一种基于非局部均值和预分割的图像去噪算法

一种改进的非局部均值图像去噪算法刘晓明，田 雨，何 徽，仲元红(重庆大学通信工程学院，重庆 400030)摘 要：传统非局部均值滤波算法中使用指数型加权核函数，容易导致图像细节因过度平滑而变得模糊。

为此，在指数型加权核函数的基础上，采用余弦系数加权的高斯核函数，设计一种改进的非局部均值图像去噪算法，并将其应用于加权系数计算中。

实验结果表明，该算法的去噪性能优于传统算法，且能更好地保留原图像的细节信息，峰值信噪比最大可以提升1.6 dB 。

关键词：图像处理；图像去噪；非局部均值；加权平均；高斯噪声；加权核函数Improved Non-local Means Algorithm for Image DenoisingLIU Xiao-ming, TIAN Yu, HE Hui, ZHONG Yuan-hong(College of Communication Engineering, Chongqing University, Chongqing 400030, China)【Abstract 】Aiming at the problem of the over-smoothness and blurs the details, which are caused by exponential kernel function used in original non-local means algorithm, this paper proposes a cosine Gaussian kernel function based on exponential kernel function and combined with a cosine coefficient and Gaussian kernel. It is used in the weight-computing of the improved algorithm. Experimental results show the algorithm has a superior denoising performance than the original one, especially with detail information in the image, and PSNR can be improved by 1.6 dB at most.【Key words 】image processing; image denoising; non-local means; weighted average; Gaussian noise; weighted kernel function DOI: 10.3969/j.issn.1000-3428.2012.04.065计 算 机 工 程Computer Engineering 第38卷 第4期 V ol.38 No.4 2012年2月February 2012·图形图像处理· 文章编号：1000—3428(2012)04—0199—03文献标识码：A中图分类号：TP3911 概述图像去噪是图像处理领域中最基础和广泛研究的热点问题。

一种用于图像去噪的非局部算法摘要我们提出了一种新的方法噪声方法来评估和比较数字图像去噪方法的性能。

我们首先计算和分析这种方法噪声的一大类去噪算法，即局部平滑滤波器。

其次，基于图像中所有像素的非局部平均，我们提出了一种新的算法- 非局部均值（NL-means）。

最后，我们介绍一些比较NL均值算法和局部平滑滤波器的实验。

1.介绍图像去噪方法的目标是从噪声测量中恢复原始图像，其中v（i）是观测值，u（i）是“真”值，n（i）是像素i处的噪声扰动。

模拟噪声对数字图像影响的最简单方法是添加高斯白噪声。

在那种情况下，n（i）是i.i.d. 具有零均值和方差σ2的高斯值。

已经提出了几种方法来消除噪音并恢复真实的图像。

尽管它们在工具上可能有很大不同，但必须强调的是，广泛的类别具有相同的基本评论：去噪是通过平均来实现的。

这种平均可以在本地进行：高斯平滑模型（Gabor [7]），各向异性过滤（Perona-Malik [11]，Alvarez等人[1]）和邻域过滤（Yaroslavsky [16]，Smith 等人。

[14]，Tomasi等人[15]）通过变分计算：总变差最小化（Rudin-Osher-Fatemi [13]）或频域中：经验维纳滤波器（Yaroslavsky [16] ）和小波阈值法（Coiffman-Donoho [5,4]）。

