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1、ABSTRACTTheconceptofframewasintroducedbyDuffinandSchaefferwhentheystudiednonharmonicFourierseriesin1952.AdiscreteframeinaseparableHilbertspaceisalmostasgoodasanorthonormalbasisforexpandingarbitraryelements.Framethe-oryasanewresearchdirectiondevelopedafterth
2、ewavelettheory,it’sthecombinationoffunctionalanalysis,operatortheory,thenolinearapproximationandtheinformationtheory.Frameshavestabledecompositionofasignalforanalysisortransmission,whilealsopromtingsparseexpansionsinsignalprocessing.However,whenthesignal
3、dimen-sionislarge,thecomputationoftheframemesaurementsofasignaltypicallyrequiresalargenumberofadditionsandmultiplications,andthismakesaframedecompositiondifficultinapplicationswithlimitedcomputingbudget.Inordertosolvetheproblem,weintroducesparsityforsuchfr
4、amesasanewfeatureinfinite-dimensionalHilbertspacesinthisthesis.Asparseframeisaframewhoseeveryelementhasasparserepresentationinanorthonormalbasis,therebyenablinglowcomplexityframedecompositions.Wetakethesumofthenumbersofvectorsforthisorthonormalbasiswhenex
5、pandingeachframevectorassparsitymeasure.Thisthesisconsistsoffivechapters.Chapter1introducestheoriginoftheframeconcept,theframeandresearchcontentsofsparseframes,andsketchesthestructureofthethesis.Chapter2listssomebasictheoremstobeusedthroughoutthethesis,an
6、dstatestheSpectralTetrisalgorithmforconstructingunitnormframes.Byusingthekeyidea,anewblockmatrixT(r)of3×3isconstructed.Chapter3introducesthebackgroundofsparseframe,andgivesthedefinitionofsparseframeandtheconceptofoptimallysparseframes.Chapter4isoneofthema
7、incontents.Anoptimallyresultforsparseframeisestablishedwhentheeigenvaluesoftheframeoperatorequalto2oraregreaterthan2.Chapter5isanothermaincontent.Thethedefinitionofprimeanddivisibletightframesarestated,andtheconditionwhichSTalgorithmcanworkisgivenwhenthee
8、igenvaluesoftheframeoperatoraresmallerthan2.III基于ST算法的框架稀疏性若干问题研究KEYWORDS：Frameoperator,sparseframes,synthesismatrix,tightframes.IV目录中文摘要.............................................................................I英文摘要...
