MORPHOLOGICAL SIGNAL ADAPTIVE MEDIAN FILTER FOR NOISE REMOVAL

一种基于Rank变换的改进中值滤波夏道平;董方敏;潘天浩;姚刚;刘勇【摘要】In view of the defects of the isolate noise and continuous noise can not effectively filtered in conventional median filter algorithm, an improved median filter algorithm based on rank transform is proposed.Firstly, the isolate noise points can be found by rank transform; and then filtering all the isolate noise points by using median filter, and maintaining the image details, which can effectively filter the noise and protect the image details, the filter algorithm has a good effect of isolate noise. Secondly, as for continuous noise, the iterative algorithm is used to improve the median filter algorithm proposed before, by which to solve the problem of filtering continuous noise. The Experimental results show that the filter effect of algorithm proposed is better than the traditional filter algorithm; it can effectively denoising and can better keep the image details and edge.%针对传统中值滤波对孤立噪声点和连续噪声不能有效滤波等问题,提出了一种改进算法:首先通过Rank变换,找出图像中所有的孤立噪声点,然后遍历图像对孤立的噪声点采用中值滤波,最大限度保持图像细节,有效地解决了在抑制图像噪声和保护图像细节方面的矛盾,对图像中孤立噪声点有较好的滤波效果;随后,进一步针对少量连续噪声点的情况,采用迭代算法对上述改进中值滤波算法结果进行处理,来解决连续噪声的滤波问题.试验结果表明,本文算法滤波后的图像效果明显好于传统滤波方法,能够有效地去噪,并能较好地保持图像细节和边缘.【期刊名称】《三峡大学学报（自然科学版）》【年(卷),期】2011(033)002【总页数】4页(P100-103)【关键词】Rank变换;中值滤波;迭代算法【作者】夏道平;董方敏;潘天浩;姚刚;刘勇【作者单位】三峡大学智能视觉与图像信息研究所,湖北宜昌443002;三峡大学科技学院,湖北宜昌443002;三峡大学智能视觉与图像信息研究所,湖北宜昌443002;三峡大学电气与新能源学院,湖北宜昌443002;三峡大学智能视觉与图像信息研究所,湖北宜昌443002;三峡大学智能视觉与图像信息研究所,湖北宜昌443002【正文语种】中文【中图分类】TP391.4图像滤波技术可以从复杂的图像信号中提取所需要的信号,抑制不必要的信号,使图像更加清晰.近年来主要有两大类滤波方法:一类是空域滤波器,如均值滤波[1-2],中值滤波[3-5],统计滤波[6]等,由于此类方法的滤波效果主要取决于对像素邻域的处理方法和邻域大小,而对邻域处理的同时会模糊了图像细节,从而丢失了图像信息;另一类频域滤波,如高斯滤波[1],巴特沃斯滤波器[1],基于小波变换[7]的滤波算法等,由于此类滤波方法主要是对图像高频分量进行处理来实现图像滤波,而图像边缘和噪声频率分量均在高频部分,所以对高频分量进行降噪的同时,会使得边缘被错误判断为噪声点,从而使得图像目标信息被滤除,丢失了图像信息.近年来,由Matheron G 和Serra J等人创立的形态学滤波器[8]是从数学形态学中发展出来的新型的非线性滤波器,利用预先定义的结构元素对信号进行匹配和局部修正,达到抑制噪声的目的.目前发展出组合形态学滤波[9]、自适应形态学滤波[10]、多结构元素滤波[11]等改进的形态学滤波方法,但是这些滤波方法主要存在的问题是在抑制噪声的同时模糊了图像,丢失了图像信息.Tukey在1971年提出的中值滤波[12-13]是一种常用的非线性滤波方法,标准的中值滤波存在最大缺点是由于它对图像中所有像素点采用统一的处理方法,这种处理改变了噪声点的值,也有可能改变信号点的值,并有可能产生新的噪声等问题.本文针对目前中值滤波方法中存在丢失图像细节的问题和误判噪声点问题,对中值滤波算法进行了改进,引入Rank变换,对孤立噪声点和连续噪声点进行滤波处理,期望能达到既可有效保持图像细节,又能实现较好的图像滤波效果.1 Rank变换及其噪声检测原理像素的Rank变换是以该像素点为中心取一个矩形区域(称为Rank窗口),统计Rank窗口中所有灰度值小于中心像素灰度值的像素的个数,并以这个数代替原来中心像素点的灰度值.通过每个像素的Rank变换后,整个图像被转换为一个整数矩阵,这个整数矩阵称为Rank图像[14].定义1 设f(x,y)表示图像当前像素(x,y)的灰度值,N(x,y)表示以(x,y)为中心的矩形窗口像素集合,则对像素(x,y)的Rank变换定义为如图1所示3×3窗口的中心像素f(x,y)的灰度为160,由(1)、(2)式,N(x,y)转换为δ(x,y),求δ (x,y)所有元素的和,即为 f(x,y)以 N(x,y)为Rank变换窗口的Rank变换值r(x,y).也可以直接从N(x,y)中看出,有5个像素灰度值小于中心像素,因此r(x,y)=5.图1显示了求解的过程.经过Rank变换后,像素的灰度值(0～255)就转换为一个范围较小的整数(0到R-1,R是N(x,y)内的像素总数).图1 Rank变换求解过程孤立点即满足中心像素点f(x,y)与窗口(窗口大小3×3)邻域点f(x+ξ,y+η)之间的如下关系:如果将原始图像经过Rank变换后,在Rank变换域内孤立点(x,y)应该满足式(5),其含义表示在滤波窗口内中心像素值要么均大于相邻像素值,要么均小于相邻像素值,这样可以认为中心像素点是孤立点.2 基于Rank变换的改进中值滤波算法本文所提出的基于 Rank变换的中值滤波算法主要分以下2个步骤.Step1:利用Rank变换检测出孤立点.对于图像像素点,边缘点一般都是连续的,孤立点一般都是噪声,也有可能是边缘点,利用这个特性,可以将图像中所有的孤立点单独检测出来进行滤波;本文正是利用Rank变换的特性,将图像灰度值转换为中心像素点f(x,y)和其邻域之间的相关特性,对图像 f(x,y)使用公式(1)和(2)进行Rank变换得到r(x,y),最后利用孤立点特征式(5)检测出图像上的孤立点.Step2:遍历整个图像像素点,对孤立点进行中值滤波,取孤立点的领域窗口,并对窗口内像素进行排序取中值,用中值代替孤立点的值;对非孤立点仍然保留原灰度值不变.遍历整个图像的像素点.通过以上算法的步骤及分析可知,本文提出的基于Rank变换的改进中值滤波算法相对传统的中值滤波算法的优势在于:传统中值滤波算法是针对图像所有像素点无论是噪声点还是非噪声点都进行中值替换处理,这样会导致丢失图像细节;而本文提出的基于Rank变换的改进中值滤波算法主要分成两个阶段:第一个阶段主要是分辨噪声点和非噪声点;第二个阶段则专门以噪声点为对象进行中值滤波处理,而对于非噪声点将保留原灰度值,因此,很好地保留了图像细节,从而避免模糊图像.3 基于Rank变换的中值滤波迭代算法对于一幅图片而言,可能既存在离散的噪声点,也有可能存在连续的噪声点,而本文上述算法只适合于离散的噪声点的处理,而对于连续的噪声点不能进行有效的滤波.针对上述算法的弊端,可以进一步提出迭代改进算法如下.Step1:利用Rank变换检测出孤立点;Step2:遍历图像所有像素点,对孤立点进行中值滤波,非孤立点仍然保留灰度值不变; Step3:对 step2结果进行多次迭代操作,重复step1,step2;Step4:如果第i次迭代和第i+1次迭代图像上的每个限速的Rank变化结果没有变化,即整个图像r(i,j)值趋于稳定,停止算法.本文分别提出了两种基于 Rank变换的改进中值滤波算法,其算法的核心思想是通过检测图像上的噪声点,然后对噪声点进行滤波,而对非噪声点不做任何处理,首先从算法复杂度上,本文算法仅仅对图像上部分被检测出的噪声点进行处理,而原始中值滤波算法则需要对图像上每个像素都进行处理,所以算法的复杂度比原中值滤波算法要低;而对于时间复杂度,本文算法和原中值滤波算法的复杂度均取决于图像的大小,算法的时间复杂度是相同的.4 实验结果及分析实验过程采用256×256的Lena图片作为实验对象.对图像添加0.05的椒盐噪声进行实验.如图2所示是将本文提出的算法及改进算法和传统几种滤波算法进行的对比实验结果.图2 椒盐噪声图像对比从图2可以看出,对于椒盐噪声,均值滤波由于是对图像中每个像素都进行领域处理,因此滤波效果不是很理想(如图2(c));中值滤波对图像中每个像素使用中值进行平滑,收到比较好的效果(如图2 (d));而本文提出的基于Rank变换的中值滤波效果比较理想,不用对全部像素点都用中值进行平滑,只需要对检测出来的噪声点采用中值平滑,不仅能很好地消除大部分噪声,还能很好地保持图像细节信息,没有模糊图像(如图2(e)),而改进的迭代算法在上述两者上有更明显的优势,得到了非常好的滤波效果(如图2(f)).为了验证算法的通用性,图3将本文算法及改进算法和几种传统滤波算法进行了对比实验.从图3可以看出,均值滤波由于是对图像中每个像素都进行领域处理,因此滤波效果不是很理想,如图3(c)所示;中值滤波对每个像素点进行中值平滑,效果一般,如图3(d)所示;本文提出的改进中值滤波效果对于高斯噪声而言,没有椒盐噪声滤除效果理想,但相对传统滤波算法而言,仍然有较好效果,改进的迭代算法的滤波效果如图3(f)所示.图3 高斯噪声图像对比从两组对比试验中看到,本文所提出的算法对于椒盐噪声更有效,而对于高斯噪声,由于噪声的分布比较连续,所以所检测出来的噪声点也是连续的,所以进行中值操作的像素点会比较多,也会造成图像部分像素点产生模糊现象.噪声的产生是一个随机过程,噪声分布的概率密度函数很难使用数学函数来表达,通常使用信噪比来衡量噪声强度.为了说明本文提出算法的可行性和通用性,本文在对比滤波算法滤波效果的同时采用峰值信噪比PSNR[1]来衡量.计算结果见表1.表1 PSNR滤波评价参数噪声类型均值滤波中值滤波改进算法改进迭代算法椒盐噪声 15.7732 17.5504 17.0507 17.8927高斯噪声 16.3820 16.2902 16.3753 16.9443从表1中可以看出,本文提出的两种算法的峰值信噪比是最大的,说明本文算法相对于原始图像的失真度最小.由图2,图3的视觉效果和表1的数据,说明本文算法具有很好的滤波效果.5 结论本文提出了一种基于Rank变换的改进中值滤波算法,对于目前滤波过程中所存在改变图像细节,产生新的噪声,模糊细节等问题进行了改进和优化,能较大程度解决上述问题,并达到较好的图像滤波效果.本文提出的算法仍然无法解决噪声点个数远大于像素总数一半,即噪声密度较大时,滤波效果较差的问题;本文在检测噪声点的过程中,没有考虑像素之间的位置关系,同时通过迭代算法来解决连续噪声问题导致了算法效率不高等问题,有待在后续研究中进一步改进.参考文献:[1] Gonzalez R C,Woods R E.数字图像处理[M].2版.阮秋琦,阮宇智,译.北京:电子工业出版社,2003:132-148.[2] 蔡靖,杨晋生,丁润涛.模糊加权均值滤波器[J].中国图象图形学报,2000,5(1):52-56.[3] Hwang H,Haddad R A.Adaptive Median Filters:New Algorithmsand Results[J].IEEE Trans.Signal Process,1995,4(4):499-502.[4] 王晓凯,李锋.改进的自适应中值滤波[J].计算机工程与应用,2010,46(30):175-176.[5] 张恒,雷志辉,丁晓华.一种改进的中值滤波算法[J].中国图形图像学报,2004,9(4):408-411.[6] Arce G.Detail-preserving Ranked-order Based Filter for Image Processing[J].IEEE Trans.Acoust,Speech, Signal Processing,1989,37:83-98.[7] 焦李成,谭山.图像的多尺度几何分析:回顾和展望[J].电子学报,2003,13(12):1975-1980.[8] Serra J.Morphological Filtering:An Overview[J]. IEEE Trans.Signal Processing,1994,38(1):3-11.[9] 陈虎,周朝辉,王守尊.基于数学形态学的图像去噪方法研究[J].工程图学学报,2004,2(2):116-119.[10]赵春晖,乔景渌,孙坚和.一类多结构元自适应广义形态滤波器[J].中国图像图形学报,1997,11(2):806-809.[11]杨平先,孙兴波,干树川.一种改进的数学形态学图像滤波算法[J].华北电力大学学报,2005,33(6):56-59.[12]黄颖,王卫星.分类中值滤波算法的研究[J].计算机工程与应用,2009,45(11):34-36.[13]Wang Xiaokai,Li Feng.Improved Adaptive Median Filtering[J].Computer Engineeringand Applications, 2010,46(3):175-176.[14]郭龙源,夏永泉,杨静宇.RANK变换在立体匹配中的应用研究[J].系统仿真学报,2007,19(9):2121-2123, 2126.。

