一种改进的原始对偶法求解TV-L1图像去噪模型

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一种改进的原始对偶法求解TV-L1图像去噪模型徐静, 刘俊皓浙江工商大学统计与数学学院, 杭州 310018 An Improved TV-L1 Image Denoising Model Solved by Primal-Dual Method XU Jing, LIU JunhaoCollege of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018

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摘要数字图像在采集过程中通常会因为硬件问题被椒盐噪声所污染，椒盐噪声强度大，分布随机，对图像的后续处理会产生极大的影响.因此，椒盐噪声的去除对图像处理十分重要.在处理椒盐噪声的方法中，传统的中值滤波法在噪声强度增强时容易出现恢复不完全现象，自适应中值滤波法根据噪声强弱自动选择滤波窗口大小改善了传统的中值滤波法，但在噪声强度增强时容易过度平滑图像，丢失图像的纹理细节.研究表明，变分模型去噪时能够克服滤波法的缺点，有效地保持图像的纹理细节.其中，TV-L1模型相对于传统变分模型对椒盐噪声有更好的去噪效果，但在图像平滑区域容易产生阶梯效应.对此，本文提出一种自适应中值滤波和TV-L1交替迭代的去噪模型.在求解TV-L1模型时采用原始对偶算法求解以增大求解空间，克服了TV-L1模型在求解时的不可微性.仿真实验与Chambolle提出的原始对偶求解TV-L1模型，以及加入Huber范数的TV-L1改进模型进行对比.实验结果表明，尤其在椒盐噪声强度较大的情况下，该模型相比以上对比模型的PSNR值及视觉效果均有所提高，在较好去除噪声的同时保持了纹理细节，改善了阶梯效应.

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收稿日期: 2020-02-19

PACS:

O241.82

引用本文:

徐静, 刘俊皓. 一种改进的原始对偶法求解TV-L1图像去噪模型[J]. 应用数学学报, 2020, 43(4): 684-699. XU Jing, LIU Junhao. An Improved TV-L1 Image Denoising Model Solved by Primal-Dual Method. Acta Mathematicae Applicatae Sinica, 2020, 43(4): 684-699.