在形式上，我们定义了一个降噪方法Dh作为分解其中v是噪声图像，h是通常取决于噪声标准偏差的滤波参数。

理想情况下，Dhv比v更平滑，n（Dh，v）看起来像是白噪声的实现。

光滑部分与非光滑部分或振荡部分之间的图像分解是当前研究的主题（例如Osher等人[10]）。

在[8]中，Y.Meyer研究了适合这种分解的功能空间。

后一个研究的主要范围不是去噪，因为振动部分包含噪音和纹理。

去噪方法不应改变原始图像u。

现在，大多数去噪方法会降低或消除u的细节和纹理。

为了更好地理解这种移除，我们将介绍和分析方法噪声。

专利名称：一种分区域SAR图像非局部均值去噪方法专利类型：发明专利
发明人：辛志慧,麻伟,王志旭,孙雨,宣嘉裕
申请号：CN202110486169.2
申请日：20210430
公开号：CN113191979B
公开日：
20220624
专利内容由知识产权出版社提供
摘要：本发明涉及一种分区域SAR图像非局部均值去噪方法，包括：S1：对SAR图像进行预处理，将其噪声转变为加性噪声，得到SAR预处理图像；S2：对SAR预处理图像进行目标边缘提取，并根据提取得到的目标边缘轮廓，得到封闭的目标填充区域；S3：对目标填充区域进行标记，根据标记结果将SAR预处理图像，分为标记区域和未标记区域；S4：采用第一加权函数对标记区域进行滤波处理，采用第二加权函数对未标记区域进行滤波处理，得到SAR滤波图像；S5：对SAR滤波图像进行指数函数变换处理，得到SAR去噪图像；本发明的方法，在保留目标的细节纹理信息的同时，可以将非标记区域的噪声很大程度地平滑掉，既去除了噪声，又更好的保留了目标的细节以及纹理信息。

申请人：云南师范大学
地址：650000 云南省昆明市五华区一二一大街298号
国籍：CN
代理机构：西安嘉思特知识产权代理事务所(普通合伙)
代理人：王海栋
更多信息请下载全文后查看。

