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基于二阶差分的频域滤波反锐化增强算法作者：贺明李成柱宋文爱来源：《计算机时代》2021年第01期摘要：針对图像处理中存在噪声放大、过度增强高频分量的问题，提出了一种基于二阶差分的频域滤波反锐化增强算法。
首先在频率域内利用同态滤波器和高斯低通滤波器对图像进行对比度增强和平滑处理，并将二者进行减运算得到图像细节;然后利用二阶差分曲率控制细节成分对输出图像的贡献;最终通过反锐化掩膜法进行增强处理。
实验结果表明，增强后的图像有效地抑制了噪声，突出了图像细节信息，具有较好的视觉效果。
关键词：图像增强; 同态滤波; 低通滤波; 反锐化掩膜; 二阶差分中图分类号：TP391 文献标识码：A 文章编号：1006-8228（2021）01-16-05Image unsharp masking algorithm in frequency domain based on second-order differenceHe Ming1， Li Chengzhu1， Song Wenai2（1. Army Special Operations College， Guangxi， Guilin 541002， China; 2. College of Software， North University of China）Abstract： Aiming at the problems of noise amplification and excessive enhancement of high-frequency components in image processing， an image unsharp masking algorithm based on second-order difference in frequency domain filtering is proposed. Firstly， in the frequency domain，homomorphic filtering and Gaussian low-pass filtering are used to enhance and smooth the contrast of the image， and subtract the two to obtain image details; Then use the second-order differential curvature to control the contribution of the detail component to the output image; Finally， the unsharp masking method is used for enhancement processing. The experimental results show that the enhanced image effectively suppresses the noise， highlights the image details， and has a better visual effect.Key words： image enhancement; homomorphic filtering; low-pass filtering; unsharp masking; second order difference0 引言近年来，图像处理技术的使用越来越广泛，已覆盖军事、航空航天、通信工程、生物医学工程、农业等领域。
专利名称：Fuzzy device for image noise reduction发明人：Pennino, Laura,Mancuso, Massimo,Travaglia,Federico,Poluzzi, Rinaldo,Rizzotto, Gianguido申请号：EP94830408.4申请日：19940825公开号：EP0698990A1公开日：19960228专利内容由知识产权出版社提供专利附图：摘要：Fuzzy device for image noise reduction, comprising: interface means adapted to retrieve the gray level of a pixel to be processed of an image and of neighbouring pixels;difference means connected to said interface means adapted to generate a difference ofthe gray levels between said neighbouring pixels and said pixels to be processed; fuzzy flat area smoothing means connected to said difference means adapted to perform a low-pass smoothing of an almost homogeneous region defined by said pixel and by said neighbouring pixels; edge preserving smoothing means connected to said difference means adapted to perform low-pass filtering on a high-pass information region defined by said pixel and by said neighbouring pixels; region voter means connected to said interface means adapted to give a measure for considering whether said region defined by said pixel and said neighbouring pixels is almost homogeneous; and soft switching means connected to the outputs of said smoothing means adapted to perform the weighting of the said outputs of said smoothing means on the basis of said measure.申请人：SGS-THOMSON MICROELECTRONICS S.r.l.,CONSORZIO PER LA RICERCA SULLA MICROELETTRONICA NEL MEZZOGIORNO地址：Via C. Olivetti, 2 I-20041 Agrate Brianza (Milano) IT,Stradale Primosole, 50 I-95121 Catania IT国籍：IT,IT代理机构：Modiano, Guido, Dr.-Ing.更多信息请下载全文后查看。
Accessories （附/配件）Anti-shake （防抖）Aperture （光圈）Aperture priority （光圈优先）Auto bracketing （自动包围）Auto focus （自动对焦）Auto rotation （自动旋转）Background （背景）Backlit (背光的)背光的主体（backlit subject）Battery grip （电池手托）Built-in flash （内置闪光灯）Composition （构图）Depth of field (DOF) （景深）Digital zoom （数码变焦）SLR （单反相机）DSLR （数码单反相机）Effective pixels （有效像素）Exposure （曝光）Exposure compensation （曝光补偿）Electromagnetic diaphragm (EMD) 电磁光圈External speedlite （外置闪光灯）Film （胶卷，菲林）Filter (滤光镜)Focus (对焦)对焦环（focusing ring）自动对焦（auto-focusing）Foreground （前景）Full frame (全幅/全片幅)Full pressing （全按）Halfway pressing （半按）High key (高调/亮调)Histogram (光暗分布图)Hood (遮光罩)Image stabilization （成像稳定）Image stabilizer (IS) (成像稳定系统/器) LCD monitor （液晶显示器）Lens （镜片/头）自动对焦镜头(auto-focusing lens)标准镜头(standard lens)标准变焦镜头(standard zoom lens)超广角变焦镜头(ultra wide lens)中距远摄镜头（medium telephoto lens）远摄变焦镜头(telephoto zoom lens) 远摄镜头(telephoto lens)超远摄镜头(super telephoto lens)微距镜头（macro lens）移轴镜头（tilt and shift lens）Light（光）低光/暗光（low light）Lighting （用光）Low key（低调/暗调）Macro （微距）Manual （手动）Metering （测光）矩阵/评估测光（matrix / evaluative metering）中央权重平均测光（center-weighted average metering）点测光（spot (partial) metering）Noise reduction （减噪）Optical zoom （光学变焦）Photographer（摄影者/家）Photography (摄影)文献摄影（documentary photography）艺术摄影（fine art photography）风光摄影（landscape photography）裸体摄影（nude photography）扫街摄影（street photography）肖像摄影(portrait photography)Picture angle （图像对角）Playback （回放显示）Red-eye reduction （红眼消除）Remote switch （遥控开关）Sensitivity (ISO) （感光度）Sensor （感光器/芯片）Setting （设置）Shape (形状)Sharpening （锐度）Shutter （快门）快门按钮(shutter button)Shutter priority （快门优先）Shutterspeed （快门速度）Subject （拍摄主体）Subject distance （主体距离）Texture (质地，质感)Tripod (三脚架)Viewfinder （取景器）Ultrasonic Motor (USM) （超声波马达）White balance （白平衡）Wide （广角）Zoom (变焦)变焦环（zoom ring）相机英文词汇大全(字母序)AAberration 像差Accessory 附件Accessory Shoes 附件插座、热靴Achromatic 消色差的Active 主动的、有源的Acutance 锐度Acute-matte 磨砂毛玻璃Adapter 适配器Advance system 输片系统AE Lock(AEL) 自动曝光锁定AF(Autofocus) 自动聚焦AF Illuminator AF照明器AF spotbeam projector AF照明器Alkaline 碱性Ambient