第39卷第6期2020年12月Vol.39,No.6Dec.2020海洋通报MARINE SCIENCE BULLETINDoi:10.11840/j.issn.1001-6392.2020.06.012基于热红外图像的海面油膜面积的测算方法王利锋1，辛丽平1，于波1，鞠莲23,魏来2,胡湛波4（1.青岛理工大学信息与控制工程学院，山东青岛266000； 2.国家海洋局北海环境监测中心，山东青岛266033；3.山东省海洋生态环境与防灾减灾重点实验室，山东青岛266033；4.广西大学资源环境与材料学院，广西南宁530000）摘要：针对现有油膜检测技术难以准确测算油膜面积且检测精度受天气条件影响大的问题，本文提出了一种基于热红外图像的海面油膜面积测算方法。

采用波段为8〜14滋m的红外热像仪获取海面油膜的热红外图像，对采集的油膜图像进行预处理（灰度化、中值滤波和锐化）；基于图像灰度分布特征分割油膜区域（感兴趣区域，ROI）,采用形态学操作对ROI进行填充、腐蚀与膨胀，并对ROI进行数学表征；通过像素面积法计算ROI实际物理面积。

实验结果表明：在不同的外界天气环境下（如海浪、海风、海雾、不同光照等环境），该方法对不同黏度的石油样品在海面形成的油膜均有良好的检测精度，ROI面积计算平均误差为3.77%。

关键词：油膜面积；热红外图像；图像处理技术；像素面积法中图分类号：X55文献标识码：A文章编号:1001-6932（2020）06-0750-11A calculation method for oil film area at sea surface based onthermal infrared imageWANG Lifeng1,XIN Liping1,YU Bo1,JU Lian2,3,WEI Lai2,HU Zhanbo4(1.School of Information and Control Engineering,Qingdao University of Technology,Qingdao266000,China;2.North China Sea Environment Monitoring Center,State Oceanic Administration,Qingdao266033,China;3.Key Laboratory of Marine Ecological Environment and Disaster Prevention and Reduction,Shandong Province.Qingdao266033,China;4.School of Resources Environment and Materials,Guangxi University,Nanning530000,China)Abstract:Due to the influence of weather conditions,it is difficult to measure the oil film area at the sea surface accurately.This paper proposed a method to measure and calculate the oil film area at the sea surface based on the thermal infrared im­age.The image of oil film is obtained by infrared thermal imager with band of8-14滋m and preprocessed by gray conversion, median filtering and sharpening.Based on the grayscale of each image,the oil film region(region of interest,ROI)is seg­mented.Then,the morphological operator is used to fill,erode and dilate the oil film region of the image,and ROI is mathe­matically characterized.The pixel area calculation method is used to calculate the actual physical area of ROI.The experi­mental results show that this method is accurate and reliable for calculating the area of the oil film from some oil samples with different viscosity in different external weather environments,such as the presence of waves,sea winds,sea fog,and different light intensity.The mean error of ROI area is3.77%.Key words:oil film area;thermal infrared image;image pre-processing;pixel area calculation method近年来，随着海上石油生产与运输行业的快速发展，溢油事故（如船舶溢油、管道溢油、油井平台溢油）频频发生，溢油污染问题日益受到国内外的重视（张彤等，2015；王召伟等，2019）。

ENVI 支持一种滤波类型：Convolution、Morphological、Texture、Adaptive 和FFT 滤波，它们都可以经过ENVI 主菜单的Filters 菜单得到。

1、Convolution Filtering (卷积滤波)卷积是一种滤波方法，它产生一幅输出图像（图像上，一个给定像元的亮度值是其周围像元亮度值加权平均的函数）。

用户选择变换核用于图像列卷积生成一个新的空间滤波图像。

下面将介绍进行卷积需要的一般配置以及每一种滤波类型的详细情况。

使用卷积滤波用于滤波的文件选择对话框，不象其它ENVI 文件选择对话框，它包括一个“File/Band” 箭头切换按钮，这一按钮可以让你选择输入一个文件或输入一个独立的波段。

