参数自适应调整的稀疏贝叶斯重构算法.pdf

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1、第36卷第6期电子与信息学报Vo1．36NO．62014年6月JournalofElectronics＆InformationTechnologyJun．2014参数自适应调整的稀疏贝叶斯重构算法夏建明杨俊安陈功(电子工程学院合肥230037)(安徽省电子制约技术重点实验室合肥230037)摘要：稀疏表示模型中的正则化参数由未知的噪声和稀疏度共同决定，该参数的设置直接影响稀疏重构性能的好坏。然而目前稀疏表示问题优化求解算法或依靠主观、或依靠相关先验信息、或经过实验设置该参数，均无法自适应地设置调整该参数。

2、针对这一问题，该文提出一种无需先验信息的参数自动调整的稀疏贝叶斯学习算法。首先对模型中各参数进行概率建模，然后在贝叶斯学习的框架下将参数设置及稀疏求解问题转化为一系列混合L1范数与加权L2范数之和的凸优化问题，最终通过迭代优化得到参数设置和问题求解。由理论推导和仿真实验可知，已知理想参数时，该算法与其它非自动设置参数的迭代重加权算法性能相当，甚至更优；在理想参数未知时，该算法的重构性能要明显优于其它算法。关键词：压缩感知；稀疏重构：迭代重加权；稀疏贝叶斯学习；参数自动调整中图分类号：TN911．72文献标

3、识码：A文章编号：1009—5896(2014)06—1355—07DOI：10．3724／SP．J．1146．2013．00629BayesianSparseReconstructionwithAdaptiveParametersAdjustmentXiaJian-mingYangJun—anChenGong(ElectronicEngineeringInstitute，Hefei230037，China)(KeyLaboratoryElectronicRestriction，AnhuiProvince

4、，Hefei230037，China)Abstract：Theregularizationparameterofsparserepresentationmodelisdeterminedbytheunknownnoiseandsparsity．Meanwhile，itcandirectlyaffecttheperformancesofsparsityreconstruction．However，theoptimizationalgorithmofsparsityrepresentationissue，wh

5、ichissolvedwithparametersettingbyexpertreasoning，prioriknowledgeorexperiments，cannotsettheparameteradaptively．Inordertosolvetheissue，thesparsityBayesianlearningalgorithmwhichcansettheparameteradaptivelywithoutprioriknowledgeisproposed．Firstly，theparameter

6、sinthemodelisconstructedwiththeprobability．Secondly，onthebasisoftheframeworkofBayesianlearning，theissueofparametersettingandsparsityresolvingistransformedtotheconvexoptimizationissuewhichistheadditionofaseriesofmixtureL1normalandtheweightedL2norma1．Finall

7、y，theparametersettingandsparsityresolvingareachievedbytheiterativeoptimization．Theoreticalanalysisandsimulationsshowthattheproposedalgorithmiscompetitiveandevenbettercomparedwithotherparameternon—adjustedautomaticallyiterativereweightedalgorithmswhenideal

8、parameterisknown，andthereconstructionperformanceoftheproposedalgorithmissignificantlybetterthantheotheralgorithmswhenchoosingthenon—idealparameters．Keywords：Compressivesensing；Sparsesignalreconstruction：Iterativerew