light 环境光Amplification factor 放大倍率Angle finder 弯角取景器Angle of view 视角Anti-Red-eye 防红眼Aperture 光圈Aperture priority 光圈优先APO(APOchromat) 复消色差APZ(Advanced Program zoom) 高级程序变焦Arc 弧形ASA(American Standards Association) 美国标准协会Astigmatism 像散Auto bracket 自动包围Auto composition 自动构图Auto exposure 自动曝光Auto exposure bracketing 自动包围曝光Auto film advance 自动进片Auto flash 自动闪光Auto loading 自动装片Auto multi-program 自动多程序Auto rewind 自动退片Auto wind 自动卷片Auto zoom 自动变焦Automatic exposure(AE) 自动曝光Automation 自动化Auxiliary 辅助的BBack 机背Back light 逆光、背光Back light compensation 逆光补偿Background 背景Balance contrast 反差平衡Bar code system 条形码系统Barrel distortion 桶形畸变BAse-Stored Image Sensor (BASIS) 基存储影像传感器Battery check 电池检测Battery holder 电池手柄Bayonet 卡口Bellows 皮腔Blue filter 蓝色滤光镜Body-integral 机身一体化Bridge camera 桥梁相机Brightness control 亮度控制Built in 内置Bulb B 门Button 按钮CCable release 快门线Camera 照相机Camera shake 相机抖动Cap 盖子Caption 贺辞、祝辞、字幕Card 卡Cartridges 暗盒Case 机套CCD(Charge Coupled Device) 电荷耦合器件CdS cell 硫化镉元件Center spot 中空滤光镜Center weighted averaging 中央重点加权平均Chromatic Aberration 色差Circle of confusion 弥散圆Close-up 近摄Coated 镀膜Compact camera 袖珍相机Composition 构图Compound lens 复合透镜Computer 计算机Contact 触点Continuous advance 连续进片Continuous autofocus 连续自动聚焦Contrast 反差、对比Convetor 转换器Coreless 无线圈Correction 校正Coupler 耦合器Coverage 覆盖范围CPU(Central Processing Unit) 中央处理器Creative expansion card 艺术创作软件卡Cross 交叉Curtain 帘幕Customized function 用户自选功能DData back 数据机背Data panel 数据面板Dedicated flash 专用闪光灯Definition 清晰度Delay 延迟、延时Depth of field 景深Depth of field preview 景深预测Detection 检测Diaphragm 光阑Diffuse 柔光Diffusers 柔光镜DIN (Deutsche Industrische Normen) 德国工业标准Diopter 屈光度Dispersion 色散Display 显示Distortion 畸变Double exposure 双重曝光Double ring zoom 双环式变焦镜头Dreams filter 梦幻滤光镜Drive mode 驱动方式Duration of flash 闪光持续时间DX-code DX编码EED(Extra low Dispersion)超低色散Electro selective pattern(ESP)电子选择模式EOS(Electronic Optical System) 电子光学系统Ergonomic人体工程学EV(Exposure value)曝光值Evaluative metering综合评价测光Expert专家、专业Exposure曝光Exposure adjustment曝光调整Exposure compensation曝光补偿Exposure memory曝光记忆Exposure mode曝光方式Exposure value(EV)曝光值Extension tube近摄接圈Extension ring近摄接圈External metering外测光Extra wide angle lens超广角镜头Eye-level fixed眼平固定Eye-start眼启动Eyepiece目镜Eyesight correction lenses视力校正镜FField curvature 像场弯曲Fill in 填充(式)Film 胶卷(片)Film speed 胶卷感光度Film transport 输片、过片Filter 滤光镜Finder 取景器First curtain 前帘、第一帘幕Fish eye lens 鱼眼镜头Flare 耀斑、眩光Flash 闪光灯、闪光Flash range 闪光范围Flash ready 闪光灯充电完毕Flexible program 柔性程序Focal length 焦距Focal plane 焦点平面Focus 焦点Focus area 聚焦区域Focus hold 焦点锁定Focus lock 焦点锁定Focus prediction 焦点预测Focus priority 焦点优先Focus screen 聚焦屏Focus tracking 焦点跟踪Focusing 聚焦、对焦、调焦Focusing stages 聚焦级数Fog filter 雾化滤光镜Foreground 前景Frame 张数、帧Freeze 冻结、凝固Fresnel lens 菲涅尔透镜、环状透镜Frontground 前景Fuzzy logic 模糊逻辑GGlare 眩光GN(Guide Number) 闪光指数GPD(Gallium Photo Diode) 稼光电二极管Graduated 渐变HHalf frame 半幅Halfway 半程Hand grip 手柄High eye point 远视点、高眼点High key 高调Highlight 高光、高亮Highlight control 高光控制High speed 高速Honeycomb metering 蜂巢式测光Horizontal 水平Hot shoe 热靴、附件插座Hybrid camera 混合相机Hyper manual 超手动Hyper program 超程序Hyperfocal 超焦距IIC(Integrated Circuit) 集成电路Illumination angle 照明角度Illuminator 照明器Image control 影像控制Image size lock 影像放大倍率锁定Infinity 无限远、无穷远Infra-red(IR) 红外线Instant return 瞬回式Integrated 集成Intelligence 智能化Intelligent power zoom 智能化电动变焦Interactive function 交互式功能Interchangeable 可更换Internal focusing 内调焦Interval shooting 间隔拍摄ISO(International Standard Association) 国际标准化组织JJIS(Japanese Industrial Standards)日本工业标准LLandscape 风景Latitude 宽容度LCD data panel LCD数据面板LCD(Liquid Crystal Display) 液晶显示LED(Light Emitting Diode) 发光二极管Lens 镜头、透镜Lens cap 镜头盖Lens hood 镜头遮光罩Lens release 镜头释放钮Lithium battery 锂电池Lock 闭锁、锁定Low key 低调Low light 低亮度、低光LSI(Large Scale Integrated) 大规模集成MMacro微距、巨像Magnification放大倍率Main switch主开关Manual手动Manual exposure手动曝光Manual focusing手动聚焦Matrix metering矩阵式测光Maximum最大Metered manual测光手动Metering测光Micro prism微棱Minimum最小Mirage倒影镜Mirror反光镜Mirror box反光镜箱Mirror lens 折反射镜头Module模块Monitor监视、监视器Monopod独脚架Motor电动机、马达Mount卡口MTF (Modulation Transfer Function调制传递函数Multi beam多束Multi control多重控制Multi-dimensional多维Multi-exposure多重曝光Multi-image多重影Multi-mode多模式Multi-pattern多区、多分区、多模式Multi-program多程序Multi sensor多传感器、多感光元件Multi spot metering多点测光Multi task多任务NNegative 负片Neutral 中性Neutral density filter 中灰密度滤光镜Ni-Cd battery 镍铬(可充电)电池OOff camera 离机Off center 偏离中心OTF(Off The Film) 偏离胶卷平面One ring zoom 单环式变焦镜头One touch 单环式Orange filter 橙色滤光镜Over exposure 曝光过度PPanning 摇拍Panorama 全景Parallel 平行Parallax 平行视差Partial metering 局部测光Passive 被动的、无源的Pastels filter 水粉滤光镜PC(Perspective Control) 透视控制Pentaprism 五棱镜Perspective 透视的Phase detection 相位检测Photography 摄影Pincushion distortion 枕形畸变Plane of focus 焦点平面Point of view 视点Polarizing 偏振、偏光Polarizer 偏振镜Portrait 人像、肖像Power 电源、功率、电动Power focus 电动聚焦Power zoom 电动变焦Predictive 预测Predictive focus control 预测焦点控制Preflash 预闪Professional 专业的Program 程序Program back 程序机背Program flash 程序闪光Program reset 程序复位Program shift 程序偏移Programmed Image Control (PIC) 程序化影像控制QQuartz data back 石英数据机背RRainbows filter 彩虹滤光镜Range finder 测距取景器Release priority 释放优先Rear curtain 后帘Reciprocity failure 倒易律失效Reciprocity Law 倒易律Recompose 重新构图Red eye 红眼Red eye reduction 红眼减少Reflector 反射器、反光板Reflex 