·选择一个用于卷积滤波处理的文件：1 选择Filter > Convolutions > 一种滤波类型。

2 出现Convolution Input File 对话框时，选择一个输入文件名，若需要可以输入一个空间子集。

·处理单个波段：1 选择Filter > Convolutions > 一种滤波类型。

2 点击“Select By” 附近的箭头按钮，选择“Band”。

这时，在窗口的左边一栏“Select Input Band” 文本框里出现所有可利用波段的列表。

3 通过点击波段名选择需要的波段。

一旦选择了，你还可以选择一个空间子集。

设置卷积参数卷积滤波需要选择一个变换核的大小。

多数滤波变换核呈正方形，默认的变换核大小是3×3 。

原始图像卷积结果中“Adding back” 部分有助于保持空间联系，代表性地被处理成尖锐化的图像。

在文件选择对话框里，选择好数据以后：1 点击“OK”。

2 出现Convolution Parameters 对话框时，在“Size” 文本框里键入一个变换核的大小。

注意一些特别的滤波（如Sobel 和Roberts）有自己的默认值，是不能改变的。

limma包的使用技巧原文地址：limma包的使用技巧作者：牛牛龙limmar package是一个功能比较全的包，既含有cDNA芯片的RAW data输入、前处理（归一化）功能，同时也有差异化基因分析的“线性”算法（limma: Linear Models forMicroarray Data），特别是对于“多因素实验（multifactor designedexperiment）”。

limmar包的可扩展性非常强，单通道（one channel）或者双通道（towchannel）数据都可以分析差异基因，甚至也包括了定量PCR 和RNA-seq（第一次见分析microarray的包也能处理RNA-seq）。

limmarpackage是一个集大成的包，对载入数据、数据前处理（背景矫正、组内归一化和组间归一化都有很多种选择方法）、差异基因分析都有很多的选择。

而且，所设计的线性回归和经验贝叶斯方法找差异基因非常值得学习。

1. 读入样本信息使用函数读readTargets(file="Targets.txt",path=NULL, sep="t", s=NULL,quote=""",...)。

这个函数其实是一个包装了的read.table()，读入的是样本的信息，创建的对象类似于marray包的marrayInfos和Biobase包的AnnotatedDataFrame。

2. 读入探针密度数据与marray包一致，Bioconductor不能读入原始的TIFF图像文件，只能输出扫描仪输入的、转换成数字信号的文本文件。

使用函数read.maimages(files=NULL,source="generic", path=NULL, ext=NULL, names=NULL, columns=NULL,other.columns=NULL, annotation=NULL, green.only=FALSE, wt.fun=NULL,verbose=TRUE, sep="t", quote=NULL, ...)参数说明：files需要通过函数dir(pattern = "Mypattern")配合正则表达式筛选（规范命名很重要），同时该函数可以读入符合格式的压缩过的文件，比如*.txt.gz的文件，这极大的减小的数据储存大小；source的取值分为两类，一类是“高富帅”，比如“agilent”、“spot”等等（下表），它们是特定扫描仪器的特定输出格式；如果不幸是“屌丝”，即格式是自己规定的，可以选定source="generic"，这时需要规定columns；任何cDNA文件都要有R/G/Rb/Gb四列（Mean 或者Median）；annotation可以规定哪些是注释列；wt.fun用于对点样点进行质量评估，取值为0表示这些点将在后续的分析中被剔除，取值位1表示需要保留，对点样点的评估依赖于图像扫描软件的程序设定，比如SPOT和GenePix软件，查看QualityWeights（现成函数或者自己写函数）。