Region-based non-local means algorithm for noise removalW.L.Zeng and X.B.LuThe non-local means (NLM)provides a useful tool for image denoising and many variations of the NLM method have been proposed.However,few works have tried to tackle the task of adaptively choos-ing the patch size according to region characteristics.Presented is a region-based NLM method for noise removal.The proposed method first analyses and classifies the image into several region types.According to the region type,a local window is adaptively adjusted to match the local property of a region.Experimental results show the effectiveness of the proposed method and demonstrate its superior-ity to the state-of-the-art methods.Introduction:The use of the non-local means (NLM)filter for noise removal has been extensively studied in the past few years.The NLM filter was first addressed in [1].The discrete version of the NLM is as follows:u (k ,l )=(i ,j )[N (k ,l )w (k ,l ,i ,j )v (i ,j )(1)where u is the restored value at pixel (k,l )and N (k,l )stands for theneighbourhood of the pixel (k,l ).The weight function w (k,l,i,j )is defined asw (k ,l ,i ,j )=1exp −||T k ,l v −T i ,j v ||22,a(2)where T k,l and T i,j denote two operators that extract two patches of sizeq ×q centred at pixel (k,l )and (i,j ),respectively;h is the decay para-meter of the weights; . 2,a is the weighted Euclidean norm using a Gaussian kernel with standard deviation a ,and Z (k,l )is the normalised constantZ (k ,l )= (i ,j )exp −||T k ,l v −T i ,j v ||22,ah 2(3)The core idea of the NLM filter exploits spatial correlation in the entireimage for noise removal and can produce promising results.This method is time consuming and not able to suppress any noise for non-repetitive neighbourhoods.Numerous methods were proposed to accel-erate the NLM method [2–4].Also,variations of the NLM method have been proposed to improve the denoising performance [5–7].In smooth areas,a large matching window size could be used to reduce the influ-ence of misinterpreting noise as local structure.Conversely,a small matching window size could be used for the edge /texture region,which means not only the local structure existing within a neighbour-hood can be effectively used but can also speed up the matching process.To the best of our knowledge,few works have tried to tackle the task of adaptively choosing the patch size according to region characteristics.To overcome the disadvantage of the NLM method and its variances,in this Letter we present an adaptive NLM (ANLM)method for noise removal.The proposed method first analyses and classifies the image into several region types based on local structure information of a pixel.According to the region type,a local window is adaptively adjusted to match the local property of a region.Experimental results show the effectiveness of the proposed method.Proposed NLM algorithm:The adaptive patches based non-local means algorithm is conducted according to the region classification results,owing to the fact that the structure tensor can obtain more local structure information [8].Therefore,we use it to classify the region.For each pixel (i,j )of the region,the structure tensor matrix is defined asT s =t 11t 12t 12t 22 =G s ∗(g x (i ,j ))2G s ∗g x (i ,j )g y (i ,j )G s ∗g y (i ,j )g x (i ,j )G s ∗(g y (i ,j ))2where g x and g y stand for gradient information in the x and y directions,G s denotes a Gaussian kernel with a standard deviation s .Theeigenvalues l 1and l 2of T s are given byl 1=12t 11+t 22+ (t 11−t 22)2+4t 212 and l 2=1t 11+t 22− (t 11−t 22)2+4t 212 For a pixel in the smooth region,there is a small eigenvalue difference;for a pixel in an edge /texture region,there is a large eigenvalue differ-ence.Therefore,region classification can be achieved by examining the eigenvalue difference of each pixel.Let l (i ,j )=|l 1(i ,j )−l 2(i ,j )|.We propose the following classifi-cation scheme to partition the whole image region into n classes {c 1,···,c n }:(i ,j )[c 1,if l (i ,j )≤l min +(l max −l min )n c 2,if l (i ,j )≤l min +2(l max −l min )n ...c n ,if l (i ,j )≤l min +n (l max −l min )n ⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎩where l min and l max are the minimum and maximum of {l (i ,j ):(i ,j )[V },respectively.To exploit the local structure information and reduce noise in different regions,we adaptively choose the matching window based on the region classification result.The scheme for selecting the matching window is asfollows:if (k ,l )[c r ,T k ,l :=T r k ,l ,where T rk ,l denotes an operator of the r-type region that extracts one patch of size q r ×q r .To reduce the influ-ence of misinterpreting noise as local structure,a larger patch size is adopted for a smooth region.In contrast,a small patch size is employed for the edge /texture region.Intuitively,the number of the class n should be as big as possible.In practice,the gain is insignificant for n greater than 4.Therefore,we choose n ¼4in our experiments.Table 1:PSNR performance comparison of ‘Lena’,‘Barbara’,‘Peppers’imagesFig.1Comparison of results with additive Gaussian noise of s ¼35a Original image b Noisy image c NLM d WUNLM e ANLMExperimental results:In this Section,we compare our proposed ANLM method with the NLM method [2]and the weight update NLM (WUNLM)method [3].We test the proposed method on ‘Lena’,‘Barbara’,and ‘Peppers’,which were taken from the USC-SIPI Image Database (/database/base).The performance of the method was evaluated by measuring the peak signal-to-noise ratio (PSNR).In general h corresponds to the noise level and is usuallyELECTRONICS LETTERS 29th September 2011Vol.47No.20,1125-1127fixed to the standard deviation of the noise.The size of the search window is21×21.Table1shows results obtained with three methods across four noise levels.Figs.1a and b,show the‘Barbara’image and the corresponding noisy image generated by adding Gaussian white noise with variance s¼35,respectively.Figs.1c–e show denoised images by using the NLM,WUNLM,and ANLM methods,respectively.From the standpoint of perceptual view and PSNR values,the proposed ANLM method produced the best quality. Conclusions:An adaptive NLM(ANLM)method for noise removal is presented.In the method,an image isfirst analysed and classified into several region types.According to the region type,a local window is adaptively adjusted to match the local property of a region. Experimental results show the effectiveness of the proposed method and demonstrate its superiority to the state-of-the-art methods. Acknowledgments:This work was supported by the National Natural Science Foundation of China under grant60972001,the National Key Technologies R&D Program of China under grant2009BAG13A06 and the Scientific Innovation Research of College Graduate in Jiangsu Province under grant CXZZ_0163.#The Institution of Engineering and Technology20115August2011doi:10.1049/el.2011.2456W.L.Zeng(School of Transportation,Southeast University,Nanjing 210096,People’s Republic of China)X.B.Lu(School of Automation,Southeast University,Nanjing210096, People’s Republic of China)E-mail:xblu2008@References1Budades,A.,Coll,B.,and Morel,J.M.:‘A review of image denoising algorithms,with a new one’,Multiscale Model Simul.,2005,4,(2), pp.490–5302Mahmoudi,M.,and Sapiro,G.:‘Fast image and video denoising via nonlocal means of similar neighborhoods’,IEEE Signal Process.Lett., 2005,12,(12),pp.839–8423Vignesh,R.,Oh,B.T.,and Kuo,C.-C.J.:‘Fast non-local means(NLM) computation with probabilistic early termination’,IEEE Signal Process.Lett.,2010,17,(3),pp.277–2804Brox,T.,Kleinschmidt,O.,and Cremers,D.:‘Efficient nonlocal means for denoising of textural patterns’,IEEE Trans.Image Process.,2008, 17,(7),pp.1083–10925Kervrann,C.,and Boulanger,J.:‘Optimal spatial adaptation for patch-based image denoising’,IEEE Trans.Image Process.,2006,15,(10), pp.2866–28786Ville,D.V.D.,and Kocher,M.:‘SURE-based non-local means’,IEEE Signal Process.Lett.,2009,16,(11),pp.973–9767Park,S.W.,and Kang,M.G.:‘NLM algorithm with weight update’, Electron.Lett.,2010,16,(15),pp.1061–10638Brox,T.,Weickert,J.,Burgeth,B.,and Mrazek,P.:‘Nonlinear structure tensors’,Image put.,2006,24,pp.41–55ELECTRONICS LETTERS29th September2011Vol.47No.20。