反光Remote control terminal 快门线插孔Remote cord 遥控线、快门线Resolution 分辨率Reversal films 反转胶片Rewind 退卷Ring flash 环形闪光灯ROM(Read Only Memory) 只读存储器Rotating zoom 旋转式变焦镜头RTF(Retractable TTL Flash) 可收缩TTL闪光灯SSecond curtain 后帘、第二帘幕Secondary Imaged Registration(SIR) 辅助影像重合Segment 段、区Selection 选择Self-timer 自拍机Sensitivity 灵敏度Sensitivity range 灵敏度范围Sensor 传感器Separator lens 分离镜片Sepia filter 褐色滤光镜Sequence zoom shooting 顺序变焦拍摄Sequential shoot 顺序拍摄Servo autofocus 伺服自动聚焦Setting 设置Shadow 阴影、暗位Shadow control 阴影控制Sharpness 清晰度Shift 偏移、移动Shutter 快门Shutter curtain 快门帘幕Shutter priority 快门优先Shutter release 快门释放Shutter speed 快门速度Shutter speed priority 快门速度优先Silhouette 剪影Single frame advance 单张进片Single shot autofocus 单次自动聚焦Skylight filter 天光滤光镜Slide film 幻灯胶片Slow speed synchronization 慢速同步SLD(Super Lower Dispersion) 超低色散SLR(Single Lens Reflex) 单镜头反光照相机SMC(Super Multi Coated) 超级多层镀膜Soft focus 柔焦、柔光SP(Super Performance) 超级性能SPC(Silicon Photo Cell) 硅光电池SPD(Silicon Photo Dioxide) 硅光电二极管Speedlight 闪光灯、闪光管Split image 裂像Sport 体育、运动Spot metering 点测光Standard 标准Standard lens 标准镜头Starburst 星光镜Stop 档Synchronization 同步TTele converter增距镜、望远变换器Telephoto lens长焦距镜头Trailing-shutter curtain后帘同步Trap focus陷阱聚焦Tripod三脚架TS(Tilt and Shift)倾斜及偏移TTL flashTTL闪光TTL flash metering TTL闪光测光TTL(Through The Lens)通过镜头、镜后Two touch双环UUD(Ultra-low Dispersion) 超低色散Ultra wide 超阔、超广Ultrasonic 超声波UV(Ultra-Violet) 紫外线Under exposure 曝光不足VVari-colour 变色Var-program 变程序Variable speed 变速Vertical 垂直Vertical traverse 纵走式View finder 取景器WWarm tone 暖色调Wide angle lens 广角镜头Wide view 广角预视、宽区预视Wildlife 野生动物Wireless remote 无线遥控World time 世界时间XX-sync X-同步ZZoom 变焦Zoom lens 变焦镜头Zoom clip 变焦剪裁Zoom effect 变焦效果其他：TTL 镜后测光NTTL 非镜后测光UM 无机内测光，手动测光MM 机内测光，但需手动设定AP 光圈优先SP 快门优先PR 程序暴光。
快速高效去除图像椒盐噪声的均值滤波算法何海明;齐冬莲;张国月;张建良【摘要】Fast and efficient mean filter algorithm is proposed to overcome the drawbacks of some classic algorithms.For the suspected noise pixel,the algorithm firstly create a set composed of signal pixels selected from the borders of 3 ×3 filtering window,then noise is removed by means of mean filtering if the set composed of signal pixels is not emp-ty;else the image is restored based on the method mentioned above by enlarging filtering window until the set com-posed of signal pixels is not empty. The experimental results show that this algorithm has excellent filtering perform-ance for all noise ratios from 1% to 99%,besides,the algorithm can preserve the details of the image very well and the computation time is very short,it is useful in practical application.%针对常见滤除椒盐噪声算法需要使用阈值、运算时间长、去除噪声效果不理想等缺陷，提出了一种快速高效去除图像椒盐噪声的均值滤波算法。
第 22卷第 12期2023年 12月Vol.22 No.12Dec.2023软件导刊Software Guide基于PCA降噪的改进型CLAHE算法张学典，王文明（上海理工大学光电信息与计算机工程学院，上海 200093）摘要：为解决可见光成像设备采集的图像细节特征识别困难的问题，结合两种不同方法提出一种主成分分析和改进型的各向异性扩散滤波器的模糊裁剪对比度受限自适应直方图均衡化（ADFS-CLAHE-FC）图像增强技术，从图像中提取有意义的信息。
首先通过PCA对图像进行降噪处理，然后利用ADFS-CLAHE-FC对降噪后的图像作增强处理，最后基于ADFS-CLAHE-FC进一步降低图片的噪声，保持对比度和亮度。
实验表明，该方法在增强图像对比度的同时消除了图像噪声，在视觉上效果更好，相较于直方图均衡化（HE）、对比度受限自适应直方图均衡化（CLAHE）方法及其他方法在提升图像质量和保持图像细节方面性能更优，有助于提升图像分割和提取的准确性。
关键词：图像增强；CLAHE；主成分分析；对比度增强；直方图均衡化DOI：10.11907/rjdk.222402开放科学（资源服务）标识码（OSID）：中图分类号：TP183 文献标识码：A文章编号：1672-7800（2023）012-0200-09Improved CLAHE Algorithm Based on PCA Noise ReductionZHANG Xuedian， WANG Wenming（School of Optical-Electrical and Computer Engineering， University of Shanghai for Science and Technology， Shanghai 200093， China）Abstract：To address the difficulty in identifying detailed features of images captured by visible light imaging devices， a fuzzy cropping con‐trast limited adaptive histogram equalization （ADFS-CLAHE-FC） image enhancement technique is proposed by combining principal compo‐nent analysis and an improved anisotropic diffusion filter with two different methods to extract meaningful information from the image. Firstly，the image is denoised using PCA， and then the denoised image is enhanced using ADFS-CLAHE-FC. Finally， the noise of the image is fur‐ther reduced based on ADFS-CLAHE-FC，maintaining contrast and brightness. Experiments have shown that this method enhances image contrast while eliminating image noise，resulting in better visual performance. Compared to histogram equalization （HE），contrast limited adaptive histogram equalization （CLAHE）， and other methods， it performs better in improving image quality and preserving image details，which helps to improve the accuracy of image segmentation and extraction.Key Words：image enhancement； CLAHE； principal component analysis； contrast enhancement； histogram equalization0 引言计算机视觉系统的成功很大程度取决于图像质量，因为它决定了信息检索和解释的准确性，图像质量差会给目标识别、分割和特征提取带来很大阻碍。