MINI REVIEW ARTICLEpublished:17September2013doi:10.3389/fonc.2013.00221 Role of epithelial-mesenchymal transition in pancreatic ductal adenocarcinoma:is tumor budding the missing link? Eva Karamitopoulou1,2*1Clinical Pathology Division,Institute of Pathology,University of Bern,Bern,Switzerland2Translational Research Unit,Institute of Pathology,University of Bern,Bern,SwitzerlandEdited by:Inti Zlobec,University of Bern, SwitzerlandReviewed by:Parham Minoo,University of Calgary, CanadaQianghua Xia,The Children’s Hospital of Philadelphia,USA*Correspondence:Eva Karamitopoulou,Clinical Pathology Division,Institute of Pathology,University of Bern, Murtenstrasse31,CH-3010Bern, Switzerlande-mail:eva.diamantis@pathology.unibe.ch Pancreatic ductal adenocarcinoma(PDAC)ranks as the fourth commonest cause of cancer death while its incidence is increasing worldwide.For all stages,survival at5years is<5%. The lethal nature of pancreatic cancer is attributed to its high metastatic potential to the lymphatic system and distant ck of effective therapeutic options contributes to the high mortality rates of PDAC.Recent evidence suggests that epithelial-mesenchymal transition(EMT)plays an important role to the disease progression and development of drug resistance in PDAC.Tumor budding is thought to reflect the process of EMT which allows neoplastic epithelial cells to acquire a mesenchymal phenotype thus increasing their capacity for migration and invasion and help them become resistant to apoptotic signals. In a recent study by our own group the presence and prognostic significance of tumor budding in PDAC were investigated and an association between high-grade budding and aggressive clinicopathological features of the tumors as well as worse outcome of the patients was found.The identification of EMT phenotypic targets may help identifying new molecules so that future therapeutic strategies directed specifically against them could potentially have an impact on drug resistance and invasiveness and hence improve the prognosis of PDAC patients.The aim of this short review is to present an insight on the morphological and molecular aspects of EMT and on the factors that are involved in the induction of EMT in PDAC.Keywords:pancreatic cancer,epithelial-mesenchymal transition,tumor budding,prognosis,biomarkerPANCREATIC CANCERPancreatic ductal adenocarcinoma(PDAC)is a common can-cer with dismal prognosis(1)that escapes early detection and resists treatment(2).Most patients have advanced stage dis-ease at presentation with a median survival of less than1year (1,3).Surgical resection is the only potentially curative treat-ment of PDAC(3).Classical histomorphological features like tumor size,blood vessel,or lymphatic invasion,and presence of lymph node metastases constitute essential prognostic deter-minants in pancreatic cancer and are invariably included in the pathology reports,with tumor stage being the most important of all(3).The lethal nature of PDAC has been attributed to the propensity of PDAC cells to rapidly disseminate to the lym-phatic system and distant organs(4).However,even patients with completely resected,node-negative PDACs eventually die of their disease.Within this context and considering the fact that the management of PDAC remains suboptimal and that adjuvant therapy has resulted to limited progress,the identification of addi-tional reliable and reproducible prognostic markers that would enable better patient stratification and eventually provide a guide toward a more successful and individualized therapy,is mandatory (1,5).EPITHELIAL-MESENCHYMAL TRANSITIONEpithelial-mesenchymal transition is a biologic process that allows epithelial cells to undergo the biochemical changes that enable them to acquire a mesenchymal phenotype,including enhanced migratory capacity,invasiveness,elevated resistance to apoptosis, and increased production of extracellular matrix(ECM)compo-nents(6,7).EMT is characterized by loss of cell adhesion,down regulation of E-cadherin expression,acquisition of mesenchy-mal markers(including N-cadherin,Vimentin,and Fibronectin), and increased cell motility(6).Both EMT and mesenchymal-epithelial transition(MET),the reversion of EMT,are essential for developmental and repair processes like implantation,embryo for-mation,and organ development as well as wound healing,tissue regeneration,and organfibrosis(8).However,EMT also occurs in neoplastic cells that have undergone genetic and epigenetic changes.These changes affect both oncogenes and tumor sup-pressor genes that enable cancer cells to invade and metastasize. Moreover,some neoplastic cells may go through EMT retaining many of their epithelial properties while other cells are becoming fully mesenchymal(9).Many molecular processes are involved in the initiation of EMT including activation of transcription factors,expression of specific cell-surface proteins,reorganization and expression of cytoskeletal proteins,production of ECM-degrading enzymes,and changes in the expression of specific microRNAs(miRNAS).The above fac-tors can also be used as biomarkers to detect cells in EMT state(10). EMT has been linked to cellular self-renewal programs of cancer stem cells and apoptosis-anoikis resistance,which are features of therapeutic resistance(11).The zincfinger transcription factors Snail,Slug,Zeb1,and Twist repress genes responsible for the epithelial phenotype and represent important regulators of EMT(6,7,12).In PDAC Snail expression has been reported to be seen in nearly80%of the cases and Slug expression in50%(13).Snail expression was inversely correlated with E-cadherin expression and decreased E-cadherin expression was associated with higher tumor grade. Similarly,poorly differentiated pancreatic cancer cell lines showed higher levels of Snail and lower levels of E-cadherin compared with moderately differentiated cell lines(13)while silencing of Zeb1leaded to up-regulation of E-cadherin and restoration of an epithelial phenotype(14).Zeb1expression in PDAC also corre-lated with advanced tumor grade and worse outcomes(14–16) and was shown to be primarily responsible for the acquisition of an EMT phenotype,along with increased migration and inva-sion in response to NF-κB signaling in pancreatic cancer cells (16).EMT AND TUMOR BUDDINGTumor budding reflects a type of diffusely infiltrative growth con-sisting of detached tumor cells or small cell clusters of up tofive cells at the invasive front of gastrointestinal carcinomas(17–22). Tumor buds represent a non-proliferating,non-apoptotic,highly aggressive subpopulation of tumor cells that display migratory and invasive capacities(23).The aim of tumor buds seems to be the invasion of the peritumoral connective tissue,the avoidance of the host’s defense andfinally the infiltration of the lymphatic and blood vessels with the consequence of local and distant metastasis. The EMT process by allowing a polarized cell to assume a more mesenchymal phenotype with increased migratory capacity,inva-siveness,and resistance to apoptosis seems to play a major role in the development of tumor buds.In fact,tumor buds are thought to result from the process of EMT.Thus,although formally tumor budding cannot be equated with EMT,several similarities between the two processes,including activation in WNT signaling,can be shown(24).The detachment of tumor buds from the main tumor body is accomplished by loss of membranous expression of the adhesion molecule E-cadherin.Activation of WNT sig-naling is further suggested by nuclear expression of b-catenin in tumor-budding cells,as well as increase of laminin5gamma2and activation of Slug and Zeb1(24,25).The presence of high-grade tumor budding has been consis-tently associated with negative clinicopathologic parameters in gastrointestinal tumors(26–30).In a previous study from our group we could show that tumor budding occurs frequently in pancreatic cancer and is a strong,independent,and reproducible, highly unfavorable prognostic factor that may be used as a para-meter of tumor aggressiveness and as an indicator of unfavorable outcome,even within this group of patients with generally poor prognosis.Moreover,tumor budding was proven to have a more powerful prognostic ability than other more classic prognostic fac-tors including TNM stage,thus adding relevant and independent prognostic information(31).EMT AND miRNAsMicroRNAS are small non-coding RNAs of18–25nucleotides, excised from60to110nucleotide RNA precursor structures (32).MiRNAs are involved in crucial biological processes, including development,differentiation,apoptosis,and pro-liferation,through imperfect pairing with target messenger RNAs of protein-coding genes and the transcriptional or post-transcriptional regulation of their expression(33,34).Recent studies illustrate the role of miRNAs on the regula-tion of gene expression and proteins in metastasis.For exam-ple,it has been shown that miR-10b,which is up-regulated by EMT transcription factor Twist,is associated with increased invasiveness and metastatic potential(35,36).Furthermore,it was shown that the miR-200family(miR-200a,miR-200b,miR-200c,miR-141,and miR-429)and miR-205play critical roles in regulating EMT by directly targeting the mRNAs encoding E-cadherin repressors Zeb1and Zeb2(37).Moreover,recent studies showed that members of the miR-200family by induc-ing EMT can regulate the sensitivity to epidermal growth fac-tor receptor(EGFR)in bladder cancer cells and to gemcitabine in pancreatic cancer cells(38).Conversely,Zeb1represses the transcription of miR-200genes by directly binding to their promoter region,thereby forming a double-negative feedback loop(39).On the other hand,miR-200family can also pro-mote the conversion of mesenchymal cells to epithelial-like cells (MET)suggesting that these miRNAs may also favor metastatic outgrowth.Recent studies aiming at the evaluation of miRNAs in pan-creatic cancer have shown that specific miRNAs are dysregulated in PDAC while the higher expression of some miRNA species was able to distinguish between benign and malignant pancre-atic tissue(40).For example,miR-21was shown to be over-expressed in79%of pancreatic cancers as opposed to27%of chronic pancreatitis(41).In resected PDAC specimens high lev-els of miR-200c expression strongly correlated with E-cadherin levels and were associated with significantly better survival rates compared with patients whose tumors had low levels of miR-200c expression(42).CHEMORESISTANCE AND EMTCells undergoing EMT become invasive and develop resistance to chemotherapeutic agents.Moreover,EMT can be induced by chemotherapeutic agents,and stress conditions such as exposure to radiation or hypoxia(43,44).Up-regulation of Twist has been shown to be associated with resistance to paclitaxel in nasopharyngeal,bladder,ovarian,and prostate cancers(45).In colorectal cancer cell lines,chronic expo-sure to oxaliplatin leaded to the development of the ability to migrate and invade with phenotypic changes resembling EMT(spindle-cell shape,loss of polarity,intercellular separa-tion,and pseudopodia formation)by the oxaliplatin-resistant cells(46).Pancreatic cancer remains today an extremely lethal disease largely because of its resistance to existing treatments(47).EMT has been shown to contribute significantly to chemoresistance in several cancers,including pancreatic cancer(30,48,49).Induction of gemcitabine resistance in previously sensitive cell lines resulted in development of an EMT phenotype and was associated with an increased migratory and invasive ability compared to gemc-itabine sensitive cells(49).Moreover,gene expression profiling ofchemoresistant cells showed a strong association between expres-sion of the EMT transcription factors Zeb1,Snail,and Twist and decreased expression of E-cadherin(39,50).Silencing of Zeb1 with siRNA resulted to MET(51)and restored chemosensitivity (14).Interestingly,maintenance of chemoresistance in cell lines that have undergone EMT is dependent on Notch and NF-κB signaling(30).Inhibition of Notch-2down regulates Zeb1,Snail, and Slug expression,attenuates NF-κB signaling,and reduces the migratory and invasive capacity of the gemcitabine resistant cells(30).Epithelial-mesenchymal transition can also confer resistance to targeted agents.For example,lung cancer cell lines that have undergone EMT,became resistant to the growth inhibitory effects of EGFR kinase inhibition(erlotinib)in vitro and in xenografts(47)as well as other EGFR inhibitors such as gefitinib and cetuximab(48)Thus,EMT can lead to resis-tance to multiple agents and result to rapid progression of the tumor.Clarifying the correlation between EMT and drug resistance may help clinicians select an optimal