使用双边和非局部均值滤波进行医学图像去噪摘要医学图像的瓶颈之一是信噪比很低，因此需要对同一对象进行长时间和重复性的获取来降低噪声和模糊。

为了获取一个高信噪比而不需要长时间重复性的扫描，数据的后期处理（例如去噪）就具有重要意义。

双边滤波和非局部均值滤波经常被用来进行医学图像去噪。

本文提出了一种阈值方案即通过对通用的阈值引入比例因子进行小波和轮廓波变换的去噪。

同时本文提出的轮廓波阈值方案也可作为双边和NLM滤波的预处理步骤。

仿真实验表明本文提出的单个实体包括预处理步骤和双边或NLM去噪步骤，在PSNR和感觉质量方面明显优于单个的双边滤波或单个的NLM去噪。

1、介绍先进医学图像技术的快速发展例如磁共振成像（MRI），正电子发射断层扫描（PET）和CT技术在病人体内进行无创性诊断提供了新的方式。

基于成像模式的一些先进技术仍在研究阶断，但是从没有达到常规的临床应用中。

瓶颈之一就是由于信噪比低，对于同一对象需要进行长时间和重复性的获取来降低噪声和模糊。

例如，一个高信噪比的扩散张量成像数据集需要一个小时获取数据。

一个高信噪比的高角分辨率扩散成像数据的获取需要13个小时。

为了从噪声和模糊图像中恢复高信噪比图像，而不需要长时间重复性扫描，数据的后处理在以下两个方面具有置关重要的角色：（1）自动去噪和去模糊算法恢复数据能降低时间消耗；（2）计算目标的分割技术能够从噪声观测值中直接、自动地将数据提取出来。

