Table Of ContentMedical Image Processing,
Reconstruction and Analysis
TTaayylloorr aanndd FFrraanncciiss SSeerriieess iinn SSiiggnnaall PPrroocceessssiinngg aanndd CCoommmmuunniiccaattiioonnss
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Medical Image Processing,
Reconstruction and Analysis
Concepts and Methods
Second Edition
ř
Ji í Jan
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LibraryofCongressCataloging-in-PublicationData
Names:Jan,Jiří,author.
Title:Medicalimageprocessingreconstructionandanalysis:conceptsandmethods/JiriJan.
Othertitles:Medicalimageprocessing,reconstruction,andrestoration
Description:Secondedition.|BocaRaton:CRCPress,2019.|PrecededbyMedicalimageprocessing,
reconstruction,andrestoration/JiříJan.2006.
Identifiers:LCCN2019012187|ISBN9781138310285(hardback:alk.paper)
Subjects:|MESH:ImageProcessing,Computer-Assisted–methods|DiagnosticImaging–methods|
SignalProcessing,Computer-Assisted
Classification:LCCRC78.7.D53|NLMWN26.5|DDC616.07/54–dc23
LCrecordavailableathttps://lccn.loc.gov/2019012187
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Contents
Preface................................................................................................................................xvii
Acknowledgments................................................................................................................xxi
AuthorBiography..............................................................................................................xxiii
PART I Images as Multidimensional Signals
Chapter1 Analogue(Continuous-Space)ImageRepresentation..........................................3
1.1 MultidimensionalSignalsasImageRepresentation.....................................3
1.1.1 GeneralNotionofMultidimensionalSignals...................................3
1.1.2 SomeImportantTwo-DimensionalSignals......................................5
1.2 Two-DimensionalFourierTransform..........................................................8
1.2.1 ForwardTwo-DimensionalFourierTransform.................................8
1.2.2 InverseTwo-DimensionalFourierTransform.................................10
1.2.3 PhysicalInterpretationoftheTwo-DimensionalFourier
Transform.......................................................................................11
1.2.4 PropertiesoftheTwo-DimensionalFourierTransform..................13
1.3 Two-DimensionalContinuous-SpaceSystems............................................15
1.3.1 TheNotionofMultidimensionalSystems......................................15
1.3.2 LinearTwo-DimensionalSystems:
Original-DomainCharacterization.................................................17
1.3.3 LinearTwo-DimensionalSystems:
Frequency-DomainCharacterization.............................................19
1.3.4 NonlinearTwo-DimensionalContinuous-SpaceSystems...............21
1.3.4.1 PointOperators.................................................................21
1.3.4.2 HomomorphicSystems.....................................................22
1.4 ConceptofStochasticImages.....................................................................25
1.4.1 StochasticFieldsasGeneratorsofStochasticImages.....................26
1.4.2 CorrelationandCovarianceFunctions...........................................29
1.4.3 HomogeneousandErgodicFields..................................................31
1.4.4 Two-DimensionalSpectraofStochasticImages.............................34
1.4.4.1 PowerSpectra...................................................................34
1.4.4.2 Cross-Spectra....................................................................35
1.4.5 TransferofStochasticImagesviaTwo-Dimensional
LinearSystems................................................................................36
1.4.6 LinearEstimationofStochasticVariables—Principle
ofOrthogonality.............................................................................38
Chapter2 DigitalImageRepresentation.............................................................................41
2.1 DigitalImageRepresentation.....................................................................41
2.1.1 SamplingandDigitizingImages.....................................................41
v
vi Contents
2.1.1.1 Sampling...........................................................................41
2.1.1.2 Digitization.......................................................................45
2.1.2 ImageInterpolationfromSamples..................................................48
2.2 DiscreteTwo-DimensionalOperators.........................................................49
2.2.1 DiscreteLinearTwo-DimensionalOperators..................................50
2.2.1.1 GenericOperators.............................................................50
2.2.1.2 SeparableOperators..........................................................51
2.2.1.3 LocalOperators................................................................52
2.2.1.4 ConvolutionalOperators..................................................54
2.2.2 NonlinearTwo-DimensionalDiscreteOperators............................56
2.2.2.1 PointOperators.................................................................56
2.2.2.2 HomomorphicOperators..................................................57
2.2.2.3 OrderStatisticsOperators.................................................58
2.2.2.4 NeuronalOperators..........................................................58
2.3 DiscreteTwo-DimensionalLinearTransforms...........................................65
2.3.1 Two-DimensionalUnitaryTransformsGenerally...........................66
2.3.2 Two-DimensionalDiscreteFourierandRelatedTransforms..........68
2.3.2.1 Two-DimensionalDFTDefinition....................................68
2.3.2.2 PhysicalInterpretationofTwo-DimensionalDFT............69
2.3.2.3 RelationofTwo-DimensionalDFTto
Two-DimensionalIntegralFTandItsApplications
inSpectralAnalysis...........................................................71
2.3.2.4 PropertiesoftheTwo-DimensionalDFT..........................75
2.3.2.5 FrequencyDomainConvolution.......................................76