基于模糊支持向量机的曲波域图像去噪算法王向阳;牛盼盼;张宇【摘要】图像去噪是图像处理领域的研究热点,数字图像去噪方法研究仍然是一项富有挑战性的工作.本文以性能卓越的曲波(Curvelet)变换理论为基础,提出了一种基于模糊支持向量机(FSVM)的曲波域图像去噪算法.该算法的基本工作原理为:首先,对原始噪声图像做曲波分解以获得变换系数;然后,结合噪声分布特点确定系数空间性,并构造出FSVM的训练特征;最后,对高频曲波系数进行模糊分类与自适应阈值去噪,并进一步对去噪后系数进行曲波重构以得到去噪图像.通过仿真实验结果,证明了本文算法在消除伪吉布斯(Gibbs)现象的同时,具有较强的抑制噪声能力和边缘保护能力.【期刊名称】《辽宁师范大学学报（自然科学版）》【年(卷),期】2016(039)001【总页数】6页(P44-49)【关键词】图像去噪;曲波变换;模糊支持向量机;自适应阈值【作者】王向阳;牛盼盼;张宇【作者单位】辽宁师范大学计算机与信息技术学院,辽宁大连 116029;辽宁师范大学计算机与信息技术学院,辽宁大连 116029;辽宁师范大学计算机与信息技术学院,辽宁大连 116029【正文语种】中文【中图分类】TP391图像去噪是图像处理领域的研究热点，分析其原因主要有两个方面:一是图像去噪能够有效地控制噪声，以便为诸如边缘检测、目标识别等后续图像处理提供更为精准的图像信息;二是图像去噪方法的研究使得诸如图像恢复、图像分割等其他图像处理及分析问题得到解决．因此，数字图像去噪方法在近年一直是图像处理领域的重要研究课题［1］．现有图像去噪方法主要分为以下5类，即:基于双边滤波的图像去噪方法、基于条件随机场的图像去噪方法、基于各向异性扩散的图像去噪方法、基于非局部均值的图像去噪方法、基于统计模型法的图像去噪方法［2-6］．其中，双边滤波在去除噪声的同时实现了对边缘信息的良好保留，但其不能有效处理Speckle噪声，且常常使图像过于平滑．条件随机场(CRFs)建模时特征选择十分灵活，并且不需要提供确切的先验模型，但是这种方法常常遇到两个挑战:第一，CRFs的能量函数计算必须是可行的，但在真实世界中，为大部分能量函数找到全局最小值是一个NP难题;第二，很难在期望的解决方案中找到合适的能量函数，使其求取出全局最小值．基于各向异性扩散的图像去噪方法其优点是能够在保持边缘的前提下平滑噪声，但该方法过于平滑图像且边界过于尖锐，以至于丧失了很多纹理信息．非局部均值方法是利用图像中具有重复结构的性质来去除噪声，但其客观质量和视觉效果通常比其他去噪方法差．近年来，人们陆续提出了多种变换域统计模型图像去噪方法，该类方法主要是通过捕获变换系数间的尺度内相关性、尺度间相关性等达到去噪目的，但实验结果表明该类方案无法获得较为理想的去噪效果．笔者以曲波(Curvelet)变换与模糊支持向量机(FSVM)理论为基础，提出了一种基于FSVM分类的自适应曲波域图像去噪算法，获得了较好的去噪效果．基于统计学习理论与结构风险最小化原则，1995年，Vapnik等人提出了一种著名的分类方法——支持向量机(SVM)分类，这种分类方法使“维数灾难”和“过学习”等传统困难得到克服，并在小样本、非线性和高维模式识别问题中显示出其独特的优点．支持向量机分类方法具有较好的泛化能力，但所有的样本在构建最优分类面时作用均相同，从而导致了当训练样本中含有噪声时，特征空间中靠近分类面附近的这些样本往往都含有“异常”信息，使得到的分类面并不是正确的最优分类面．为有效克服传统支持向量机所存在的上述不足，一种改进的支持向量机(SVM)分类方法——模糊支持向量机(FSVM)理论被Lin等［7］提出．模糊支持向量机理论是在支持向量机基础上应用模糊技术，将不同的惩罚权系数应用到不用的样本上，从而使得不同样本在构造目标函数的过程中具有不同的贡献．为了消除噪声样本的影响，即可通过将较小的权值赋值给含有噪声训练样本的方法来实现．为了使样本信息得到充分利用，模糊支持向量机方法给样本x建立了一个模糊隶属度函数mi，j(x):于是，第i类的模糊隶属度函数表示为:这样，待分类样本x满足下式条件时就可以被划分到第i类:显然，通过使用模糊隶属度函数，不仅能够有效解决多类别的不可划分问题，而且更进一步地提高了分类精度．E．J．Candes等提出［8］的曲波(Curvelet)变换是一种方向性、多尺度几何变换，其以小波变换为基础，引入了方向性参数．在二维空间R2中，x表示空间位置变量，w表示频率域变量，r和θ表示频率域的极坐标变量．W(r)表示半径窗，V(t)表示角度窗，r∈(1/2，2)和t∈［－1，1］表示其支撑区间，且满足以下两个容许条件:．对所有j≥j0的尺度，频率窗定义为其中，|j/2|是j/2的整数部分．Uj为极坐标下的一种楔形窗，由半径窗W和角度窗V限制得到的楔形区域构成了楔形窗的支撑区间，其具有各向异性尺度的性质．我们用φj(x)表示母曲波函数Uj(W)表示傅里叶变换，φj经过平移和旋转可以得到在2－j尺度上的曲波，其中表示平移参数表示均匀的旋转角度序列．综合以上概念，定义在尺度2－j、方向θl、平移参数(k1，k2)处的曲波为其中，而曲波变换可以表示为上述曲波系数可进行简单的定义，设CKD(i，j)表示图像经过曲波变换后得到的曲波系数，其中，K代表尺度参数，D代表方向参数，那么，(i，j)表示第K尺度第D个方向上的坐标．在实际应用中，曲波变换的尺度受图像大小的影响［9］，设图像大小为［m，n］=size(image)，则图像经曲波变换后的尺度与图像大小的关系即为:scales=log2(n)－3．表1列举了标准灰度图像Lena(512×512)经过曲波变换后所得到的曲波系数各尺度各方向的结构，由图像大小与曲波变换尺度的对应关系可知，图像被分解为6个尺度，具体曲波系数结构如表1．表1表明，图像经过曲波变换后，第1层方向数为1，是由21×21的像素矩阵表示的低频系数构成，低频系数层能够很好地体现图像的主要信息;第2层到第5层为图像经变换后的中频系数层，各个层上的方向数不同，其中每个中频系数层都有4个大方向，第2层包含4个小方向，第3层和第4层包含8个小方向，第5层包含16个小方向，这是曲波变换具有良好的方向特性的具体体现;第6层方向数为1，是由512×512的像素矩阵表示的高频系数构成，高频系数层只能体现图像很少的细节信息，包含的能量最少。
去除高光谱图像脉冲噪声的模型及算法孔祥阳;孙涛;李欣星;王梦莹【摘要】In the process of acquisition and transmission of hyperspectral image,the influence of impulse noise in image data was relatively large,especially when the noise level was high.In order to effectively remove the impulse noise in hyperspectral image,a new method based on total variation is proposed to remove the impulse noise from the image.The algorithm considers the hyperspectral image of low rank characteristics and spatial spectral correlation,it effectively removes the noise through the split Bregman iteration method,and preserves the original structure informations of the image better.%在高光谱图像的获取和传输过程中,脉冲噪声对图像数据的影响比较大,尤其是当噪声浓度比较高时.为了有效地去除高光谱图像中的脉冲噪声,结合图像的特征和噪声特性,提出一种基于全变分的噪声去除算法.该算法考虑了高光谱图像的低秩特性和空间-光谱相关性,通过分裂bregman迭代的方法有效地去除了噪声,同时较好地保留图像的原有的结构信息.【期刊名称】《德州学院学报》【年(卷),期】2018(034)006【总页数】6页(P40-45)【关键词】脉冲噪声;核范数;全变分;分裂bregman【作者】孔祥阳;孙涛;李欣星;王梦莹【作者单位】四川工程职业技术学院, 四川德阳 618000;西北工业大学自动化学院, 陕西西安 710072;四川工程职业技术学院, 四川德阳 618000;四川工程职业技术学院, 四川德阳 618000;四川工程职业技术学院, 四川德阳 618000【正文语种】中文【中图分类】TP3911 引言从上世纪70年代初开始，由成像技术和光谱技术相结合而产生的高光谱遥感技术逐渐发展起来.该技术不仅能够获取目标的空间特征图像,而且能够对每个空间像元经过色散形成几十乃至几百个窄波段进行连续的光谱覆盖,从而可以获取目标的光谱特征.由于高光谱图像所包含的丰富的空间、辐射和光谱三重信息，使得其在农业[1,2]、湿地研究[3]等方面的发挥着越来越重要的作用.随着传感技术的进步，传感器的性能得到极大的提高，从而使获得的高光谱图像更加清晰.然而，尽管如此，在高光谱图像的获取、传输和存储过程中，仍然会受到不同程度的脉冲噪声污染.根据脉冲噪声的特性，即使其浓度较低，往往也会使所获得的图像信息受到极大地损坏.而受损的图像在进一步的应用上往往会产生较大的影响.所以，在保留图像原有基本信息的同时能够有效地去除高光谱图像中的脉冲噪声变得非常必要，并且已经成为一个热门的研究领域[4].在脉冲噪声的去除算法中，当噪声浓度较低时，标准中值滤波算法由于其良好的滤波效果和较快的运算速度而成为一种常用的算法[5].然而，当噪声浓度较高时，该算法通常会使图像中很多原始信息遭到破环，从而造成图像细节模糊. 为此，许多学者对该算法进行了不同的改进.这些改进算法有：加权中值滤波算法[6,7]，中心像素加权中值滤波算法[8-10]，递归中值滤波算法[11,12]，自适应中值滤波算法[14]，改进型中值滤波器[14]，以及自适应窗口中值滤波算法[13].虽然这些算法的滤波效果较标准中值滤波算法有了较大的改善，但在去除高浓度噪声的效果方面仍需要进一步改进.为此，有学者又提出了非局部中均值滤波方法[17,18].但是，这些方法对先验信息的依赖性较强，参数较多，算法的复杂度较高.上述算法大都是基于自然图像提出的，针对高光谱图像的脉冲噪声的去除的研究较少.2 问题描述2.1 脉冲噪声脉冲噪声通常是在传感器、解码器处理过程中产生的随机值噪声，这些随机值要么很小(几乎为黑色)，要么很大(几乎为白色).含有脉冲噪声的图像的某一点处的灰度值是无噪图像的灰度值与脉冲噪声灰度值之和，因此，与周围相邻像素点相比，其在灰度特征上有较明显的区别.脉冲噪声的概率密度函数为其中，a<b，灰度值a在图像中显示为一个暗点，b显示为一个亮点.如果pa=0或pb=0，那么脉冲噪声为单极脉冲噪声.如果pa≠0，pb≠0且pa≈pb，那么脉冲噪声为双极脉冲噪声也称为椒盐噪声.一般情况下所指的脉冲噪声即是椒盐噪声.2.2 全变分(TV)模型近年来，由于全变分(TV)去噪模型能够较好地保持边缘信息，所以得到越来越多的关注.文献[19]中提出了图像去噪的全变分正则化方法为(1)TV(x)=‖Dh*x‖1+‖Dv*x‖1(2)其中，TV(x)表示x的全变分，‖·‖1表示向量的L1范数，Dh和Dv分别表示水平和垂直变分算子.3 模型的提出与求解3.1 高光谱图像获取模型假设无噪的高光谱数据立方体为X∈Rh×w×b，其中h,w,b分别表示其高度、宽度和波段数.通常在处理过程中把X的每个波段的图像按列级联为一个向量，由此X可表示为X：=X=[x1,x2,…,xb]，其中xi∈Rhw×1(i=1,2,…,b).高光谱数据的获得过程可表示为Y=X+S+T(3)其中Y是观测到的含噪HSI，X是无噪的HSI，S是脉冲噪声，T是其它稀疏噪声，且Y,X,S,T∈Rh×w×b.3.2 TV基HSI去噪模型根据脉冲噪声的特性，其去除问题可看作L1范数最小化稀疏恢复问题，结合(1)、(2)、(3)可得HSI去噪模型为(4)文献[20]认为无噪高光谱图像应该是低秩的，由此上述模型可以修正为(5)其中rank(·)表示矩阵的秩.而一个矩阵的秩可看做是其奇异值的L0范数，而L0范数是非凸的，所以上目标函数(5)的解是不唯一的.为此，这里将秩算子松弛为矩阵的核范数，从而目标函数(5)可改写为(6)3.3 模型求解对X和T来说，模型(6)是一个高维非可微优化问题.既然X是不可分的，那么可以将(6)写成有约束优化问题(7)通过引入二次惩罚项，可以将上述约束优化问题写成无约束优化问题(8)问题(8)的解法有很多，这里选用分裂bregman方法[21],通过引入bregman变量B1,B2,B3,B4,B5得(9)问题(9)可以分成下列5个子问题：(10)(11)(12)(13)(14)(15)其中上述前4个子问题都有共同的形式：(16)因此都可以用软阈值算子[22]进行求解，其解的形式为：子问题(14)可以用奇异值阈值方法进行求解[23].若令A=μ1DhTDh+μ1DvTDv+μ2+μ3则由线性方程组可解得X.4 仿真实验与分析采用峰值信噪比(PSNR)指数[23]和结构相似度(SSIM)指标[25]对去噪效果进行对比，其定义如下：其中PSNR的单位为分贝(dB).