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[1]	肖佳, 张俊华, 梅礼晔. 基于改进BM3D算法的椒盐噪声去噪. 计算机工程与应用, 2018, 54(21):170-175(Xiao J, Zhang J H, Mei L Y. Salt and pepper noise denoising based on improved BM3D algorithm. J. Computer Engineering and Applications, 2018, 54(21):170-175)
[2]	周冲, 张鹏程, 刘欢, 桂志国. 自适应反距离加权法滤除椒盐噪声. 中北大学学报(自然科学版), 2019, 40(04):372-377+384(Zhou C, Zhang P C, Liu H, et.al Filtering salt and pepper noise by adaptive inverse distance weighting. J. Journal of North University of China (Natural Science Edition), 2019, 40(04):372-377+384)
[3]	杨楠. 基于决策判别的高密度椒盐噪声去除方法研究. 兰州大学, 2018(Yang N. Study on the Removal of High Density Salt and Pepper Noise Based on Decision-baesd Algorithm. D. Lanzhou University, 2018)
[4]	张龙, 刘朝霞, 刘洪琛. 一种去除椒盐噪声带L1保真项的混合变分模型. 计算机工程与应用, 2019, 55(01):210-216(Zhang L, Liu Z X, Liu H C. Mixed variational with L1 fidelity model for removal of salt and pepper noise. J.Computer Engineering and Applications, 2019, 55(01):210-216)
[5]	李健, 丁小奇, 陈光等. 基于改进高斯滤波算法的叶片图像去噪方法. 南方农业学报, 2019, 50(06):1385-1391(Li J, Ding X Q, Chen G. Blade image denoising method based on improved Gaussian filtering algorithm. Journal of Southern Agriculture, 2019, 50(06):1385-1391)
[6]	高飞, 朱磊, 冯子金, 韩普. 基于变差系数的SAR图像非局部均值滤波算法. 信息通信, 2019, 10:42-44 Gao F, Zhu L, Feng Z J, et.al. Nonlocal Mean Filtering Algorithm for SAR Images Based on Variation Coefficients. J. Information and Communications, 2019, 10:42-44
[7]	Stork M. Median filters theory and applications. Third International Conference on Electrical and Electronics Engineering Papers-Chamber of Electrical Engineering, 2003, Bursa, Turkey, December 3-7
[8]	Hwang H, Haddad R A. Adaptive median filters:new algorithms and results. IEEE Transaction on Image Processing, 1995, 4(4):499-502
[9]	Tikhonov A N, Arsenin V Y. Solutions of Ⅲ-posed problems. Mathematics of Computition, 1977, 32:491
[10]	Rudin L, Osher S, Fatemi E. Nonlinear total variation based noise removal algorithms. Physica D Nonlinear Phenomena, 1992, 60:259-268
[11]	Lee C-O, Nam C, Park J. Domain Decomposition Method Using Dual Conversion for the Total Variation Minimization with L1 Fidelity Term. Journal of Scientific Computing, 2018, 78(2):951-970
[12]	Chan T, Esedoglu S. Aspects of total variation regularized L1 function approximation. Siam Journal on Applied Mathematics, 2005, 65(5):1817-1837
[13]	Nikolova M. A variational approach to remove outliers and impulse noise. Journal of Mathematical Imaging and Vision, 2004, 20(1/2):99-120
[14]	Federica S, Dong Y Q, Martin S A. Total Variation Based Parameter-Free Model for Impulse Noise Removal. Numerical Mathematics:Theory, Methods and Applications, 2017, 20:186-204
[15]	Strekalovskiy E, Chambolle A, Cremers D. Convex Relaxation of Vectorial Problems with Coupled Regularization. Siam Journal On Imaging Sciences, 2014, 20:294-336
[16]	芦碧波, 王乐蓉, 郑艳梅, 王永茂, 李晓莹, 秦钰翔. 基于各向异性全变分的迭代滤波算法. 图学学报, 2018, 39(02):186-192(Lu B B, Wang L R, Zhen Y M, Wang Y M, Li X Y, Qin Y X. An Iterative Image Filter Based on Anisotropic Total Variation. Journal of Graphics, 2018, 39(02):186-192)
[17]	王乐蓉. 图像去噪的变分引导滤波及其快速算法. 河南理工大学, 2018(Wang L R. Total Variation Guided Filtering and Its Fast Algorithm for Image Denoising. Henan Polytechnic University, 2018)
[18]	芦碧波, 王乐蓉. 全变分引导的双边滤波图像去噪方法. 光学技术, 2018, 44(02):194-200) (Lu B B, Wang L R. Total variation guided bilateral filtering for image denoising. Optical Technique, 2018, 44(02):194-200
[19]	黄文笔, 战荫伟, 陈家益, 徐秋燕. 改进的自适应中值滤波算法. 计算机系统应用, 2018, 27(10):183-188) (Huang W B, Zhan Y W, Chen J Y, Xu Q Y. Improved Adaptive Median Filtering Algorithm. Computer Systems and Applications, 2018, 27(10):183-188)
[20]	Chambolle A. An Algorithm for Total Variation Minimization and Applications. Journal of Mathematical Imaging and Vision, 2004, 20:1-2
[21]	Chambolle A, Pierre-Louis Lions. Image recovery via total variation minimization and related problems. Numerische Mathematic, 1997, 76:2
[22]	Chambolle A, Pock T. A first-order primal-dual algorithm for convex problems with applications to imaging. Journal of Mathematical Imaging and Vision, 2011, 40(1):120-145

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[2]	邱松强, 陈中文. 一个无惩罚型原始对偶内点算法及其收敛性分析[J]. 应用数学学报(英文版), 2014, 37(3): 423-436.

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