数值计算与计算机应用
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数值计算与计算机应用  2018, Vol. 39 Issue (1): 44-59    DOI:
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一种求解带有冲击噪声的图像去模糊去噪问题的变步长分裂Bregman算法
申远, 李瑶
南京财经大学应用数学学院, 南京 210023
A NEW SPLIT BREGMAN METHOD WITH VARIATE STEP FOR IMAGE DEBLURRING AND DENOISING WITH IMPULSE NOISE
Shen Yuan, Li Yao
School Applied Mathematics, Nanjing University of Financeand Economics, Nanjing 210023, China
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摘要 分裂Bregman算法是一种有效的求解L1正则化问题的算法,Chen等人结合线性化、变步长、非单调等技术,改进了固定步长的分裂Bregman算法,提出了变步长分裂Bregman算法(BOSVS),并将该算法用于求解带有高斯噪声的图像去模糊去噪问题,其数值实验结果令人满意.但是它不能求解带有冲击噪声的图像去模糊去噪问题,我们在BOSVS算法基础上,提出了一种新的变步长分裂Bregman算法,用于求解带有冲击噪声的图像去模糊去噪问题.该算法一方面保留了BOSVS算法的线性化、变步长、非单调等特点;另一方面通过在原模型目标函数上增加一个L1正则项,使得模型不仅可以处理高斯噪声,还可以处理冲击噪声,因而适用范围比BOSVS算法更为广泛.初步数值实验结果表明,新算法得到结果的质量明显优于FTVd,且计算时间、算法效率也较有竞争力.
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关键词图像去模糊去噪   Barzilai-Borwein步长   分裂Bregman算法     
Abstract: The Split Bregman method is an effective method for solving the problem with L1 regularization. Chen and et al. improved the split Bregman method by adopting the linearization technique, variate and nonmonotone step size, and proposed a new split Bregman method with variate step size (BOSVS). The BOSVS can be used to solve image deblurring and denoising problem with Gaussian noise, and its numerical results are satisfactory. However, it can not be used to solve image deblurring and denoising problem with impulse noise. In this paper, we improve the BOSVS and propose a new split Bregman method with variate step size for solving image deblurring and denoising problem with impulse noise. On one hand, it retains the advantages of BOSVS such as linearization technique, variate and nonmonotone step size; on the other hand, by adding a L1 regularization term to the objective function, the model can deal with Gaussian noise as well as impulse noise. Therefore, the new method has wider range of application than the BOSVS. Preliminary experimental results show that, compared with an efficient method for the same problem, the new method can obtain a better result, and its computation time and algorithm efficiency are also competitive.
Key wordsImage deblurring and denoising   Barzilai-Borwein stepsize   Split Bregman method   
收稿日期: 2017-03-16;
基金资助:

国家自然科学基金青年项目(11401295);国家自然科学基金数学天元基金数学访问学者项目(11726618);江苏省自然科学基金青年项目(BK20141007);国家社科基金重点项目(12\&ZD114);国家社科基金一般项目(15BGL58);江苏省社科基金青年项目(14EUA001)和江苏省青蓝工程项目.

引用本文:   
. 一种求解带有冲击噪声的图像去模糊去噪问题的变步长分裂Bregman算法[J]. 数值计算与计算机应用, 2018, 39(1): 44-59.
. A NEW SPLIT BREGMAN METHOD WITH VARIATE STEP FOR IMAGE DEBLURRING AND DENOISING WITH IMPULSE NOISE[J]. Journal of Numerical Methods and Computer Applicat, 2018, 39(1): 44-59.
 
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