像去模糊模型

冯象初, 刘鑫, 杨春雨, 王卫卫

西安电子科技大学数学与统计学院, 西安 710071

收稿日期:2017-11-16 出版日期:2018-02-28 发布日期:2018-01-04
作者简介:刘鑫(1992-),男,硕士生,E-mail:liuxin386@126.com;冯象初(1962-),男,教授,博士生导师.
基金资助:
国家自然科学基金项目（61271294，61472303，61772389）；中央高校基本科研业务费专项资金项目（NSIY21）

L₁-Nonlocal Means Regularization Model for Image Deblurring Problem

FENG Xiang-chu, LIU Xin, YANG Chun-yu, WANG Wei-wei

School of Mathematics and Statistics, Xidian University, Xi'an 710071, China

Received:2017-11-16 Online:2018-02-28 Published:2018-01-04

摘要/Abstract

摘要： 为了保护图像边缘、细节等信息，建立了l₁范数约束的非局部均值正则模型.首先通过实验证明了非局部均值去噪算法余项的概率密度函数具有较强的拖尾性质，符合Laplace分布的特点.基于此，使用l₁范数约束的非局部均值去噪算法余项作为新的正则项，提出了新的正则模型.然后利用Bregman算子分裂算法求解得到相应的优化算法，并且可将新算法看成Plug-and-Play Priors算法的推广.实验结果表明，新模型在去除模糊，保护图像边缘、细节等信息方面的性能都优于l₂范数约束的非局部均值正则模型和Plug-and-Play Priors模型.

关键词: 图像去模糊, 非局部均值算法, 正则模型, Bregman算子分裂算法

Abstract: An l₁-nonlocal means regularization model was proposed in order to preserve the edges and details while deblurring the blurred image. Firstly, the article empirically gave out that the distribution of the residual in the nonlocal means denoising algorithm (differences between the noisy image and the denoised result) is heavy-tailed, which well fits the Laplacian distribution. Based on this observation, a new regularization model was proposed by using the l₁-norm constrained residual as the new regularization term. Then the corresponding optimization algorithm was designed by utilizing the Bregmanized operator splitting algorithm, which can be regarded as an extension of plug-and-play Priors algorithm. Experiments show that the new model achieves better performance than the l₂-nonlocal means regularization model and the plug-and-play priors model in terms of both restoration results and preserving the edges and details of the image.

Key words: image deblurring, non-local means algorithm, regularization model, Bregmanized operator splitting

中图分类号:

TN929.53

冯象初, 刘鑫, 杨春雨, 王卫卫. L₁范数约束的非局部均值正则图像去模糊模型[J]. 北京邮电大学学报, 2018, 41(1): 81-87.

FENG Xiang-chu, LIU Xin, YANG Chun-yu, WANG Wei-wei. L₁-Nonlocal Means Regularization Model for Image Deblurring Problem[J]. JOURNAL OF BEIJING UNIVERSITY OF POSTS AND TELECOM, 2018, 41(1): 81-87.

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L₁范数约束的非局部均值正则图像去模糊模型

L₁-Nonlocal Means Regularization Model for Image Deblurring Problem

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