两种指标值越高，说明恢复的图像与原图更接近. 在脉冲噪声浓度较高时，传统中值滤波的去噪效果并不理想，而中值滤波是可以迭代使用的[26].因此算法与多次中值滤波进行比较.为了验证算法的有效性，分别在三个数据集上进行实验.它们分别是：Washington DC、Indian Pines和Salinas.三个数据集在不同噪声浓度下的去噪结果分别见表1、表2及表3.三个数据集在噪声浓度为0.05时的去噪结果见图1、图2及图3.表1 WashingtonDC数据集在不同噪声浓度下的去噪结果噪声浓度算法0.050.150.250.35PSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIM含噪图像18.93960.220014.17020.049311.95400.025410.49450.0167多次中值35.99580.821329.18720.783825.20590.753125.26050.7195本文算法40.64810.889239.84830.864838.96970.833938.02430.7965表2 Indian Pines数据集在不同噪声浓度下的去噪结果噪声浓度算法0.050.150.250.35PSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIM含噪图像18.12080.265413.32710.065011.10670.03269.64800.0206多次中值32.12320.703631.13500.625929.91780.566928.65750.5144本文算法39.08280.796037.62930.752836.58670.724735.65560.7209表3 Salinas数据集在不同噪声浓度下的去噪结果噪声浓度算法0.050.150.250.35PSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIM含噪图像18.04250.268513.23450.066311.02480.03359.55770.0212多次中值31.59390.668030.43430.577429.05320.515427.96570.4651本文算法39.48790.815138.01870.761336.72390.719635.37800.6480(a)原图 (b)含噪图像 (c)本文算法结果 (d)多次中值算法结果图1 Washington DC数据集在噪声浓度为0.05时的去噪结果(a)原图 (b)含噪图像 (c)本文算法结果 (d)多次中值算法结果图2 Indian Pines数据集在噪声浓度为0.05时的去噪结果(a)原图 (b)含噪图像 (c)本文算法结果 (d)多次中值算法结果图3 Salinas数据集在噪声浓度为0.05时的去噪结果从上述实验结果可以看出，多次中值滤波比中值滤波的去噪效果要好，尤其是在噪声浓度较大时，一次中值滤波并不能最大可能地消除噪声，但是多次中值滤波去噪后的图像边缘仍然存在大量毛刺，视觉效果较差.而本文的算法在去除噪声的同时能够较好地保留图像细节.5 结论受脉冲噪声污染图像的最大特点就是其只有部分像素受到破坏，而其它像素灰度值并未发生改变，并且受污染像素的灰度与原灰度值无关.因此针对高光谱图像中脉冲噪声的去除问题进行研究，通过对脉冲噪声的特点以及高光谱图像性质的分析，建立了基于全变分的高光谱图像的退化和恢复模型，然后利用分裂bregman方法对模型进行求解.最后在多个数据集上进行仿真实验来验证算法的有效性.从客观评价指标值上可以看出，当噪声浓度不同时，本文算法较多次中值算法在PSNR值上平均提高5-8dB，SSIM值平均提高0.1-0.25.同时，随着噪声浓度的增加，本文算法的PSNR和SSIM值的降低速度较多次中值算法更慢，因此本文算法对噪声浓度变化的鲁棒性更好.从视觉效果对比上可知，利用全变分(TV)滤波器进行去噪时不会使图像模糊或边缘扭曲，能够较好地保持图像的细节和边缘信息. 参考文献:【相关文献】[1]李瑞, 傅隆生. 基于高光谱图像的蓝莓糖度和硬度无损测量[J]. 农业工程学报, 2017, 33(s1):362-366.[2]孙世鹏, 彭俊, 李瑞,等. 基于近红外高光谱图像的冬枣损伤早期检测[J]. 食品科学, 2017,38(2):301-305.[3]孙钦佩, 马毅, 张杰. 滨海湿地稀疏采样重构高光谱图像分类精度评价[J]. 海洋技术学报, 2017,36(2):77-82.[4]Gonzalez RC,Woods R E.Digital image processing[M].NJ:Prentice Hall,2002.[5]YuH,Zhao L,Wang H.An efficient procedure for removing random-valued impulse noisein images[J].IEEE Signal Processing Letters,2008,15(1):922-925.[6]Qiu G.An improved recursive median filtering scheme for image processing[J].IEEE Transactions on Image Processing, 1996,5(4):646-648.[7]McLoughlin M P,Arce G R.Deterministic properties of the 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Noise Reduction by Fuzzy Image Filtering Dimitri Van De Ville,Member,IEEE,Mike Nachtegael,Dietrich Van der Weken,Etienne E.Kerre, Wilfried Philips,Member,IEEE,and Ignace Lemahieu,Senior Member,IEEEAbstract—A new fuzzy filter is presented for the noise reduc-tion of images corrupted with additive noise.The filter consists of two stages.The first stage computes a fuzzy derivative for eight dif-ferent directions.The second stage uses these fuzzy derivatives to perform fuzzy smoothing by weighting the contributions of neigh-boring pixel values.Both stages are based on fuzzy rules which make use of membership functions.The filter can be applied it-eratively to effectively reduce heavy noise.In particular,the shape of the membership functions is adapted according to the remaining noise level after each iteration,making use of the distribution of the homogeneity in the image.A statistical model for the noise distribu-tion can be incorporated to relate the homogeneity to the adapta-tion scheme of the membership functions.Experimental results are obtained to show the feasibility of the proposed approach.These results are also compared to other filters by numerical measures and visual inspection.Index Terms—Additive noise,edge preserving filtering,fuzzy image filtering,noise reduction.I.I NTRODUCTIONT HE application of fuzzy techniques in image processing isa promising research field[1].Fuzzy techniques have al-ready been applied in several domains of image processing(e.g., filtering,interpolation[2],and morphology[3],[4]),and have numerous practical applications(e.g.,in industrial and medical image processing[5],[6]).In this paper,we will focus on fuzzy techniques for image filtering.Already several fuzzy filters for noise reduction have been developed,e.g.,the well-known FIRE-filter from [7]–[9],the weighted fuzzy mean filter from[10]and[11], and the iterative fuzzy control based filter from[12].Most fuzzy techniques in image noise reduction mainly deal with fat-tailed noise like impulse noise.These fuzzy filters are able to outperform rank-order filter schemes(such as the median filter).Nevertheless,most fuzzy techniques are not specif-ically designed for Gaussian(-like)noise or do not produce convincing results when applied to handle this type of noise.Manuscript received November24,2001;revised June27,2002and November13,2002.The work of D.Van De Ville was supported by the Fund for Scientific Research—Flanders(Belgium)through a mandate of Research Assistant.The work of M.Nachtegael and D.Van der Weken was supported by the GOA-project12.0513.98by Ghent University,Belgium.D.Van De Ville was with Ghent University,Belgium.He is