treat-ment.CONCLUSIONPancreatic cancer remains an extremely lethal disease partly because of the poor response to existing treatments.Accumulat-ing evidence suggests that EMT plays an important role in PDAC progression,is associated with stem cell features of the PDAC cells and seems to significantly contribute to the chemoresistance of pancreatic cancer.Moreover,is associated with more aggressive tumor characteristics and with poor patient survival.Because of its role in therapy response and tumor progression,targeting EMT could potentially reduce drug resistance and have a great impact in the survival of PDAC patients.Tumor budding thought to be the result of the EMT process is commonly observed in PDAC and high-grade tumor budding has been proven to have an independent adverse prognostic impact in the survival of PDAC patients.Figure1depicts tumor bud-ding as a possible transition between a fully epithelial and a fully mesenchymal phenotype of the tumor cells in PDAC.Moreover, cancer cells in tumor buds have been shown to have EMT and cancer stem cell characteristics.The further characterization of the budding cells at a protein and gene level in order to iden-tify a“molecular budding-promoting profile”will lead to a better understanding of the tumor-stroma interaction at the area of the invasive front and help to further elucidate the similarities between budding cells,EMT process and cancer stem cells in pancreatic cancer.Investigating these issues will allow us to gain further insight into pancreatic carcinogenesis,and provide us with a platform on which to build future studies leading to the identification of new therapeutic interventions.REFERENCES1.Hidalgo M.Pancreatic cancer.NEngl J Med(2010)362:1605–17.doi:10.1056/NEJMra09015572.Tuveson DA,Hingorani SR.Duc-tal pancreatic cancer in humans and mice.Cold Spring Harb Symp Quant Biol(2005)70:65–72.doi:10.1101/ sqb.2005.70.0403.Fernandez-del-Castillo C,JimenezRE,Steer ML.Surgery in the treatment of exocrine pancreas and prognosis.In:Tanabe KK,edi-tor(2013).Available from:www.4.Li Y,Kong D,Ahmad A,Bao B,Sarkar FH.Pancreatic cancer stem cells:emerging target for designing novel therapy.Cancer Lett(2012).Available from:/10.1016/j canlet.2012.03.018,5.Welsch T,Kleeff J,Friess H.Molecu-lar pathogenesis of pancreatic can-cer:advances and challenges.Curr Mol Med(2007)7:504–21.doi:10.2174/1566524077813870826.Kalluri R,Weinberg RA.The basicsof epithelial-mesenchymal transi-tion.J Clin Invest(2009)119:1420–8.doi:10.1172/JCI391047.Thiery JP,Acloque H,Huang RYJ,Nieto MA.Epithelial-mesenchymal transitions in development and dis-ease.Cell(2009)139:871–90.doi:10.1016/j.cell.2009.11.0078.Rasheed ZA,Yang J,Wang Q,Kowal-ski J,Freed I,Murter C,et al.Prog-nostic significance of tumorigenic cells with mesenchymal features in pancreatic adenocarcinoma.J Natl Cancer Inst(2010)102:340–51.doi:10.1093/jnci/djp5359.Iwatsuki M,Mimori K,YokoboriT,Ishi H,Beppu T,Nakamori S.Epithelial–mesenchymal transi-tion in cancer development and its clinical significance.Cancer Sci (2010)101(2):293–9.doi:10.1111/j.1349-7006.2009.01419.x10.Kalluri R.EMT:when epithelial cellsdecide to become mesenchymal-like cells.J Clin Invest(2009)119:1417–9.doi:10.1172/JCI3967511.Krantz SB,Shields MA,Dangi-Garimella S,Munshi HG,Bentrem DJ.Contribution of epithelial-to-mesenchymal transition and cancer stem cells to pancreatic cancer progression.J Surg Res(2012)173: 105–12.doi:10.1016/j.jss.2011.09.02012.Lee JM,Dedhar S,Kalluri R,Thompson EW.The epithelial-mesenchymal transition:new insights in signaling,devel-opment,and disease.J Cell Biol(2006)172:973–81.doi:10.1083/jcb.20060101813.Hotz B,Arndt M,Dullat S,BhargavaS,Buhr HJ,Hotz HG.Epithelial tomesenchymal transition:expressionof the regulators snail,slug,andtwist in pancreatic cancer.ClinCancer Res(2007)13:4769–76.doi:10.1158/R-06-292614.Arumugam T,Ramachandran V,Fournier KF,Wang H,MarquisL,Abbruzzese JL,et al.Epithe-lial to mesenchymal transition con-tributes to drug resistance in pan-creatic cancer.Cancer Res(2009)69:5820–8.doi:10.1158/0008-5472.CAN-08-281915.Buck E,Eyzaguirre A,Barr S,Thompson S,Sennello R,Y oung D,et al.Loss of homotypic cell adhe-sion by epithelial-mesenchymaltransition or mutation limits sen-sitivity to epidermal growth factorreceptor inhibition.Mol CancerTher(2007)6:532–41.doi:10.1158/1535-7163.MCT-06-046216.Maier HJ,Schmidt-Strassburger U,Huber MA,Wiedemann EM,BeugH,Wirth T.NF-kappaB promotesepithelial-mesenchymal transition,migration and invasion of pancre-atic carcinoma cells.Cancer Lett(2010)295:214–28.doi:10.1016/j.canlet.2010.03.00317.Prall F.Tumour budding in col-orectal carcinoma.Histopathology(2007)50:151–62.doi:10.1111/j.1365-2559.2006.02551.x18.Brown M,Sillah K,Griffiths EA,Swindell R,West CM,Page RD,et al.Tumour budding and a lowhost inflammatory response areassociated with a poor progno-sis in oesophageal and gastro-oesophageal junction cancers.Histopathology(2010)56:893–9.doi:10.1111/j.1365-2559.2010.03559.x19.Koike M,Kodera Y,Itoh Y,Nakayama G,Fujiwara M,Hamajima N,et al.Multivariateanalysis of the pathologic featuresof esophageal squamous cell cancer:tumor budding is a significantindependent prognostic factor.AnnSurg Oncol(2008)15:1977–82.doi:10.1245/s10434-008-9901-620.Miyata H,Y oshioka A,YamasakiM,Nushijima Y,Takiguchi S,Fujiwara Y,et al.Tumor bud-ding in tumor invasive front pre-dicts prognosis and survival ofpatients with esophageal squa-mous cell carcinomas receivingneoadjuvant chemotherapy.Cancer(2009)115:3324–34.doi:10.1002/cncr.2439021.Roh MS,Lee JI,Choi PJ.Tumorbudding as a useful prognosticmarker in esophageal squamous cellcarcinoma.Dis Esophagus(2004)17:333–7.doi:10.1111/j.1442-2050.2004.00436.x22.Ohike N,Coban I,Kim GE,Bas-turk O,Tajiri T,Krasinskas A,etal.Tumor budding as a strongprognostic indicator in invasiveampullary adenocarcinomas.Am JSurg Pathol(2010)34:1417–24.doi:10.1097/PAS.0b013e3181f0b05a23.Zlobec I,Lugli A.Epithelial mes-enchymal transition and tumorbudding in aggressive colorectalcancer:tumor budding as oncotar-get.Oncotarget(2010)1:651–61.24.Muto T,Mochizuki H,Masaki T edi-tors.Tumor Budding in ColorectalCancer:Recent Progress in ColorectalCancer Research(Horizons in Can-cer Research).(Vol.8).Tokyo:Nova(2006).25.Schmalhofer O,Brabletz S,Brabletz T.E-cadherin,beta-catenin,and ZEB1in malignantprogression of cancer.CancerMetastasis Rev(2009)28:151–66.doi:10.1007/s10555-008-9179-y26.Karamitopoulou E,Zlobec I,KölzerV,Kondi-Pafiti A,Patsouris ES,Gen-natas K,et al.Proposal for a10-high-power-fields scoring methodfor the assessment of tumor bud-ding in colorectal cancer.ModPathol(2013)26:295–301.doi:10.1038/modpathol.2012.15527.Nakamura T,Mitomi H,KikuchiS,Ohtani Y,Sato K.Evaluationof the usefulness of tumor bud-ding on the prediction of metasta-sis to the lung and liver after cura-tive excision of colorectal cancer.Hepatogastroenterology(2005)52:1432–5.28.Ueno H,Mochizuki H,HashiguchiY,Hatsuse K,Fujimoto H,HaseK.Predictors of extrahepatic recur-rence after resection of colorectalliver metastases.Br J Surg(2004)91:327–33.doi:10.1002/bjs.442929.Ueno H,Murphy J,Jass JR,Mochizuki H,Talbot IC.Tumour‘budding’as an indexto estimate the potential ofaggressiveness in rectal cancer.Histopathology(2002)40:127–32.doi:10.1046/j.1365-2559.2002.01324.x30.Wang LM,Kevans D,Mulcahy H,O’Sullivan J,Fennelly D,Hyland J,et al.Tumor budding is a strong andreproducible prognostic marker inT3N0colorectal cancer.Am J SurgPathol(2009)33:134–41.doi:10.1097/PAS.0b013e318184cd5531.Karamitopoulou E,Zlobec I,BornD,Kondi-Pafiti A,Patsouris E,Gen-natas K,et al.Tumor budding isa strong and independent prognos-tic factor in pancreatic cancer.EurJ Cancer(2013)49:1032–9.doi:10.1016/j.ejca.2012.10.02232.Calin GA,Croce CM.Micro RNAsignatures in human cancers.NatRev Cancer(2006)6:857–66.doi:10.1038/nrc199733.McShane L,Altman DG,SauerbreiW,Taube SE,Gion M,Clark GM,etal.REporting recommendations fortumor MARKer prognostic studies(REMARK).Eur J Cancer(2005)41:1690–6.doi:10.1016/j.ejca.2005.03.03234.Pasquinelli AE,Hunter S,BrachtJ.MicroRNAs:a developing story.Curr Opin Gen Dev(2005)15:200–5.doi:10.1016/j.gde.2005.01.00235.Peter ME.Let-7and miR-200microRNAs:guardians againstpluripotency and cancer progres-sion.Cell Cycle(2009)8:843–52.doi:10.4161/cc.8.6.790736.Preis M,Gardner TB,Gordon SR,Pipas JM,Mackenzie TA,Klein EE,et al.MicroRNA10b expression cor-relates with response to neoadju-vant therapy and survival in pan-creatic ductal adenocarcinoma.ClinCancer Res(2011)17:5812–21.doi:10.1158/R-11-069537.Gregory PA,Bert AG,Paterson EL,Barry SC,Tsykin A,Farshid G,et al.The miR-200family and miR-205regulate epithelial to mesenchymaltransition by targeting ZEB1andSIP1.Nat Cell Biol(2008)10:593–601.doi:10.1038/ncb172238.Burk U,Schubert J,Wellner U,Schmalhofer O,Vincan E,SpadernaS,et al.A reciprocal repressionbetween ZEB1and members of themiR-200family promotes EMT andinvasion in cancer cells.EMBO Rep(2008)9:582–9.doi:10.1038/embor.2008.7439.Wellner U,Schubert J,Burk UC,Schmalhofer O,Zhu F,Sonntag A,et al.The EMT-activator ZEB1pro-motes tumorigenicity by repress-ing stemness-inhibiting microR-NAs.Nat Cell Biol(2009)11:1487–95.doi:10.1038/ncb199840.Panarelli NC,Chen YT,ZhouXK,Kitabayashi N,Yantiss RK.MicroRNA expression aids thepreoperative diagnosis of pancre-atic ductal adenocarcinoma.Pan-creas(2012)41:685–90.doi:10.1097/MPA.0b013e318243a90541.Dillhoff M,Liu J,Frankel W,CroceC,Bloomston M.MicroRNA-21is overexpressed in pan-creatic cancer and a potentialpredictor of survival.J Gas-trointest Surg(2008)12:2171–6.doi:10.1007/s11605-008-0584-x42.Yu J,Ohuchida K,Mizumoto K,Sato N,Kayashima T,Fujita H, et al.MicroRNA,hsa-miR-200c, is an independent prognos-tic factor in pancreatic cancer and its upregulation inhibits pancreatic cancer invasion but increases cell prolifera-tion.Mol Cancer(2010)9:169.doi:10.1186/1476-4598-9-169 43.Li C,Heidt DG,Dalerba P,BurantCF,Zhang L,Adsay V,et al.Identification of pancreatic can-cer stem cells.Cancer Res(2007) 67:1030–7.doi:10.1158/0008-5472.CAN-06-203044.Lee CJ,Dosch J,Simeone DM.Pan-creatic cancer stem cells.J Clin Oncol(2008)26:2806–12.doi:10.1200/JCO45.Hong SP,Wen J,Bang S,ParkS,Song SY.CD44-positive cells are responsible for gemc-itabine resistance in pancreatic cancer cells.Int J Cancer(2009)125:2323–31.doi:10.1002/ijc.2457346.Hermann PC,Huber SL,HerrlerT,Aicher A,Ellwart JW,GubaM,et al.Distinct populations ofcancer stem cells determine tumorgrowth and metastatic activity inhuman pancreatic cancer.Cell StemCell(2007)1:313–23.doi:10.1016/j.stem.2007.06.00247.Li Y,VandenBoom TG,Kong D,Wang Z,Ali S,Philip PA,et al.Up-regulation of miR-200and let-7bynatural agents leads to the reversalof epithelial-to-mesenchymal tran-sition in gemcitabine-resistant pan-creatic cancer cells.Cancer Res(2009)69:6704–12.doi:10.1158/0008-5472.CAN-09-129848.Yang AD,Fan F,Camp ER,vanBuren G,Liu W,Somcio R,etal.Chronic oxaliplatin resistanceinduces epithelial-to-mesenchymaltransition in colorectal cancercell lines.Clin Cancer Res(2006)12:4147–53.doi:10.1158/1078-R-06-003849.Shah AN,Summy JM,Zhang J,Park S,Parikh N,Gallick GE.Development and characterizationof gemcitabine-resistant pancre-atic tumor cells.Ann Surg Oncol(2007)14:3629–37.doi:10.1245/s10434-007-9583-550.Shimono Y,Zabala M,ChoRW,Lobo N,Dalerba P,QianD,et al.Downregulation ofmiRNA-200c links breast cancerstem cells with normal stemcells.Cell(2009)138:592–603.doi:10.1016/j.cell.2009.07.01151.Conroy T,Paillot B,Francois E,Bugat R,Jacob JH,Stein U,etal.Irinotecan plus oxaliplatin andleucovorin-modulatedfluorouracilin advanced pancreatic cancer–aGroupe Tumeurs Digestives of theFederation Nationale des Centres deLutte Contre le Cancer study.J ClinOncol(2005)23:1228–36.doi:10.1200/JCO.2005.06.050Conflict of Interest Statement:Theauthor declares that the research wasconducted in the absence of anycommercial orfinancial relationshipsthat could be construed as a potentialconflict of interest.Received:24July2013;accepted:11August2013;published online:17Sep-tember2013.Citation:Karamitopoulou E(2013)Role of epithelial-mesenchymal tran-sition in pancreatic ductal adenocar-cinoma:is tumor budding the miss-ing link?Front.Oncol.3:221.doi:10.3389/fonc.2013.00221This article was submitted to Gastroin-testinal Cancers,a section of the journalFrontiers in Oncology.Copyright©2013Karamitopoulou.Thisis an open-access article distributed underthe terms of the Creative CommonsAttribution License(CC BY).The use,distribution or reproduction in otherforums is permitted,provided the origi-nal author(s)or licensor are credited andthat the original publication in this jour-nal is cited,in accordance with acceptedacademic practice.No use,distribution orreproduction is permitted which does notcomply with these terms.。

