Chemometrics: from basics to wavelet transform

327 Pages·2004·2.581 MB·English

by  Foo-Tim Chau, Yi-Zeng Liang, Junbin Gao, Xue-Guang Shao

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Chemometrics
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CHEMICAL ANALYSIS
ASERIESOFMONOGRAPHSONANALYTICALCHEMISTRY
ANDITSAPPLICATIONS
Edited by
J.D.WINEFORDNER
VOLUME164
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Chemometrics
From Basics to Wavelet Transform
FOO-TIMCHAU
HongKongPolytechnicUniversity
YI-ZENGLIANG
CentralSouthUniversity
JUNBINGAO
UniversityofNewEngland
XUE-GUANGSHAO
UniversityofScienceandTechnologyofChina
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Copyright?2004byJohnWiley&Sons,Inc.Allrightsreserved.
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LibraryofCongressCataloging-in-PublicationData:
Chemometrics:frombasicstowavelettransform/Foo-timChau... [etal.].
p. cm.---(Chemicalanalysis;1075)
Includesbibliographicalreferences.
ISBN0-471-20242-8(acid-freepaper)
1.Instrumentalanalysis---Dataprocessing.2.Instrumentalanalysis---Automation.
3.Wavelets(Mathematics)I.Chau,Foo-tim.II.Chemicalanalysis;v.1075.
QD79.I5C442004
543(cid:1).07(cid:1)0285---dc21
2003002429
PrintedintheUnitedStatesofAmerica.
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CONTENTS
PREFACE xiii
CHAPTER1 INTRODUCTION 1
1.1. ModernAnalyticalChemistry 1
1.1.1. DevelopmentsinModernChemistry 1
1.1.2. ModernAnalyticalChemistry 2
1.1.3. MultidimensionalDataset 3
1.2. Chemometrics 5
1.2.1. IntroductiontoChemometrics 5
1.2.2. InstrumentalResponseandData
Processing 8
1.2.3. White,Black,andGraySystems 9
1.3. Chemometrics-BasedSignalProcessing
Techniques 10
1.3.1. CommonMethodsforProcessing
ChemicalData 10
1.3.2. WaveletsinChemistry 11
1.4. ResourcesAvailableonChemometricsand
WaveletTransform 12
1.4.1. Books 12
1.4.2. OnlineResources 14
1.4.3. MathematicsSoftware 15
CHAPTER2 ONE-DIMENSIONALSIGNALPROCESSING
TECHNIQUESINCHEMISTRY 23
2.1. DigitalSmoothingandFilteringMethods 23
2.1.1. Moving-WindowAverageSmoothing
Method 24
2.1.2. Savitsky--GolayFilter 25
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vi contents
2.1.3. KalmanFiltering 32
2.1.4. SplineSmoothing 36
2.2. TransformationMethodsofAnalytical
Signals 39
2.2.1. PhysicalMeaningoftheConvolution
Algorithm 39
2.2.2. MultichannelAdvantageinSpectroscopy
andHadamardTransformation 41
2.2.3. FourierTransformation 44
2.2.3.1. DiscreteFourierTransformation
andSpectralMultiplex
Advantage 45
2.2.3.2. FastFourierTransformation 48
2.2.3.3. FourierTransformationas
AppliedtoSmooth
AnalyticalSignals 50
2.2.3.4. FourierTransformationas
AppliedtoConvolution
andDeconvolution 52
2.3. NumericalDifferentiation 54
2.3.1. SimpleDifferenceMethod 54
2.3.2. Moving-WindowPolynomial
Least-SquaresFittingMethod 55
2.4. DataCompression 57
2.4.1. DataCompressionBasedonB-Spline
CurveFitting 57
2.4.2. DataCompressionBasedonFourier
Transformation 64
2.4.3. DataCompressionBasedon
Principal-ComponentAnalysis 64
CHAPTER3 TWO-DIMENSIONALSIGNALPROCESSING
TECHNIQUESINCHEMISTRY 69
3.1. GeneralFeaturesofTwo-DimensionalData 69
3.2. SomeBasicConceptsforTwo-Dimensional
DatafromHyphenatedInstrumentation 70
3.2.1. ChemicalRankandPrincipal-
ComponentAnalysis(PCA) 71
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3.2.2. Zero-ComponentRegionsand
EstimationofNoiseLeveland
Background 75
3.3. Double-CenteringTechniqueforBackground
Correction 77
3.4. CongruenceAnalysisandLeast-Squares
Fitting 78
3.5. DifferentiationMethodsforTwo-Dimensional
Data 80
3.6 ResolutionMethodsforTwo-Dimensional
Data 81
3.6.1. LocalPrincipal-Component
AnalysisandRankmap 83
3.6.2. Self-ModelingCurveResolutionand
EvolvingResolutionMethods 85
3.6.2.1. EvolvingFactorAnalysis
(EFA) 88
3.6.2.2. WindowFactorAnalysis
(WFA) 90
3.6.2.3. HeuristicEvolvingLatent
Projections(HELP) 94
CHAPTER4 FUNDAMENTALSOFWAVELETTRANSFORM 99
4.1. IntroductiontoWavelet