在医学图像中我们经常会面临一个相对较低信噪比或者与一个较好的SNR有一个较低对比度情况，庆幸的是人类视觉系统在结构识别（甚至存在相当大的噪声）都是卓有成效的。

但是如果SNR太小或对比度太低就很难检测解剖结构。

定义整体图像质量包括实际和感觉标准。

此外，它在很大程度上取决于特定的诊断任务。

在某些情况下，需要一个高的空间分辨率和一个高的对比度，然而，在其它情况下，更多是是需要知觉的标准。

对于一个医学图像的视觉分析，细节的清晰（主要包括边缘信息和对象的可见度）是很重要的。

基于图像分割的非局部均值去噪算法徐苏;周颖玥【期刊名称】《计算机应用》【年(卷),期】2017(37)7【摘要】针对传统非局部均值(NLM)算法的滤波参数非自适应及去噪后边缘易模糊的缺点,提出一种基于图像分割的非局部均值去噪算法.该算法分为两个阶段:第一阶段根据噪声大小及图像纹理自适应确定滤波参数的值,并采用传统非局部均值算法得到去噪结果图;第二阶段根据像素点方差的不同,将该去噪结果图分为细节区域和背景区域,再对属于不同区域的图像块分别去噪,同时为了更有效地去除噪声,还采用了反向投影的方式,充分利用了第一阶段方法噪声中残留的结构信息.实验结果表明,与传统非局部均值算法及其三种改进算法相比,所提算法的峰值信噪比(PSNR)及结构相似性(SSIM)更高,纹理细节和边缘结构更完整,图像更清晰,本真信息保留更完整.%Focusing on the problems of non-adaption of filtering parameters and edge blur of Non-Local Means (NLM) algorithm,an improved NLM denoising algorithm based on image segmentation was proposed.The proposed algorithm is composed of two phases.In the first phase,the filtering parameter was determined according to the noise level and image structure,and traditional NLM algorithm was used to remove the noise and generate the rough clean image.In the second phase,the estimated clean image was divided into detailed region and background region based on pixel variance,and the image patches belonged to different regions were denoised separately.To effectively remove the noise,the back projectionwas utilized to make full use of the residual structure from the method noise of the first phase.The experimental results show that compared with traditional NLM and three NLM-improved algorithms,the proposed algorithm achieves higher Peak Signal-to-Noise Ratio (PSNR) and Structural SIMilarity (SSIM),while maintaining more structure details and edges,making the denoised image clear and retaining the complete real information.【总页数】6页(P2078-2083)【作者】徐苏;周颖玥【作者单位】西南科技大学信息工程学院,四川绵阳621010;特殊环境机器人技术四川省重点实验室(西南科技大学),四川绵阳621010;西南科技大学信息工程学院,四川绵阳621010;特殊环境机器人技术四川省重点实验室(西南科技大学),四川绵阳621010【正文语种】中文【中图分类】TP391.413【相关文献】1.基于梯度特征的双核非局部均值去噪算法 [J], 张玉征;杨词慧;林泉2.基于局部边沿方向的非局部均值图像去噪算法 [J], 贾丽娜;焦枫媛;刘瑞强;桂志国3.基于直觉模糊散度的自适应非局部均值去噪算法 [J], 张宁; 宋小鹏; 刘祎; 张鹏程; 桂志国4.基于3维轴距与非局部均值的无人机巡检图像去噪算法 [J], 唐丽丽;马宪民;商立群5.基于边缘检测的非局部均值图像去噪算法 [J], 李向前因版权原因，仅展示原文概要，查看原文内容请购买。

BM3D（Block Matching and 3D Filtering）去噪原理是一种先进的图像去噪算法，它基于非局部均值（NL-Means）的思想，通过分块匹配和三维滤波来去除图像中的噪声。

以下是BM3D去噪原理的详细解释：
1.分块匹配：首先将含噪图像分割成大小相等的小块，然后对每个小块进行变换（如离散余弦变换
DCT）。

接着，通过块匹配算法找到与每个小块相似的其他小块，并将它们组合成一个三维矩阵。

这个过程中，块匹配是基于小块之间的相似性度量（如欧氏距离）进行的，相似的小块被认为具有相似的噪声模式。

2.三维滤波：在得到三维矩阵后，BM3D算法对其进行三维变换（如三维DCT）以将信号和噪声
分离。

然后，采用硬阈值滤波或软阈值滤波等方法去除低于一定幅度的变换系数，即去除噪声成分。

最后，进行三维逆变换以恢复去噪后的信号。

3.聚合：将经过三维滤波后的三维矩阵重新分块，并将每个小块按照原始图像中的位置还原。

对于
重叠部分的小块，采用逐像素加权平均的方法得到最终的去噪图像。

BM3D算法通过分块匹配和三维滤波的方式，能够有效地降低图像中的噪声，同时保留图像细节。

它在去噪过程中充分利用了图像中相似块之间的冗余信息，提高了去噪效果。

因此，BM3D算法被广泛应用于图像去噪、图像增强和图像恢复等领域。