信号处理的小波导引(英文版·第2版)

本书取材于作者在多所国际知名大学讲授”小波信号处理”课程时的讲义，作者以信号处理的问题为背 景，用浅显的数学语言阐述小波理论及应用，使读者可以透过复杂的数学公式来窥探小波的精髓，但又不致 陷入小波纯数学理论的迷宫。 本书既可以让计算机及电子工程系的学生了解工程问题的数学描述．又可以让数学系的学生了解数学公 式的工程意义，是一本极有价值的教材及参考书。 作者简介： stephanemallat是纽约大学courant学院计算机科学系的教授，法国巴黎ecole理工大学应用数学系的教授，并兼任麻省理工学院电子工程系以及特拉维夫大学应用数学系的客座教授。 mallat博士还曾荣获 ·1990年ieee信号处理学会评选的论文奖。 ·1993年“斯隆”数学研究基金。 ·1997年spie光学仪器工程师学会评选的杰出成就奖。 ·1997年法国科学院评选的应用数学方面的“blaise帕斯卡”奖。 PREFACExiiiPREFACETOTHESECONDEDITIONxviiiNOTATIONxxIINTRODUCTIONTOATRANSIENTWORLD1.1FourierKingdom1.2Time-FrequencyWedding1.2.1WindowedFourierTransform1.2.2WaveletTransform1.3BasesofTime-FrequencyAtoms1.3.1WaveletBasesandFilterBanks1.3.2TilingsofWaveletPacketandLocalCosineBases1.4BasesforWhat?1.4.1Approximation1.4.2Estimation1.4.3Compression1.5TravelGuide1.5.1ReproducibleComputationalScience1.5.2RoadMapIIFOURIERKINGDOM2.1LinearTime-InvariantFiltering12.1.1ImpulseResponse2.1.2TransferFunctions2.2FourierIntegralsl2.2.1FourierTransforminL1(R)2.2.2FourierTransforminL2(R)2.2.3Examples2.3Properties12.3.1RegularityandDecay2.3.2UncertaintyPrinciple2.3.3TotalVariation2.4Two-DimensionalFourierTransform12.5ProblemsIIIDISCRETEREVOLUTION3.1SamplingAnalogSignals13.1.1WhittakerSamplingTheorem3.1.2Aliasing3.1.3GeneralSamplingTheorems3.2DiscreteTime-InvariantFilters13.2.1ImpulseResponseandTransferFunction3.2.2FourierSeries3.3FiniteSignals13.3.1CircularConvolutions3.3.2DiscreteFourierTransform3.3.3FastFourierTransform3.3.4FastConvolutions3.4DiscreteImageProcessing13.4.1Two-DimensionalSamplingTheorem3.4.2DiscreteImageFiltering3.4.3CircularConvolutionsandFourierBasis3.5ProblemsIVTIMEMEETSFREQUENCY4.1Time-FrequencyAtoms14.2WindowedFourierTransform14.2.1CompletenessandStability4.2.2ChoiceofWindow24.2.3DiscreteWindowedFourierTransform24.3WaveletTransforms14.3.1RealWavelets4.3.2AnalyticWavelets4.3.3DiscreteWavelets24.4InstantaneousFrequency24.4.1WindowedFourierRidges4.4.2WaveletRidges4.5QuadraticTune-FrequencyEnergy14.5.1Wigner-VilleDistribution4.5.2InterferencesandPositivity4.5.3CohensClass24.5.4DiscreteWigner-VilleComputations24.6ProblemsVFRAMES5.1FrameTheory25.1.1FrameDefinitionandSampLing5.1.2PseudoInverse5.1.3InverseFrameComputations5.1.4FrameProjectorandNoiseReduction5.2WindowedFourierFrames25.3WaveletFrames25.4TranslationInvariance15.5DyadicWaveletTransform25.5.1WaveletDesign5.5.2"AlgorithmeaTrous"5.5.3OrientedWaveletsforaVision35.6ProblemsVIWAVELETZOOM6.1LipschitzRegularity16.1.1LipschitzDefinitionandFourierAnalysis6.1.2WaveletVanishingMoments6.1.3RegularityMeasurementswithWavelets6.2WaveletTransformModulusMaxima26.2.1DetectionofSingularities6.2.2ReconstructionFromDyadicMaxima36.3MultiscaleEdgeDetection26.3.1WaveletMaximaforImages26.3.2FastMultiscaleEdgeComputations36.4Multifractals26.4.1FractalSetsandSelf-SimilarFunctions6.4.2SingularitySpectrum36.4.3FractalNoises36.5ProblemsVIIWAVELETBASES7.1OrthogonalWaveletBases17.1.1MultiresolutionApproximations7.1.2ScalingFunction7.1.3ConjugateMirrorFilters7.1.4InWhichOrthogonalWaveletsFinallyArrive7.2ClassesofWaveletBases17.2.1ChoosingaWavelet7.2.2Shannon,MeyerandBattle-LemarieWavelets7.2.3DaubechiesCompactlySupportedWavelets7.3WaveletsandFilterBanks17.3.1FastOrthogonalWaveletTransform7.3.2PerfectReconstructionFilterBanks7.3.3BiorthogonalBasesofI2(z)z7.4BiorthogonalWaveletBases27.4.1ConstructionofBiorthogonalWaveletBases7.4.2BiorthogonalWaveletDesign27.4.3CompactlySupportedBiorthogonalWavelets27.4.4LiftingWavelets37.5WaveletBasesonanInterval27.5.1PeriodicWaveletsIXANAPPROXIMATIONTOUR9.1LinearApproximations19.1.1LinearApproximationError9.1.2LinearFourierApproximations9.1.3LinearMultiresolutionApproximations9.1.4Karhunen-LoeveApproximations29.2Non-LinearApproximations19.2.1Non-LinearApproximationError9.2.2WaveletAdaptiveGrids9.2.3BesovSpaces39.3ImageApproximationswithWavelets19.4AdaptiveBasisSelection29.4.1BestBasisandSchurConcavity9.4.2FastBestBasisSearchinTrees9.4.3WaveletPacketandLocalCosineBestBases9.5ApproximationswithPursuits39.5.1BasisPursuit9.5.2MatchingPursuit9.5.3OrthogonalMatchingPursuit9.6ProblemsXESTIMATIONSAREAPPROXIMATIONS10.1BayesVersusMinimax210.1.1BayesEstimation10.1.2MinimaxEstimation10.2DiagonalEstimationinaBasis210.2.1DiagonalEstimationwithOracles10.2.2ThresholdingEstimation10.2.3ThresholdingRefinements310.2.4WaveletThresholding10.2.5BestBasisThresholding310.3MinimaxOptimality310.3.1LinearDiagonalMinimaxEstimation10.3.20rthosymmetricSets10.3.3NearlyMinimaxwithWavelets10.4Restoration310.4.1EstimationinArbitraryGaussianNoise10.4.2InverseProblemsandDeconvolution10.5CoherentEstimation31O.5.ICoherentBasisThresholding10.5.2CoherentMatchingPursuit10.6SpectrumEstimation210.6.1PowerSpectrum10.6.2ApproximateKarhunen-LotveSearch310.6.3LocallyStationaryProcesses310.7ProblemsXlTRANSFORMCODING11.1SignalCompressionz11.1.1StateoftheArt11.1.2CompressioninOrthonormalBases11.2DistortionRateofQuantization211.2.1EntropyCoding11.2.2ScalarQuantization11.3HighBitRateCompression211.3.1BitAllocation11.3.2OptimalBasisandKarhunen-Loeve11.3.3TransparentAudioCode11.4ImageCompression211.4.1DeterministicDistortionRate11.4.2WaveletImageCoding11.4.3BlockCosineImageCoding11.4.4EmbeddedTransformCoding11.4.5MinimaxDistortionRate311.5VideoSignals211.5.1OpticalFlow11.5.2MPEGVideoCompression11.6ProblemsAppendixAMATHEMATICALCOMPLEMENTSA.1FunctionsandIntegrationA.2BanachandHilbertSpacesA.3BasesofHilbertSpacesA.4LinearOperatorsA.5SeparableSpacesandBasesA.6RandomVectorsandCovarianceOperatorsA.7DiracsAppendixBSOFTWARETOOLBOXESB.1WAVELABB.2LASTWAVEB.3FreewareWaveletToolboxesBIBLIOGRAPHYINDEX

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