currently with the Biomedical Imaging Group,the Swiss Federal Institute of Technology Lausanne (EPFL),CH1015Lausanne,Switzerland.M.Nachtegael,D.Van der Weken,and E.Kerre are with the Fuzziness and Uncertainty Research Modeling Unit,the Department of Applied Mathematics and Computer Science,Ghent University,B9000Ghent,Belgium.W.Philips is with the Department of Telecommunications and Information Processing,Ghent University,B9000Ghent,Belgium.I.Lemahieu is with the Department of Electronics and Information Systems, Ghent University,B9000Ghent,Belgium.Digital Object Identifier10.1109/TFUZZ.2003.814830Therefore,this paper presents a new technique for filtering narrow-tailed and medium narrow-tailed noise by a fuzzy filter.Two important features are presented:first,the filter estimates a“fuzzy derivative”in order to be less sensitive to local variations due to image structures such as edges;second, the membership functions are adapted accordingly to the noise level to perform“fuzzy smoothing.”The construction of the fuzzy filter is explained in Section II. For each pixel that is processed,the first stage computes a fuzzy derivative.Second,a set of16fuzzy rules is fired to determine a correction term.These rules make use of the fuzzy derivative as input.Fuzzy sets are employed to represent thepropertiesandis adapted after each iteration.The adapta-tion scheme is extensively explained in Section III and can be combined with a statistical model for the noise.In Section IV, we present several experimental results.These results are dis-cussed in detail,and are compared to those obtained by other filters.Some final conclusions are drawn in Section V.II.F UZZY F ILTERThe general idea behind the filter is to average a pixel using other pixel values from its neighborhood,but simultaneously to take care of important image structures such as edges.1The main concern of the proposed filter is to distinguish between local variations due to noise and due to image structure.In order to accomplish this,for each pixel we derive a value that expresses the degree in which the derivative in a certain direction is small.Such a value is derived for each direction corresponding to the neighboring pixels of the processed pixel by a fuzzy rule(Section II-A).The further construction of the filter is then based on the ob-servation that a small fuzzy derivative most likely is caused by noise,while a large fuzzy derivative most likely is caused by an edge in the image.Consequently,for each direction we will apply two fuzzy rules that take this observation into account (and thus distinguish between local variations due to noise and due to image structure),and that determine the contribution of the neighboring pixel values.The result of these rules(16in total)is defuzzified and a“correction term”is obtained for the processed pixel value(Section II-B).A.Fuzzy Derivative EstimationEstimating derivatives and filtering can be seen as a chicken-and-egg problem;for filtering we want a good indica-tion of the edges,while to find these edges we need filtering. 1Other fuzzy filters,such as the smoothing fuzzy control based filter[12],also take care of edges,but after instead of simultaneous with the noise filtering.1063-6706/03$17.00©2003IEEE(a)(b)Fig.1.(a)Neighborhood of a central pixel (x;y ).(b)Pixel values indicated in gray are used to compute the “fuzzy derivative”of the central pixel (x;y )for the NW -direction.TABLE IP IXELS I NVOLVED TO C ALCULATE THE F UZZYD ERIV ATIVES INE ACH DIRECTIONIn our approach,we start by looking for the edges.We try to provide a robust estimate by applying fuzzy rules.Considertheneighborhood of apixel in thedirection)isdefinedasthedifference between the pixel at.This derivative value is denotedbyinthewill be large,but also derivativevalues of neighboring pixels perpendicular to the edge’s direc-tion can expected to be large.For example,inthe,.To compute the value that expresses the degree to which the fuzzy derivative in a certain direction is small,we will makeV AN DE VILLE et al.:NOISE REDUCTION BY FUZZY IMAGE FILTERING431(a)(b)Fig.4.Original test images.(a)“Cameraman.”(b)“Boats.”use of the fuzzysetis the following [see Fig.2(a)]:,,totheFig.5.Histogram of the homogeneity of 929-blocks for the “cameraman”test image.The 20%percentileof the most homogeneous blocks shifts to the left as the image is more corrupted,i.e., equals 0.96,0.90,0.82,and 0.66for these cases.setadaptive.The proper choiceof,we fire the following tworules,and compute theirtruthnessand:,which can be added to the pixel value oflocation,(so432IEEE TRANSACTIONS ON FUZZY SYSTEMS,VOL.11,NO.4,AUGUST2003(a)(b)Fig.6.MSE (mean squared error)for (a)“cameraman”and (b)“boats.”