基于MP的信号稀疏分解算法研究

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1、西南交通大学硕士学位论文基于MP的信号稀疏分解算法研究姓名：邵君申请学位级别：硕士专业：信号与信息处理指导教师：尹忠科20061201西南交通大学硕士研究生学位论文第Ⅱ页OMP原理的分析，把在正交化后原子上的投影问题转化为在原来原子上的投影问题，并采用归纳法推导出一种投影系数的递归表达式，避免了传统OMP算法计算过程中的矩阵求逆运算。利用新的系数表达式在得到和原有OMP算法相同的稀疏分解效果的同时，更加有利于信号的压缩和识别等后继处理。针对以上每一种方法，本文都给出了实验结果，证明本文提出的基于MP的信号稀疏分解算法能够取得较好的效果。关键词：信号处理；稀疏分解；Matc

2、hingPursuit,FFT：集合划分西南交通大学硕士研究生学位论文第ⅡI页AbstractSignalsparsedecompositionbasedonMatchingPursuit(MP)hasbeenappliedtomanyareassuchasdatacompression,signalfeatureextraction,time-frequencyanalysisandere．ButitisaNPdifficultproblem．Thelargecomputationalcostisthebottleneckofsparsedecomposition．To

3、realizesparsedecompositionlastly,researchersinandaboardhaveputforwardmanyfastalgorithmssuchasgeneticalgorithmbasedMP、antcolonyalgorithmbasedMPandetc．．However,thesenewalgorithmsarebased011computationalintelligence,insomecasestheyarenotinapplicablebecauseoftherandomnessofthecomputationalint

4、elligence，Inthisthesis，thefastalgorithmsarestudiedtoovercomecomputationalrandomness．．Inthisthesis，thesparsedecompositionisintroducedfirstly,thecharacteristicandkeyproblemsofsparsedecompositionarementioned．AfterwardstheMPisintroduced．Comparedtoothersparsedecompositionalgorithm,MPiseasytoun

5、derstandandtorealize，butstillhastheproblemofhugememory,hugecomputationalcost．Thisthesisdealswiththesetwoaspects．Aimingattheproblemofthelargeover-completedictionarystorage，anewmethodisproposedbasedonsignalsetpartitioningmethod．Withtheequalrelationship，theover-completedictionarycarbepartiti

6、onedintosub·dictionaries，theintersectionsofwhicharenull．Eachsub-dictionaryCanthenberepresentedbyonlyoneselectedcorrespondingatom．Bypartitioningtheover-completedictionary,thecomputationalspacecomplexityinsignalsparsedecompositionCallbedegradedalot，whilethedecompositionresultsarekeptunchang

7、ed．Totheproblemofgreatcomputationload，auewsparsedecompositionalgorithmthatutilizesradix-2FFTispresentedbasedonanalysisofsnllcnlrepropertyoftheover-completeatomdictionaryusedinsignalsparsedecomposition．Bymakinguseofthestructureproperty,thisnewalgorithmbalancesverywel