高阶PDE模型中的松弛中值图像去噪方法

J4 ›› 2016, Vol. 38 ›› Issue (02): 338-343.

高阶PDE模型中的松弛中值图像去噪方法

芦碧波1,王建龙1,张跃2,王国东2

(1.河南理工大学计算机科学与技术学院,河南焦作 454000;2.河南理工大学电气工程与自动化学院,河南焦作 454000)

收稿日期:2015-01-12 修回日期:2015-04-24 出版日期:2016-02-25 发布日期:2016-02-25
基金资助:
国家自然科学基金(11301113,U1404103);河南省教育厅科技攻关重点项目(14A520029);河南理工大学博士基金 (B200941);河南理工大学青年骨干教师资助计划(0913)

A relaxed median image denoising method
in high order PDE model

LU Bibo1,WANG Jianlong1,ZHANG Yue2,WANG Guodong2

(1.School of Computer Science and Technology,Henan Polytechnic University,Jiaozuo 454000;
2.School of Electrical Engineering and Automation,Henan Polytechnic University,Jiaozuo 454000,China)

Received:2015-01-12 Revised:2015-04-24 Online:2016-02-25 Published:2016-02-25

摘要/Abstract

摘要：

针对平均曲率极小化模型在去噪过程中产生斑点的问题,提出了一种平均曲率和松弛中值滤波结合的迭代算法。首先,使用平均曲率模型对噪声图像处理,根据局部方差信息，利用阈值确定斑点的位置。其次,利用具一定边界保持性质的松弛中值滤波器消除斑点噪声。最后,为更有效地消除斑点，在每一次随着时间的迭代后都使用松弛中值滤波。对曲线和图像进行去噪仿真实验,结果表明，相对于平均曲率模型，本文算法在客观指标和主观视觉效果上均有更好的去噪效果和更低的时间复杂度。

关键词: 图像去噪, 偏微分方程, 平均曲率, 松弛中值滤波器, 斑点效应

Abstract:

To remove speckle effect produced by the mean curvature model, we propose an iterative image denosing algorithm, which combines the mean curvature model and the relaxed median filter. Firstly, we denoise the image by the mean curvature model. Then the speckle noise is located using a threshold according to the variance of the image. Finally the relaxed median filter is introduced. To remove the speckle noise more efficiently, the filter is applied at every iteration step. Denoising simulations on curves and images show that the proposed algorithm has better denoising effect in terms of objective indicators and subjective visual effect, as well as lower time complexity in comparison with the mean curvature model.Key words

Key words: image denoising;partial differential equation;mean curvature;relaxed median filter;speckle effect

芦碧波1,王建龙1,张跃2,王国东2. 高阶PDE模型中的松弛中值图像去噪方法[J]. J4, 2016, 38(02): 338-343.

LU Bibo1,WANG Jianlong1,ZHANG Yue2,WANG Guodong2. A relaxed median image denoising method
in high order PDE model [J]. J4, 2016, 38(02): 338-343.

