基于MATLAB的小波变换在信号分析中应用的实现

设计（论文）专用纸基于MATLAB的小波变换在信号分析中应用的实现院系：应用技术学院专业：电子信息工程姓名：李成云指导教师单位：应用技术学院指导教师姓名：王庆平指导教师职称：讲师二零一一年六月设计（论文）专用纸TheapplicationofwavelettransformbasedonMTLABinsignalanalysisFaculty：ApplicationandTechnologyInstituteProfession：ElectronicinformationengeeringName：LiChengyunTutor’sUnit：ApplicationandTechnologyInstituteTutor：WangQingpingTutor’sTitle：LecturerJune2011设计（论文）专用纸第I页目录摘要..................................................................1ABSTRACT..............................................................2前言..................................................................3第1章绪论..........................................................41.1本文的研究背景意义..............................................41.2国内外研究现状..................................................51.3本文的研究内容..................................................7第2章MATLAB简介...................................................82.1MATLAB的概况...................................................82.2MATLAB6.1的功能................................................82.3MATLAB的主要组成部分...........................................92.4MATLAB的语言特点..............................................10第3章基本理论......................................................123.1从傅里叶变换到小波变换.........................................123.1.1傅里叶变换..................................................123.1.2短时傅里叶变换..............................................133.1.3小波变换....................................................143.2连续小波变换...................................................153.3离散小波变换...................................................173.4小波包分析.....................................................183.5多分辨率分析与MALLAT算法.......................................193.5.1多分辨率分析................................................193.5.2Mallat算法..................................................193.6本章小结.......................................................20第4章小波阈值法图像去噪............................................214.1图像去噪.......................................................214.1.1邻域平均法..................................................224.1.2中值滤波法..................................................244.2小波阈值去噪...................................................274.2.1阈值去噪原理................................................284.2.2选取阈值函数................................................284.2.3几种阈值选取方法............................................29设计（论文）专用纸第II页4.3小波阈值仿真...................................................31第5章小波变换在图像边缘检测中的应用................................335.1图像边缘检测概述...............................................335.2常见的边缘检测算法。...........................................345.3小波边缘检测算法...............................................395.4小波缘检测仿真.................................................39全文总结.............................................................42谢辞.................................................................43参考文献.............................................................44附录.................................................................46英文资料...........................................................46中文翻译...........................................................60设计（论文）专用纸第1页摘要小波分析理论作为新的时频分析工具，在信号分析和处理中得到了很好的应用。平面图像可以看成是二维信号，因此，小波分析很自然地应用到了图像处理领域。图像去噪和边缘检测是图像预处理中应用非常广泛的技术，其作用是为了提高信噪比，突出图像的期望特征，以便对其进行更高层次的处理。小波变换由于其自身的优良特性而在图像处理中得到了越来越多的应用。本文从基本理论出发，首先对小波变换进行了详尽而深刻的阐述。循序渐进地介绍了从概念到小波分析等一系列相关内容，最终引出小波分析中非常重要的Mallat算法。对小波变换在图像去噪和边缘检测领域的应用本文作了重点研究。为用作对比，简要介绍了几种传统的图像去噪算法和边缘检测算法，重点研究和详细阐述了运用小波变换进行图像去噪和边缘检测算法的原理和具体实现步骤,将小波算法与传统的图像去噪算法和边缘检测算法作MATLAB仿真对比以得出结论。关键词：图像去噪；图像边缘检测；小波变换；MATLAB设计（论文）专用纸第2页ABSTRACTWaveletanalysistheory,asanewtime—frequencyanalysistool，hasbeenwellappliedintheareaofsignalanalysisandprocessing．Animageisactuallyatwo-dimensionalsignal．Soitisnaturaltoapplywaveletanalysistotheareaofimageprocessing．Imagede-noisingandedgedetectionaretwowidelyusedtechnologiesinimagepre—processing．ByenhancingSNRandhighlightingexpectedfeaturesofimage，itwillbemoreconvenientforfurtherstepofprocessing．Wavelettransformismoreandmorefrequentlyappliedtoimageprocessingaccordingtoitsownadvantages．First，beginningwithbasictheories，wavelettransformisthoroughlyanddeeplyintroducedinthisarticle．Aseriesofrelatedcontentsfromdefinitiontowaveletanalysisaregraduallyelaboratedstepbystep．Mallatalgorithmwhichisofgreatimportanceinwaveletanalysisisintroducedintheend．Second，researchesonapplicationofwavelettransformtotheareasofimagede—noisingandedgedetectionarethemajorpartofthisarticle．Forcomparison，severaltraditionalimagede—noisingmethodsandedgedetectionmethodsarebrieflyintroduced．Thetheoriesandstepsofcompletionofimagede—noisingandedgedetectionalgorithmstowhichwavelettransformisappliedareelaborated．Imagede—noisingandedgedetectionalgorithmsbetweenwavelettransformandtraditionalmethodsaresimulatedandcomparedtodrawaconclusion．Keywords：imagede-noising；imageedgedetection；wavelettransform;MATLAB设计（论文）专用纸第3页前言传统的信号理论，是建立在Fourier分析基础上的，而Fourier变换作为一种全局性的变化，其有一定的局限性。在实际应用中人们开始对Fourier变换进行各种改进，小波分析由此产生了。小波分析是一种新兴的数学分支，它是泛函数、Fourier分析、调和分析、数值分析的