基于双正交基字典学习的图像去噪方法

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1、基于双正交基字典学习的图像去噪方法摘要:为了提高图像去除白高斯噪声的性能，利用超完备字典作为图像的稀疏表示。超完备字典的冗余性可以有效地表示图像的各种几何奇异特征。在贝叶斯框架下，以图像块的稀疏表示定义了全局图像先验概率模型，给出了最大后验概率模型下的优化图像去噪算法。超完备字典使用两个不同的正交基构成，给出了基于奇异值分解（svd）的优化字典计算方法。该方法充分利用正交基的特点，采用svd方法进行高效的字典学习。基于双正交基字典的去噪算法提高了图像去噪性能，实验结果证实了所提方法的有效性。关键词:图像去噪；字典学习；稀疏表示；奇异值分解；贝叶斯估计imageden

2、oisingmethodbasedondictionarylearningwithunionoftwoorthonormalbasesxiekai*,zhangfenschoolofinformationandmechanicalelectronicengineering,beijinginstituteofgraphiccommunication,beijing102600,chinaabstract:overcompletedictionarywasusedtorepresentanimagesparselyfortheimprovementofimagede

3、noisingperformance.thesparserepresentationmayrepresentefficientlythesingulargeometryoftheimageswiththeredundancyofover-completedictionary.globalimagepriormodelbasedonthesparserepresentationofimagepatcheswaspresentedinbayesianframework.thenmaximumaposterioriprobabilityestimatorfordenoisin

4、gimagewasconstructed.thedictionaryconsistedofthetwoorthonormalbases.amethodbasedonsingularvaluedecompositionwasusedtodictionarylearning.theorthonormalpropertywasmadeuseoftoupdatetheonechosenbasiseffectively.themethodcanimprovetheperformanceofimagedenoising.experimentsresultsshowthevalidi

5、tyofthemethod.overcompletedictionarywasusedtorepresentanimagesparselyinordertoimproveimagedenoisingperformance.thesparserepresentationmayrepresentefficientlythesingulargeometryoftheimageswiththeredundancyofover.completedictionary.globalimagepriormodelbasedonthesparserepresentationofimage

6、patcheswaspresentedinbayesianframework.thenmaximumaposterioriprobabilityestimatorfordenoisingimagewasconstructed.thedictionarywascomposedoftwoorthonormalbases.amethodbasedonsingularvaluedecompositionwasusedfordictionarylearning.theorthonormalpropertywasusedtoupdatetheonechosenbasiseffect

7、ively.themethodcanimprovetheperformanceofimagedenoising.theexperimentalresultsverifythevalidityofthemethod.keywords:imagedenoising;dictionarylearning;sparserepresentation；singularvaluedecomposition(svd)；bayesianestimation图像去噪的主要目标就是把被污染噪声的图像恢复为原始图像。小波变换用于图像去噪是近十年来的主要研究方