基于矩陣奇異值分解的圖像壓縮方法研究.pdf

1、成都理工大學(xué)碩士學(xué)位論文基于矩陣奇異值分解的圖像壓縮方法研究姓名：廖文彬申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：王玉蘭20070501TheResearchofImageCompressiontechniquebasedonSVDIntroductionoftheauthor：liaowenbin，wasbornonjuly7，1981，wasawardedtheScienceMaster’sDegreeofappliedmathin

2、ChengduUniversityofTechnologyonJulyof2007，undertheguidanceofProfWangYuLanABSTRACTThesingularvaluedecomposition(SVD)hasenjoyedalonghistoryItwasintroducedinthe1870sbyBeltramiandJordanforitsownintrinsicinterest，ithasbecomea

3、ninvaluabletoolinappliedmathematicsandmathematicalmodelingSingularvalueanalysishasbeenappliedinawidevarietyofdisciplines，recently，itisbeingusedindataminingapplicationsandbysearchenginestankdocumentsinverylargedatabases，i

4、ncludingtheWebRecently，thedimensionsofmatriceswhichareusedinmanymathematicalmodelsarebecomingsolargethatclassicalalgorithmsforcomputingtheSVDcannotbeusedIt’sbecomeaproblemwhenuseSVDmethodtocompressimageContraposingthebig

5、sizeofmatrix，thispaperpresentanewmethodtodeterminethesingularvaluesofmatriceswhicharesoenormousthatuseofstandardalgorithmsInourmethod，rowsfromthematrixarerandomlyselected，andasmallermatrixisconstructedfromtheselectedrows

6、Next，wecomputethesingularvaluesofthesmallermatrixThisprocessofrandomsamplingandcomputingsingularvaluesisrepeatedasmanytimesasnecessary(usuallyafewhundredtimes)Ourmethodisatypeofrandomizedalgorithm，ie，algorithinswhichsolv

7、eproblemsusingrandomlyselectedsamplesofdatawhicharetoolargetobeprocessedbyconventionalmeansThesealgorithmsoutputcorrect(ornearlycorrect)answersmostofthetimeaslongastheinputhascertaindesirablepropertiesWenote，however，that