2021年2月第2期Vol. 42 No. 2 2021小型微 型计算 机系统Journal of Chinese Computer Systems信号自适应衰减的多壳扩散磁共振成像方法罗伶俐，王远军(上海理工大学医学影像工程研究所，上海200093)E-mail :yjusst@ 126. com摘 要：提升总体平均扩散传播算子(Ensemble Average diffusion Propagator ,EAP )的重建精度一直以来都是扩散磁共振成像领域中扩散光谱成像(Diffusion Spectrum Imaging ,DSI )的核心问题.在诸多成像算法中，用径向基函数(Radial Basis Function ,RBF)作为扩散MR 信号插值基函数的方法在纤维方向分布重建及成像统计标量重建方面均获得了理想的EAP 重建效果，为进一步提升重建效率及精度，本文基于RBF 方法提出了对信号进行自适应衰减建模的方法，并结合确保扩散张量正定性的张量求解算法，分别基于系数人仏正则化方法求解最优化参数以作对比.针对体模数据的实验结果显示，该算法在提升各项指标 重建精度及计算效率方面均取得了理想效果.关键词：扩散MRI ；扩散光谱成像；多壳扩散MR 成像中图分类号：TP391 文献标识码:A 文章编号：1000-1220(2021 )02-0374-07Multi-shell Diffusion Magnetic Resonance Imaging Method with Adaptive Signal AttenuationLUO Ling-li,WANG Yuan-jun(Institute of Medical Imaging Engineering ,University of Shanghai for Science and Technology ,Shanghai 200093 .China)Abstract : Improving the estimation accuracy of the Ensemble Average diffusion Propagator) EAP) has always been a core issue of dif ­fusion spectrum imaging in the field of diffusion magnetic resonance imaging. Among many methods , the radial basis function ( RBF) is used as the interpolation basis function for diffusion MR signal to obtain the ideal EAP reconstruction effect both in reconstruction offiber orientation estimation and scalar statistics. In order to further improve the calculation efficiency and reconstruction accuracy , a method modeling the signal adaptive attenuation based on the RBF is proposed in this paper. The tensor estimating method ensuring the positive definiteness of the diffusion tensor is combined , and the optimization is performed by method based on l x and l 2 regularizationrespectively for comparison. Experimental results about phantom data show that the algorithm has achieved ideal results in terms of im ­proving the reconstruction accuracy of various indicators and calculation efficiency.Key words : diffusion MRI ； diffusion spectrum imaging ; multi-shell diffusion MR imaging1引言扩散磁共振成像(Diffusion Magnetic Resonance Imaging ,dMRI)技术被广泛应用于诸如阿尔茨海默症、精神分裂症、脑损伤等诸多大脑疾病的研究中.dMRI 的基础原理是由于扩散加权MR 信号对器官组织中的内生水分子的随机运动十分敏感，这其中应用最为广泛的扩散加权磁共振成像(Diffu ­sion-weighted MRI,DW-MRI)是使用了两种在180。