TransformandWaveletPacketTransform 100
4.1.1. ASimpleExample:HaarWavelet 103
4.1.2. MultiresolutionSignalDecomposition 108
4.1.3. BasicPropertiesofWaveletFunction 112
4.2. WaveletFunctionExamples 113
4.2.1. MeyerWavelet 113
4.2.2. B-Spline(Battle--Lemarie´)Wavelets 114
4.2.3. DaubechiesWavelets 116
4.2.4. CoifletFunctions 117
4.3. FastWaveletAlgorithmandPacket
Algorithm 118
4.3.1. FastWaveletTransform 119
4.3.2. InverseFastWaveletTransform 122
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4.3.3. FiniteDiscreteSignalHandlingwith
WaveletTransform 125
4.3.4. PacketWaveletTransform 132
4.4. BiorthogonalWaveletTransform 134
4.4.1. MultiresolutionSignalDecomposition
ofBiorthogonalWavelet 134
4.4.2. BiorthogonalSplineWavelets 136
4.4.3. AComputingExample 137
4.5. Two-DimensionalWaveletTransform 140
4.5.1. MultidimensionalWaveletAnalysis 140
4.5.2. ImplementationofTwo-Dimensional
WaveletTransform 141
CHAPTER5 APPLICATIONOFWAVELETTRANSFORM
INCHEMISTRY 147
5.1. DataCompression 148
5.1.1. PrincipleandAlgorithm 149
5.1.2. DataCompressionUsingWavelet
PacketTransform 155
5.1.3. Best-BasisSelectionandCriteriafor
CoefficientSelection 158
5.2. DataDenoisingandSmoothing 166
5.2.1. Denoising 167
5.2.2. Smoothing 173
5.2.3. DenoisingandSmoothingUsing
WaveletPacketTransform 179
5.2.4. ComparisonbetweenWavelet
TransformandConventionalMethods 182
5.3. Baseline/BackgroundRemoval 183
5.3.1. PrincipleandAlgorithm 184
5.3.2. BackgroundRemoval 185
5.3.3. BaselineCorrection 191
5.3.4. BackgroundRemovalUsing
ContinuousWaveletTransform 191
5.3.5. BackgroundRemovalof
Two-DimensionalSignals 196
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contents ix
5.4. ResolutionEnhancement 199
5.4.1. NumericalDifferentiationUsing
DiscreteWaveletTransform 200
5.4.2. NumericalDifferentiationUsing
ContinuousWaveletTransform 205
5.4.3. ComparisonbetweenWavelet
TransformandotherNumerical
DifferentiationMethods 210
5.4.4. ResolutionEnhancement 212
5.4.5. ResolutionEnhancementbyUsing
WaveletPacketTransform 220
5.4.6. ComparisonbetweenWavelet
TransformandFastFourierTransform
forResolutionEnhancement 221
5.5. CombinedTechniques 225
5.5.1. CombinedMethodforRegressionand
Calibration 225
5.5.2. CombinedMethodforClassification
andPatternRecognition 227
5.5.3. CombinedMethodofWavelet
TransformandChemicalFactor
Analysis 228
5.5.4. WaveletNeuralNetwork 230
5.6. AnOverviewoftheApplicationsinChemistry 232
5.6.1. FlowInjectionAnalysis 233
5.6.2. ChromatographyandCapillary
Electrophoresis 234
5.6.3. Spectroscopy 238
5.6.4. Electrochemistry 244
5.6.5. MassSpectrometry 246
5.6.6. ChemicalPhysicsandQuantum
Chemistry 248
5.6.7. Conclusion 249
APPENDIX VECTORANDMATRIXOPERATIONS
ANDELEMENTARYMATLAB 257
A.1. ElementaryKnowledgeinLinearAlgebra 257
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A.1.1. VectorsandMatricesinAnalytical
Chemistry 257
A.1.2. ColumnandRowVectors 259
A.1.3. AdditionandSubtractionofVectors 259
A.1.4. VectorDirectionandLength 260
A.1.5. ScalarMultiplicationofVectors 261
A.1.6. InnerandOuterProductsbetween
Vectors 262
A.1.7. TheMatrixandItsOperations 263
A.1.8. MatrixAdditionandSubtraction 264
A.1.9. MatrixMultiplication 264
A.1.10. ZeroMatrixandIdentityMatrix 264
A.1.11. TransposeofaMatrix 265
A.1.12. DeterminantofaMatrix 265
A.1.13. InverseofaMatrix 266
A.1.14. OrthogonalMatrix 266
A.1.15. TraceofaSquareMatrix 267
A.1.16. RankofaMatrix 268
A.1.17. EigenvaluesandEigenvectorsofa
Matrix 268
A.1.18. Singular-ValueDecomposition 269
A.1.19. GeneralizedInverse 270
A.1.20. DerivativeofaMatrix 271
A.1.21. DerivativeofaFunctionwith
VectorasVariable 271
A.2. ElementaryKnowledgeofMATLAB 273
A.2.1. MatrixConstruction 275
A.2.2. MatrixManipulation 275
A.2.3. BasicMathematicalFunctions 276
A.2.4. MethodsforGeneratingVectors
andMatrices 278
A.2.5. MatrixSubscriptSystem 280
A.2.6. MatrixDecomposition 286
A.2.6.1. Singular-Value
Decomposition(SVD) 286
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