( =5).for all directions)are aggregated by computing and rescaling the mean truthness asfollows:(4)whererepresents the number of gray levels.So,each directions contributes to the correctiontermof the image canbe considered as homogeneous and as such can be used to esti-mate the noise density.We start by dividing the image insmall,we compute a rough measurefor the homogeneity of this block by considering the maximum and minimum pixelvalueof themost homogeneous blocks is determined.We assume this per-centile is a measure for the homogeneity of “typical”noise in the ing a statistical model for the noise distribution,we will show that there is a linear relationship between the ho-mogeneity and the standard deviation.Assume,independently and identically distributed,with a probability density func-tion(PDF)samples are scaledthe same way.This establishes a linear relationship between the homogeneity and the standard deviation.This can also be derived more formally.We assume the expectationvalue to be zero,and thevariance,we can obtain the following generalresult:(6)samplesasV AN DE VILLE et al.:NOISE REDUCTION BY FUZZY IMAGE FILTERING433 for which we can derive the CDFs asand,i.e.,value of the)homogeneityTherefore,there is a linear relationship between the(expectationsamples and the standarddeviation(8)where.The value of the factor)are gen-erated.Each patch consists of noise with the presumed distri-bution.The effective noise level and the homogeneity of eachpatch are measured.The mean value and standard deviation arecalculated for the whole test set.This experiment is done forseveral noise levels,resulting in the relationship between thehomogeneity and the noise level.Fig.3shows the result for thecase ofof theblocks were originally homogeneous(before the noise degra-dation).The histogram of the homogeneity of the blocks in theimage is computed,and a percentileof this percentile is related toour estimate for the noise variance,which determines the shape of the membership func-tion434IEEE TRANSACTIONS ON FUZZY SYSTEMS,VOL.11,NO.4,AUGUST2003(a)(b)(c)(d)Fig.10.Detail images of the results of Fig.9.Fig.5shows the normalized histogram of the homogeneity of “cameraman,”for the original image,but also for the imagecorrupted with different noise levels,i.e.,,,namely .To evaluate theresults,we computed the mean squared error (MSE)between the original image and the filtered image.Figs.6and 7show a plot of the MSE as function of thenumber of iterations for added noisewithand gives better results.Fig.8shows theparameteras a stop criterion as it gets sufficiently low.Another possible stop criterion could be when thechangecould also be determined using theestimate.We also compared our fuzzy filter with several other filter techniques:the mean filter,the adaptive Wiener filter [14],fuzzy median (FM)[15],the adaptive weighted fuzzy mean (AWFM1and AWFM2)[10],[11],the iterative fuzzy filter (IFC),modi-fied iterative fuzzy filter (MIFC),and extended iterative fuzzy filter (EIFC)[12].Table II summarizes the results we obtained.Quite different results are obtained between “cameraman”and “boats.”For “cameraman,”the proposed filter performs veryV AN DE VILLE et al.:NOISE REDUCTION BY FUZZY IMAGE FILTERING 435TABLE IIR ESULTS OF THE N EW F UZZY F ILTER FOR THE T EST I MAGES “C AMERAMAN ”AND “B OATS”(a)(b)(c)(d)Fig.13.(a)Original satellite image of a part of Greece.(b)Result after adaptive Wiener filtering (best result with 525support).(c)Result after fuzzy filtering ( =1,5iterations).(d)Result after fuzzy filtering ( =3,5iterations).well.Only the fuzzy median (FM)gives a better MSEfor .A closer inspection of Fig.9shows that the proposed filter better preserves details such as the grass (right side,just below the building)and the background (left side,small buildings).Also the face is slightly sharper.The detail images in Fig.10con-firm these results.Note that the grass is better preserved by the proposed filter than using the fuzzy mean.The “boats”imageprovides a different result.For low noise levels(),the pro-posed filter still performs best,but for higher noise levels,the AWFM2filter gives the best results.Fig.11shows the filtered images.The detail images of Fig.12reveal that the AWFM2filter is able to preserve the very small details (such as the narrow ropes).On the other hand,the proposed filter gives a more “nat-ural”image without the “patchy look”of the adaptive Wiener filter.Finally,we like to show a practical application of the fuzzy filter.In particular,this image restoration scheme could be used to enhance satellite images.Of course,since the original image is already corrupted by noise,it is not possible to obtain a numerical measure which indicates how “good”the image is.Fig.13shows the original image and the results after fuzzy fil-tering with different parameters.Depending on the application (e.g.,visual inspection,segmentation),one could prefer lighter or heavier filtering (bychoosing436IEEE TRANSACTIONS ON FUZZY SYSTEMS,VOL.11,NO.4,AUGUST 2003[12] F.Farbiz and M. B.Menhaj,Fuzzy Techniques in Image Pro-cessing .New York:Springer-Verlag,2000,vol.52,Studies in Fuzziness and Soft Computing,ch.A fuzzy logic control based approach for image filtering,pp.194–221.[13]H.Haussecker and H.Tizhoosh,Handbook of Computer Vision and Ap-plications .New York:Academic,1999,vol.2,ch.Fuzzy Image Pro-cessing,pp.708–753.[14]J.S.Lim,Two-Dimensional Signal and Image Processing .UpperSaddle River,NJ:Prentice-Hall,1990,ch.Image Restoration,pp.524–588.