Journal of Oil and Gas Technology 石油天然气学报, 2019, 41(4), 7-12Published Online August 2019 in Hans. /journal/jogthttps:///10.12677/jogt.2019.414049Removing Baseline Drifting in Mud PulseSignals Based on Morphological FilteringChaoyang Xu, Xianghui Ren, Qiang Xue, Qianhong CaoDirectional Drilling Service Company, CNPC Bohai Drilling Engineering Company Limited, TianjinReceived: Mar. 20th, 2019; accepted: Apr. 18th, 2019; published: Aug. 15th, 2019AbstractA morphological filter for removing mud pulse baseline drifting was established. The baselinedrifting of simulated PPM encoding signal of mud pulse was processed by least-square polynomial fitting, median filtering and morphological filtering methods, respectively. The results were quan-titatively analyzed by using signal to noise ratio (S NR), root mean square error (E rms) and norma-lized correlation coefficient (C ncc). The analysis result shows that the morphological filtering me-thod proposed is the best for removing the baseline drift of mud pulse signal.KeywordsMWD, Mud Pulse Signal, Baseline Drift, Morphological Filtering徐朝阳 等基于形态学的滤波消除泥浆脉冲信号 基线漂移徐朝阳，任祥辉，穴 强，曹乾洪中国石油集团渤海钻探工程有限公司定向井技术服务分公司，天津作者简介：徐朝阳(1985-)，男，博士，工程师，主要从事定向井仪器研发方面的工作。