参考文献［14］

［1］	Perona P,Malik J.Scalespace and edge detection using anisotropic diffusion［J］.IEEE Transactions on Pattern Analysis and Machine Intelligence,1990,12(7):629639.
［2］	Rudin L,Osher S,Fatemi E.Nonlinear total variation based noise removal algorithms［J］.Physica D,1992,60(14):259268.
［3］	You Yuli,Kaveh M.Fourthorder partial differential equations for noise removal［J］.IEEE Transactions on Image Processing,2000,9(10):17231730.
［4］	Lysaker M,Lundervold A,Tai X C.Noisy removal using fourthorder partial differential equation with applications to medical magnetic resonance images in space and time［J］.IEEE Transactions on Image Processing,2003,12(12):15791590.
［5］	Qiu Shufang,Liu Xilin,Liu Shenglan.An image denoising method based on PDE and structuretexture［J］.Journal of East China Institute of Technology (Natural Science),2013,36(1):9095.(in Chinese)
［6］	Fan Linan,Huang He,Tian Dan,et al.Comprehensive total variation denoising model based on adaptive parameters［J］.Journal of Shenyang University (Natural Science),2013,25(5):383388.(in Chinese)
［7］	Zhu W,Chan T F.Image denoising using mean curvature［EB/OL］.［20141113］.http://www.math.nyu.edu/~wzhu/.
［8］	Zhu W,Chan T.Image denoising using mean curvature of image surface ［J］.SIAM Journal on Imaging sciences,2012,5(1):132.
［9］	Yang Fenlin,Chen Ke,Yu Bo,et al.A relaxed fixed point method for a mean curvaturebased denoising model ［J］.Optimization Method and Software,2014,29 (2):274285.
［10］	BritoLoeza C,Chen Ke.Fast iterative algorithms for solving the minimization of curvaturerelated functionals in surface fairing［J］.International Journal of Computer Mathematics,2013,90(1):92108.
［11］	Brito C,Chen Ke.Multigrid algorithm for high order denoising ［J］.SIAM Journal on Imaging Sciences,2010,3 (3):363389.
［12］	Xu Weiling,Shen Minfen,Yang Jinyao.Speckle reduction for ultrasound image using edge directions in DTCWT domain［J］.Journal of Data Acquisition and Processing,2011,26(6):671675.(in Chinese)
［13］	Gao Zhi, Lin Xinqi,Wu Peng,et al.Foreground image denoising based on layered filter［J］.Journal of Data Acquisition and Processing,2014,29(1):7682.(in Chinese)
［14］	Li Yuanyuan,Pan Zhenkuan,Wei Weibo.Higher order image diffusion model based on median formula［J］.Computer Engineering and Applications,2010,46(9):159162.(in Chinese)
［15］	Kaimal R K.An improved hybrid model for molecular image denoising［J］.Journal of Mathematical Imaging and Vision,2008,31(1):7379.
［16］	He Kaiming,Sun Jian,Tang Xiaoou.Guided image filtering［J］.IEEE Transactions on Pattern Analysis and Machine Intelligence,2013,35(6):13971409.
	附中文参考文献：
［5］	邱淑芳,刘西林,刘胜兰.一种基于PDE与结构纹理分解的图像去噪方法［J］.东华理工大学学报（自然科学版）,2013,36(1):9095.
［6］	范立南,黄鹤,田丹,等.基于自适应参数的全变分综合图像去噪模型［J］.沈阳大学学报（自然科学版）,2013,25(5):383388.
［12］	许慰玲,沈民奋,杨金耀.基于DTCWT方向信息的超声图像斑点噪声消除［J］.数据采集与处理,2011,26(6):671675.
［13］	高智,林新棋,吴鹏,等.基于分层筛选方法的前景图像去噪［J］.数据采集与处理,2014,29(1):7682.
［14］	李媛媛,潘振宽,魏伟波.高阶图像扩散模型的中值公式［J］.计算机工程与应用，2010,46(9):159162.

[1]	陈新海, 刘杰, 万仟, 龚春叶, . 一种改进的基于深度神经网络的偏微分方程求解方法[J]. 计算机工程与科学, 2022, 44(11): 1932-1940.
[2]	张露文, 薛晓军, 李恒, 王海瑞, 张国银, 赵磊. 基于改进NLM的PCB图像去噪算法[J]. 计算机工程与科学, 2021, 43(09): 1608-1615.
[3]	陆海青1,2，葛洪伟1,2. 混合鲁棒权重和改进方法噪声的两级非局部均值去噪[J]. 计算机工程与科学, 2018, 40(07): 1227-1236.
[4]	杨培1，高雷阜1，王江1，訾玲玲2. 基于稀疏表示与字典学习的彩色图像去噪算法[J]. 计算机工程与科学, 2018, 40(05): 842-848.
[5]	李伟凯1,王政霞1,蒋伟2. 一种自适应分数阶偏微分图像增强模型[J]. 计算机工程与科学, 2018, 40(04): 699-706.
[6]	冀中，赵硕，王建，刘立. 基于噪声检测的总变分去噪算法[J]. 计算机工程与科学, 2018, 40(03): 507-514.
[7]	王晓燕1,2，池天河1. 结合变异粒子群和字典学习的遥感影像去噪[J]. 计算机工程与科学, 2017, 39(09): 1675-1681.
[8]	王小玉，郭晓中. 基于非局部总广义变分的图像去噪[J]. 计算机工程与科学, 2017, 39(08): 1520-1524.
[9]	许光宇，蒋社想. 椒盐噪声图像的非局部平均滤波算法[J]. 计算机工程与科学, 2017, 39(06): 1133-1140.
[10]	郑传远，李良福，肖樟树，陆铖. 一种改进的各向异性扩散深度图像增强算法[J]. 计算机工程与科学, 2016, 38(09): 1823-1829.
[11]	李嘉浪，李华君，徐庆. 基于小波阈值的非局部均值去噪[J]. J4, 2015, 37(08): 1546-1550.
[12]	李秋妮，晁爱农，史德琴，孔星炜. 一种新的小波半软阈值图像去噪方法[J]. J4, 2014, 36(08): 1566-1570.
[13]	刘西成，许海英，谌贵辉. 一种改进的脉冲噪声滤波方法[J]. J4, 2012, 34(11): 120-123.
[14]	杨居义. 基于第二代Bandelet变换的彩色图像去噪算法[J]. J4, 2010, 32(6): 68-67.
[15]	郭静,田有先. 基于各向异性扩散方程的多层次并行图像去噪[J]. J4, 2010, 32(4): 49-51.