[15]K.Arakawa,“Median filter based on fuzzy rules and its application toimage restoration,”Fuzzy Sets Syst.,pp.3–13,1996.Dimitri Van De Ville (M’02)was born in Den-dermonde,Belgium,in 1975.He received the Engineering and Ph.D.degrees in computer science from Ghent University,Ghent,Belgium,in 1998and 2002,respectively.He worked in the Medical Image and Signal Processing Group (MEDISIP)and the MultiMedia Lab,both part of Department of Electronics and Information Systems (ELIS),Ghent University.His main research interests are in signal and image pro-cessing,in particular,interpolation and resamplingrelated topics.Currently,he is working as a Senior Researcher at the Swiss Federal Institute of Technology Lausanne (EPFL)in the Biomedical Imaging Group (BIG),Lausanne,Switzerland.Mike Nachtegael was born in Sint-Niklaas,Belgium,in 1976.He received the M.Sc.degree in mathematics from Ghent University,Ghent,Belgium,in 1998.In the same year,he joined the Fuzziness and Uncertainty Modeling Research Unit of Prof.E.Kerre,where he received the Ph.D.degree on fuzzy techniques in image processing in 2002.Currently,he is active as a Postdoctoral Re-searcher in the Department of Applied Mathematics and Computer Science,Ghent University.After secondary school,he published two referencebooks on mathematics (1995)and on chemistry and physics (1996).He has authored or coauthored more than 20papers,he has coedited two books on fuzzy techniques in image processing,he has coorganized three sessions at international conferences and he was comanager of the International FLINS 2002Conference.Dietrich Van der Weken was born in Beveren,Belgium,in 1978.He received the M.Sc.degree in mathematics from Ghent University,Ghent,Belgium,in 2000.In September 2000,he joined the Department of Applied Mathematics and Computer Science,Ghent University,where he is a member of the Fuzziness and Uncertainty Modeling Research Unit working toward the Ph.D.degree with a thesis on fuzzy techniques in image processing under the promotorship of Prof.E.Kerre.One of his main research topics is the measure-ments of similarity between images.He has authored or coauthored 14papers,he has co-edited one book on fuzzy techniques in image processing,and orga-nized one session at an internationalconference.Etienne E.Kerre was born in Zele,Belgium,in 1945.He received the M.Sc.and Ph.D.degrees in mathematics from Ghent University,Ghent,Belgium,in 1967and 1970,respectively.Since 1984,he has been a Lector and,since 1991,a Full Professor at Ghent University.In 1976,he founded the Fuzziness and Uncertainty Research Modeling Unit (FUM)and,since then,his research has been focused on the modeling of fuzziness and uncertainty,and has resulted in a great number of contributions in fuzzy set theory and its variousgeneralizations,and in evidence theory.The theories of fuzzy relational calculus and fuzzy mathematical structures owe a very great deal to him.Over the years,he has also been a promoter of 16Ph.D.degrees on fuzzy set theory.His current research interests include fuzzy and intuitionistic fuzzy relations,fuzzy topology,and fuzzy image processing.He has authored or coauthored eleven books and more than 100papers of his have appeared in international refereed journals.Dr.Kerre is a referee for more than 30international scientific journals,and is also Member of the Editorial Board of international journals and conferences on fuzzy set theory.He was an Honorary Chairman at various internationalconferences.Wilfried Philips (S’90–M’93)was born in Aalst,Belgium,in 1966.He received the Diploma degree in electrical engineering and the Ph.D.degree in applied sciences from Ghent University,Ghent,Belgium,in 1989and 1993,respectively.From October 1989to October 1998,he was with the Department of Electronics and Information Systems,the University of Ghent,for the Flemish Fund for Scientific Research (FWO-Vlaanderen),first as a Research Assistant and later as a Postdoc-toral Research Fellow.Since November 1997,he hasbeen a Lecturer with the Department of Telecommunications and Information Processing,Ghent University.His main research interests are image and video restoration,image analysis,lossless and lossy data compression of images and video,and processing of multimediadata.Ignace Lemahieu (M’92–SM’00)was born in Bel-gium in 1961.He graduated in physics and received the Ph.D.degree in physics from Ghent University,Ghent,Belgium,in 1983and 1988,respectively.He joined the Department of Electronics and In-formation Systems (ELIS),Ghent University in 1989as a Research Associate with the Fund for Scientific Research (F.W.O.-Flanders),Belgium.He is now a Professor of Medical Image and Signal Processing and Head of the MEDISIP Research Group.His re-search interests comprise all aspects of image pro-cessing and biomedical signal processing,including image reconstruction from projections,pattern recognition,image fusion,and compression.He is the coau-thor of more than 200papers.Dr.Lemahieu is a Member of SPIE,the European Society for Engineering and Medicine (ESEM),and the European Association of Nuclear Medicine (EANM).。