文章编号:0427-7104(2005)06-0971-06收稿日期:2004-09-28作者简介:李 军(1977)),男,硕士研究生;通讯联系人陈光梦副教授.小波域中基于模糊的图像去噪方法李 军,陈光梦(复旦大学电子工程系,上海 200433)摘 要:在图像去噪方法中,信号局部方差估计的准确性对去噪效果起至关重要的作用.根据图像小波系数与邻近点的相关性,把模糊(Fuzzy -based)函数用于估计信号的局部方差,根据局部噪声变化自适应地去除噪声.仿真表明,提出的局部方差估计算法F LAW M L 的去噪效果相对其他算法有较好的改善,保存了图像的边缘细节,增强了图像视觉效果.关键词:图像处理;图像去噪;模糊函数;小波变换中图分类号:T N 929.533 文献标识码:A在航空航天、医疗诊断等领域总是希望获取高质量的图像,图像的细节尽可能清晰,然而由于成像设备和成像条件的限制,原始图像往往被噪声污染,去除噪声提高图像质量一直是图像处理领域一个十分活跃的研究方向.小波变换具有时频局部化和多分辨率的特性,因此图像去噪在小波域中的研究成为热点并提出了很多去噪方法.其中非线性门限方法[1~3]通过设定门限将小的小波系数清除,保留大的小波系数(硬门限)或在大的小波系数中去除噪声部分(软门限).文献[1]中Donoho 提出了全局门限T =D n2ln N ,Dn 为高斯噪声方差,N 为数据长度;但是使用全局门限去噪使得图像过度平滑,因此Donoho 又在文献[2]中提出了满足SURE(Stein .s Unbiased Risk Estimate)最小的SURE 门限T =D 2n /D w ,进一步改进去噪性能;Chang 在文献[3]中假定小波系数服从均值为零的高斯分布,提出基于软门限的Bay es 估计得到门限,BayesShink 方法性能相比SURE 门限性能更好,但是对信号的局部方差的估计对去噪性能影响较大.图像经小波变换后在层间和层内存在很强的相关性,在文献[4]中Liu 把小波统计模型分类为层内模型、层间模型和层间层内的混合模型.文献[3,5]利用层内小波系数的相关性,利用邻域信息作Bayes 估计去除噪声;M.K.M ih ®ak [5]根据图像统计特性,假定信号局部方差符合指数分布,得到优化的信号局部方差;文献[4]中分析小波系数在层间存在较强的持续性,小波域中信号系数随着尺度增加而增加,而噪声系数随着尺度的增加而减小.文献[6]利用相邻层的相同位置上的系数直接相乘的空间滤波器,突出特征信号,减少噪声.文献[7]利用层间系数的统计模型,构造一个层间系数的联合分布密度,提出了结合系数层间相关性的软门限.文献[8]结合小波域中层间系数的持续性和层内的邻域信息,利用隐马尔可夫树模型(hidden Markov tree,HM T)和Bayes 估计,给予特征点大方差,非特征点小方差;文献[9]中以层间系数直接相乘再利用邻域内系数满足相同分布得到层间-层内的混合模型.虽然上述的去噪方法[6~9]使图像性能得到一定的提高,但是由于模糊边缘位置会随着层间不同而发生位置的偏移[9],从而使层间对应位置关系很难确定,影响了去噪性能,对纹理特征复杂的图像尤为严重.模糊加权均值滤波(Fuzzy Weig hted Mean)[12]在非小波域中引进模糊理论,自适应地处理局部噪声的变化.本文在小波域中根据层内空间临近的小波系数值相似,把模糊函数用于估计信号的局部方差,根据局部噪声变化自适应地去除噪声.1 小波变换小波基函数是通过一个具有振荡特性的小波母函数的伸缩和平移生成的,<(x )和7(x )分别是尺度第44卷 第6期2005年12月复旦学报(自然科学版)Journal of Fudan Unive rsity (Natural Science )Vol.44No.6Dec.2005函数和小波函数,定义为<2j(x )=2-j2<(x /2j),72j(x )=2-j 27(x /2j ).空间函数f (x )在尺度2j 上位置x 处的小波变换为S d 2jf =f (x )<2j(x )=Q]-]f (t)<2j (x -t )d t,w d 2j f =f (x )<2j(x )=Q]-]f (t)72j (x -t )d t.推导得S d 2j=S d 2j -1fH j-1,w d 2j f =S d 2j-1f G j-1其中H j 和G j 为低通和高通正交镜像滤波器(quadrature mirror filter,QMF).对于二维图像,用QMF 对图像作小波分解如图1所示,S j +1是低频分量,W H j +1,W V j +1,W D j +1分别是图像在水平、垂直和对角的高频分量.图1(a)为2倍降采样的正交或双正交小波变换(orthogonal w avelet transform,OWT )的一次分解图,由于OWT 采用了抽样操作,因此降低了原图像的分辨率,在门限去噪时会产生视觉的Gibbs 现象[9],图1(b)为非降采样的小波变换的一次分解图,称为过完备小波扩展(over -complete w avelet ex pansion,OWE),能保留更多的冗余信息,在噪声去除中得到更好的效果[6,9],本文采用的就是OWE,具体实现细节参见文献[10].图1 小波一次分解图F ig.1 One stage decomposition of w avelet tr ansform2 小波域中基于Bayes 估计的图像去噪方法被白色高斯噪声污染的图像信号表示为g =x +E ,其中E I N (0,D 2n ).观测被噪声污染的信号g,对信号作正交小波变换得到y =w +n ,其中y 是被污染数据的小波系数,w 是原始信号的小波系数,n 是独立高斯噪声的小波系数.小波域中去噪目的就是在小波的高频细节子带中从被污染的观测数据y 中估计出原始信号w .通常认为小波系数满足均值为零的高斯分布[5,6],噪声的小波系数的概率密度函数为p n (n )=1/2PD 2n#exp -n 22D 2n,信号的小波系数的概率密度函数为p w (w )=1/2PD 2w#exp -w 22D 2w.根据经典的最大后验(maxim a posteriori probability,MAP)估计方法中选择w^(w 的估计值)使后验概率密度函数(probability density function,PDF)最大,w ^=arg max wp w /y (w /y ),(1)根据Bayes 规则,可以从观测数据y 得到w ^=arg max w [p y /w (y /w )#p w (w )]=arg max w[p n (y -w )#p w (w )].(2)不难发现(2)式等价于w ^=arg max w[log (p n (y -w ))+log (p w (w ))];(3)根据p n (n )和p w (w ),继续推导可得到估计量w^=D 2w D 2n+D 2w#y.(4)从(4)式可知,为了得到估计值,必须得到噪声小波系数的方差D 2n 和原始信号的小波系数的方差D 2w .通过972复旦学报(自然科学版)第44卷对最高频子带(HH 1)采用鲁棒的中值估计得到噪声的方差[1]D^n =median (|y i ,j |)0.675y i ,j I HH 1.(5)由于信号和噪声相互独立,所以D 2y =D 2n +D 2w ,设定大小为L @L (L 为奇数)的窗口M ,根据窗口内邻域的小波系数得到受噪声污染的小波系数的局部方差和原始信号的小波系数的方差[3]D ^2y =1N2Eyi,jI M(k)y 2i ,j ,(6)D^w =(D ^2y -D ^2n )+;(7)其中定义(g )+=0 if g <0,g others.根据(4)式就能计算出原始信号的小波系数估计值,(4)式称为LAWM L(Locally Adaptive Window -based denoising using M L)[5].3 基于模糊的局部方差估计上一节中介绍小波域中基于Bayes 估计得到的去噪方法,从(4)式可以看出小波系数的局部方差估计直接影响算法的性能,介绍一种基于模糊的局部方差估计方法.在小波域的高频细节子带上,幅值较大的小波系数通常是图像的特征点如边缘、纹理等,而在图像的平滑区小波系数的幅值比较小.同一子带中相邻的系数幅值通常具有相似性,(6)式正是基于这一特性.但是在图像变化剧烈的区域如边缘区,边缘上的点和边缘两边的点具有很大的差异,而且在噪声污染的图像中,由于噪声的污染,可能会出现幅值与周围点不一致的点.图像去噪就是要在高频细节上保存图像的边缘和平滑区的规整性.(4)式说明希望边缘上的点有较大的方差,平滑区或噪声引起的点具有较小的方差,这样能更好地去除噪声恢复原始数据.(6)式中对窗内各点简单地用同一权重计算出局部方差,一定程度上会使图像比较细小的边缘被扼杀掉,且在图像大边缘上由于方差的估计偏小,去除过量噪声而使边缘模糊.根据上面所述,对于图像边缘点估计信号局部方差时,希望邻域内边缘上的点有较大的权重,而邻域内非边缘点有较小的权重,或是说希望能在图像边缘处得到大方差而平滑区得到小方差.在平滑区由于噪声引起的奇异点,通常是孤立的或不连续的点,而图像的边缘具有一定的持续性不是孤立点.通常图像位置越靠近其小波系数的幅值相似性越强,因此本文设计了幅值相似度模糊函数u i ,j 和空间临近度模糊函数d i,j ,u i,j =exp -w i ,j -w k ,lK6,(8)d i ,j=exp -(i -k )2+(j -l )2D 2,(9)其中k ,l 是中心点的坐标,i,j 为邻域点的坐标,w k ,l 与w i ,j 分别为中心点和其邻域点的小波系数,K 为常数,D 值取为以(k ,l )为中心点的窗口M (k ,l )的边长大小L.根据幅值相似度模糊函数和空间临近度模糊函数,得到邻域内各点在计算局部方差时的权重s (i,j ),并得到新的局部方差的计算公式s(i,j )=u i,j @d i,j ,(10)D^2y =Eyi,jI M (k ,j),i X k,j X ls (i,j )@y 2i ,jEi X 0,j X ls(i,j ).(11)关于参数K 的选取,画出幅值相似度模糊函数曲线如图2(见第974页).从图中可以看出曲线可以分为4部分,当(w i ,j -w k,l )与K 的比例小于0.6时,幅值相似度大于0.96,R =(w i ,j -w k ,l )/K 大于1.973 第6期李 军等:小波域中基于模糊的图像去噪方法15时,幅值相似度小于0.06,R 并迅速趋近于零,R 在0.60~0.77和0.77~1.15之间幅值相似度近似图2 幅值相似度模糊函数及其逼近曲线F ig.2 T he curve of t he fuzzy funct ion of similariryin amptitude and its appro ximate function成线性变化.函数曲线与Pan [10]提出当门限t =D n ,2D n ,3D n 分别能去除68.3%,95.4%,99.7%噪声的原理相吻合,所以取K =c D n ,c 是3~4之间的常数.当邻域内系数与中心点的差值在D n 内,可以认为是噪声引起的变化,而不是边缘突变,这时各点幅值相似度变化较小,当差值超过1.5D n 时,幅值相似度的变化较大,近似成线性变化,所以幅值相似度模糊隶属度函数能较好地区分出邻域点与当前点的系数差值是由于噪声引起还是边缘引起.虽然(8)式能很好区分出边缘点,并计算出各点权重,但函数实现复杂.从函数曲线和前面的分析,可以采用分段函数逼近函数曲线,降低计算量.如图2中的虚线,可得到(8)式的近似表示u i ,j =1R <0.6,-0.7354R +1.39560.6[R <0.77,-2.0R +2.36930.77[R <1.15,0.001R \1.15.(12)由于邻域内各点的空间临近度d i ,j 的大小与邻域内的小波系数无关,只与邻域窗口大小有关.所以对于某个固定的窗口可以从(9)式计算出空间临近度后用固定的模板实现.5@5窗口的模板表示见下式.中心点的值为0,可有效去除孤立的噪声点.d i ,j =0.730.820.850.820.730.820.920.960.920.820.850.9600.960.850.820.920.960.920.820.730.820.850.820.73.(13)把基于本文提出的D 2w 估计的去噪算法称为FLAWML(Fuzzy-based LAWML),其实现流程如下.¹图像作小波变换得到各层的小波系数;º对各高频细节子层选择合适的窗口,根据(13)式和(12)式,(10)式计算出邻域内各点权重;»根据(11)式计算出局部方差,利用(5)式,(7)式估计出原始信号的方差估计值;¼根据(4)式得到各子层原始信号的小波系数估计值;½小波反变换得到去噪后的图像.表1 不同层的小波系数去噪结果T ab.1 Denoising r esults of different scale图像D n 所处层数PSN R /dB LAWM L FLAWM L Lena 30304040121229.6626.6827.3124.5833.4227.9131.5626.29Barbara 30304040121228.2124.3026.3422.4829.9824.5828.8022.964 试验结果FLAWM L 算法中的窗口大小取5@5,以峰值信噪比PSNR 作为性能衡量标准,试验对标准灰度图像Lena 和Barabara 加上不同强度的高斯噪声进行仿真,列出了不同算法在图像复杂度相对简单的Lena 和相对复杂的Barbara 上的试验结果,参见表1和表2.表1中数据为LAWML 和FLAWML 算法在小波域中各层对角高频分量上的中间结果比较,表2中数据为几种算法的去噪结果,表1,表2中LAWM L 及本文的FLAWM L 算法都是基于OWE,Daubechies p =2,小波层数为3.表2中其他方法的数据结果来自文献[7].由表1可以看出FLAWM L 算法在小波域中受噪声影响最大的第1层和第2层,尤其第1层中的去噪效果非常明显,相对LAWML 算法在纹974复旦学报(自然科学版)第44卷理简单的Lena 提高了4dB 左右,纹理复杂的Barbara 也提高了2dB 左右.表1和表2中LAWM L 和FLAWM L 算法的结果表明本文提出的局部方差估计方法能更好地反映原始信号的真实情况.HM T[8]是通过隐马尔可夫树模型结合层间层内信息对边缘特征点以大方差,保存图像边缘,目的与本文一样.从表2可知FLAWML 算法明显优于HMT [8],虽然Bivariate shrink [7]在纹理相对简单的Lena 时效果与FLAWML 算法相当,但是纹理复杂的Barbara 中FLAWM L 效果比Bivariate shrink [7]好.图3是Lena(512@512)在D n =30时去噪后的结果比较,从图3可以看出FLAWM L 算法去噪后的边缘效果明显,FLAWM L 算法能比较合理地去除噪声使图像边缘清晰.表2 不同去噪方法的结果比较T ab.2 Denosing results o f different methods图像D n PSN R /dBH M T [8]Bivariate shri n k [7]LAWM AP [5]BayesShrink [3]LAWM L FLAWM L Lena1033.8434.3634.1033.3234.9235.282031.7631.1930.8930.1730.6831.453028.3529.4129.0528.4827.9229.3740----26.0327.77Barbara1031.3632.2531.9931.8633.2633.372027.8028.3627.9427.1328.8129.253025.1126.2825.8025.1626.0426.7840----24.4025.23图3 L ena 的去噪结果比较Fig.3 Denoising r esults of L ena本文主要根据图像小波系数在高频细节内邻近的点的系数相似性,提出了基于模糊的局部方差估计的去噪算法,并对模糊函数进行了优化,降低计算量.从试验结果可以看出FLAWM L 相对其他方法,尤其在图像比较复杂和噪声恶劣的情况下,能较好地改善去噪性能,保存图像的边缘细节.在图像处理领域,根据图像在小波域中的统计特性认为小波系数满足高斯分布或拉普拉斯分布及软硬门限的使用,提出了很多去噪方法.本文根据小波系数满足高斯分布,并且利用图像小波系数邻域内的相关性,提出了基于模糊函数的局部方差估计方法.这种方法同样可以运用到小波域中其他图像去噪的方法,如以拉普拉斯分布为依据的方法中.下一步的研究可以围绕如何更有效地利用领域内相关性并结合层间相关性去除图像的噪声及更有效的模糊函数挖掘领域内相关性展开.参考文献:[1] Donoho D L,Johnsto ne I M.Ideal spat ial adaptation by w av elet shrinkag e [J].Biometr ik a ,1994,81(3):425-455.[2] Donoho D L.Denoising by soft -thresholding [J].I EEE T r ans I nf or m T heory ,1995,41(5):613-627.[3] Chang S,Yu B,V etterli M.Adaptive wavelet thresho lding for image denoising and compressio n [J].IEEET r ans I mage Pr ocessing ,2000,9(9):1532-1546.[4] Liu J,M oulin P.I nformation -theoretic analysis of interscale and intrascale dependencies between image wavelet -coefficients [J].I EEE T rans I mage Pr ocessing ,2001,10(11):1647-1658.975 第6期李 军等:小波域中基于模糊的图像去噪方法976复旦学报(自然科学版)第44卷[5]M K hL cak M K,Kozintsev I,Ramchandr an K,et al.Low-complexit y image denoising based on statistical mod-eling of wavelet coefficients[J].IEEE Signal Processing Lett,1999,6(12):300-303.[6]Zhang L,Bao P.Denoising by spatial correlation thresholding[J].I EEE T r ansactions on Cir cuits and Sys temsf or V ideo T echnology,2003,13(6):535-538.[7]Sendur L,Selesnick I W.Bivariate shrinkage functions for wavelet-based denoising exploiting interscale depen-dency[J].I EEE T r ansactions on Signal Pr ocessing,2002,50(11):2744-2756.[8]Crouse M,Now ak R,Baraniuk R.W av elet-based statistical signal processing using hidden M arkov models[J].I EEE T ransactions on Signal Pr ocessing,1998,42(4):886-902.[9]Zhang L,Bao P.Hybr id inter-and intr a-w avelet scal image restoration[J].Patter n Recognition,2003,36:1737-1746.[10]P an Q,Zhang L,Dai G Z,et al.T wo deno ising methods by w av elet transform[J].I EEE T ransactions on Sig-nal Processing,1999,47(12):3401-3406.[11]傅一平,李志能.利用小波系数的相关性提取噪声图像边缘[J].计算机辅助设计与图形学学报,2004,16(2):174-179.[12]王志刚,王伟.一种改进型自适应加权模糊均值滤波算法[J].高技术通讯,2003,13(2):19-24.Image Denoising Based on Fuzzy in Wavelet DomainLI Ju n,CHEN Gu ang-men g(Dep ar tment of Electr onic Engineer ing,Fudan Univer sity,S hanghai200433,China)A bstract:The similarity of the wavelet coeffients of adjacent neigbors is exploited.A fuzzy function of the similariry inspace and amptitude is proposed,which is used to estimate the signal local variance.Signal local variance is the key to have better denoising performance.Experiments show that Fuzzy-based LAWML(FLAWML)based on the present new est-i mation of local variance proposed suppresses the noise and preserves the edge details of the i mage more effectively than oth-er denoising methods.Keywords:image processing;image denoising;fuzzy function;wavelet transform。