二进小波在图像处理中应用

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1、MasterthesisSubmittedtoShanghaiJiaoTongUniversityTheApplicationsOfDyadicWaveletInTheImageProcessingAuthor:ChengyongHuangAdvisor:Prof.BaoruiSongSpecialty:ComputationalMathematicsDepartmentofMathematicsShanghaiJiaoTongUniversityNovember,2009上海交通大学硕士学位论文二进小波在图像处理中的应用摘要本论文主要

2、介绍了一种基于B样条的二进小波变换算法(µaTrous)。aTrousµ算法与Mallat算法有相似之处，但区别也明显，aTrousµ算法中不需要抽取偶数样本，重构算法也不需要插零。而且aTrousµ算法中分解和重构滤波器会随着尺度的变化做膨胀和压缩。这些特点使得二进小波变换不存在类似于Mallat算法变换后信号或图像压缩现象，所以aTrousµ算法可以用于信号或图像边缘检测。通过在原有的小波尺度积边缘检测算法基础上，对相邻的尺度积做进一步的乘积运算，获得了比原有尺度积方案更好的边缘检测效果。根据信号和噪声在二进小波变换中不同尺度的传播

3、特性，在aTrousµ算法基础上介绍了基于尺度相关性的SSNF算法，并提出了相应的改进SSNF算法用于信号和图像去噪。通过比较改进SSNF算法与其他算法去噪的对比，可以证明改进后SSNF算法能比其他算法包括SSNF算法更有效实现去噪。关键词:二进小波多尺度边缘检测aTrousµ算法SSNF算法IABSTRACTTHEAPPLICATIONSOFDYADICWAVELETINTHEIMAGEPROCESSINGABSTRACTThispaperproposesthedyadicdiscretetimewavelettransformµaT

4、rousalgo-rithmbasedBSplineFunction.althoughTheµaTrousalgorithmissimilarwiththeMallatalgorithm,theyalsohavedi®erentpart.UnlikeMallat,TheµaTrousalgorithmdoesn'textractevensamplewhiledecomposing,anditwouldn'tinsertzerosamplewhilereconstruct.Thedecomposingandreconstruct¯lter

5、coe±cientchangeswillbedonewiththescaleexpansionandcompression.Thedyadicwavelettransformdoesn'toccurcompressionphenomenonwiththehelpoftheseabovefea-tures,whenitprocesssignalorimage.ThatiswhyweoftenchoosetheµaTrousalgorithmtodetecttheedgeoftheimage.Thedyadicwavelettransfor

6、msattwoadjacentscalesaremultipliedasaproductfunctiontomagnifytheedgestructuresandsuppressthenoise.Baseonthemultipliedscalesalgorithm,thispaperin-troduceaideathatthemultipliedscaleattwoadjacentscalesaremultipliedasaproductfunctiontomagnifytheedgestructuresandsuppresstheno

7、ise.Itisshownthatthescalemultiplicationattwiceachievesbetterresultsthanscalesmultiplica-tioninonce,especiallyonthelocalizationperformance.Accordingthesignalandnoiseinthetwodi®erentscalewavelettransformhavedi®erenttransformationfea-ture,thispapergivesabriefintroductionofS

8、SNFalgorithm.AnimprovedSSNFalgorithmimplementintheimagedenosing.Experimentsonnaturalimagesarecomparedwi