2.3.2.6 Two-DimensionalCosine,Sine,and
HartleyTransforms...........................................................77
2.3.3 Two-DimensionalHadamard-WalshandHaarTransforms............80
2.3.3.1 Two-DimensionalHadamard-WalshTransform...............80
2.3.3.2 Two-DimensionalHaarTransform...................................81
2.3.4 Two-DimensionalDiscreteWaveletTransforms..............................84
2.3.4.1 Two-DimensionalContinuousWavelet
Transforms........................................................................84
2.3.4.2 Two-DimensionalDyadicWaveletTransforms.................87
2.3.5 Two-DimensionalDiscreteKarhunen-LoeveTransform................89
2.4 DiscreteStochasticImages..........................................................................91
2.4.1 DiscreteStochasticFieldsasGeneratorsofStochastic
Images............................................................................................91
2.4.2 DiscreteCorrelationandCovarianceFunctions.............................92
2.4.3 DiscreteHomogeneousandErgodicFields....................................93
2.4.4 Two-DimensionalSpectraofStochasticImages.............................94
2.4.4.1 PowerSpectra...................................................................94
2.4.4.2 DiscreteCross-Spectra......................................................95
2.4.5 TransferofStochasticImagesviaDiscrete
Two-DimensionalSystems..............................................................95
PartIReferences.................................................................................................96
Contents vii
PART II Imaging Systems as Data Sources
Chapter3 PlanarX-RayImaging........................................................................................99
3.1 X-RayProjectionRadiography...................................................................99
3.1.1 BasicImagingGeometry.................................................................99
3.1.2 SourceofRadiation......................................................................100
3.1.3 InteractionofX-RayswithImagedObjects..................................103
3.1.4 ImageDetection............................................................................104
3.1.5 Post-measurementDataProcessinginProjectionRadiography....107
3.2 SubtractiveAngiography..........................................................................109
Chapter4 X-RayComputedTomography........................................................................111
4.1 ImagingPrincipleandGeometry..............................................................111
4.1.1 PrincipleofaSliceProjectionMeasurement.................................111
4.1.2 VariantsofMeasurementArrangement........................................113
4.2 MeasuringConsiderations........................................................................117
4.2.1 TechnicalEquipment....................................................................117
4.2.2 AttenuationScale..........................................................................118
4.3 ImagingProperties....................................................................................119
4.3.1 SpatialTwo-DimensionalandThree-Dimensional
ResolutionandContrastResolution.............................................119
4.3.2 ImagingArtifacts..........................................................................120
4.4 PostmeasurementDataProcessinginComputedTomography.................123
4.5 SpectralComputedTomography..............................................................125
4.5.1 Double-EnergyCT.......................................................................126
4.5.2 Multi-Band(Spectral)CT.............................................................128
Chapter5 MagneticResonanceImaging...........................................................................131
5.1 MagneticResonancePhenomena..............................................................131
5.1.1 MagnetizationofNuclei...............................................................131
5.1.2 StimulatedNMRResponseandFreeInductionDecay................133
5.1.3 Relaxation.....................................................................................135
5.1.3.1 ChemicalShiftandFlowInfluence.................................137
5.2 ResponseMeasurementandInterpretation..............................................138
5.2.1 SaturationRecovery(SR)Techniques...........................................139
5.2.2 Spin-EchoTechniques...................................................................140
5.2.3 Gradient-EchoTechniques...........................................................144
5.3 BasicMRIArrangement...........................................................................146
5.4 LocalizationandReconstructionofImageData......................................148
5.4.1 GradientFields.............................................................................148
5.4.2 SpatiallySelectiveExcitation........................................................149
5.4.3 RFSignalModelandGeneralBackgroundforLocalization.......151
5.4.4 One-DimensionalFrequencyEncoding:Two-Dimensional
ReconstructionfromProjections...................................................155
viii Contents
5.4.5 Two-DimensionalReconstructionviaFrequencyand
PhaseEncoding............................................................................159
5.4.6 Three-DimensionalReconstructionviaFrequencyand
DoublePhaseEncoding................................................................163
5.4.7 FastMRI......................................................................................164
5.4.7.1 Multiple-SliceImaging....................................................165
5.4.7.2 LowFlip-AngleExcitation..............................................165
5.4.7.3 Multiple-EchoAcquisition..............................................166
5.4.7.4 Echo-PlanarImaging......................................................167
5.5 ImageQualityandArtifacts......................................................................170
5.5.1 NoiseProperties............................................................................170
5.5.2 ImageParameters.........................................................................171
5.5.3 Point-SpreadFunction..................................................................173
5.5.4 ResolvingPower...........................................................................173
5.5.5 ImagingArtifacts..........................................................................174
5.6 Post-measurementDataProcessinginMRI..............................................175
5.7 FunctionalMagneticResonanceImaging(fMRI)....................................177
Chapter6 NuclearImaging...............................................................................................183
6.1 PlanarGammaImaging............................................................................184
6.1.1 GammaDetectorsandGammaCamera.......................................185
6.1.2 InherentDataProcessingandImagingProperties........................189
6.1.2.1 DataLocalizationandSystemResolution......................189
6.1.2.2 TotalResponseEvaluationandScatterRejection...........191
6.1.2.3 DataPost-processing.......................................................191
6.2 Single-PhotonEmissionTomography.......................................................192
6.2.1 Principle........................................................................................192
6.2.2 DeficienciesofSPECTPrincipleandPossibilitiesofCure............193
6.3 PositronEmissionTomography................................................................197
6.3.1 PrinciplesofMeasurement............................................................197
6.3.2 ImagingArrangements.................................................................200
6.3.3 Post-processingofRawDataandImagingProperties...................202
6.3.3.1 AttenuationCorrection...................................................203
6.3.3.2 RandomCoincidences....................................................204
6.3.3.3 ScatteredCoincidences....................................................205
6.3.3.4 Dead-TimeInfluence.......................................................205
6.3.3.5 ResolutionIssues............................................................206
6.3.3.6 RayNormalization.........................................................207
6.3.3.7 ComparisonofPETandSPECTModalities...................208
Chapter7 Ultrasonography..............................................................................................209
7.1 Two-DimensionalEchoImaging...............................................................210
7.1.1 EchoMeasurement.......................................................................210
7.1.1.1 PrincipleofEchoMeasurement......................................210
7.1.1.2 UltrasonicTransducers...................................................211
Contents ix
7.1.1.3 UltrasoundPropagationandInteractionwithTissue.....216
7.1.1.4 EchoSignalFeaturesandProcessing..............................218
7.1.2 B-ModeImaging...........................................................................221
7.1.2.1 Two-DimensionalScanningMethodsandTransducers...221
7.1.2.2 FormatConversion.........................................................224
7.1.2.3 Two-DimensionalImagePropertiesandProcessing........225
7.1.2.4 ContrastImagingandHarmonicImaging......................227
7.2 FlowImaging............................................................................................229
7.2.1 PrinciplesofFlowMeasurement..................................................229
7.2.1.1 DopplerBloodVelocityMeasurement(Narrowband
Approach).......................................................................229
7.2.1.2 Cross-CorrelationBloodVelocityMeasurement
(WidebandApproach).....................................................233
7.2.2 ColorFlowImaging.....................................................................234
7.2.2.1 Autocorrelation-BasedDopplerImaging........................234
7.2.2.2 MovementEstimationImaging.......................................237
7.2.2.3 Contrast-BasedFlowImaging........................................237
7.2.2.4 Post-processingofFlowImages......................................237
7.3 Three-DimensionalUltrasonography........................................................238
7.3.1 Three-DimensionalDataAcquisition...........................................238
7.3.1.1 Two-DimensionalScan-BasedDataAcquisition.............238
7.3.1.2 Three-DimensionalTransducerPrinciples.......................240
7.3.2 Three-DimensionalandFour-DimensionalData
Post-ProcessingandDisplay.........................................................241
7.3.2.1 DataBlockCompilation.................................................241
7.3.2.2 DisplayofThree-DimensionalData...............................242
7.4 PlaneWave(Ultra-Fast)UltrasonicImaging............................................243
7.4.1 PrincipleofPlane-WaveImaging..................................................244
7.4.1.1 IndividualFrameDataAcquisition................................244
7.4.1.2 IndividualImageReconstruction....................................247
7.4.2 ImageCompounding....................................................................248
7.4.3 ShearWaveVisualizationandElastography.................................250
Chapter8 OtherModalities..............................................................................................253
8.1 OpticalandInfraredImaging...................................................................253
8.1.1 Three-DimensionalConfocalMicroscopy....................................254
8.1.2 OpticalCoherenceTomography(OCT)........................................256
8.1.3 BodySurfaceInfraredImaging.....................................................257
8.2 ElectronMicroscopy.................................................................................258
8.2.1 ScatteringPhenomenaintheSpecimenVolume............................259
8.2.2 TransmissionElectronMicroscopy...............................................259
8.2.3 ScanningElectronMicroscopy.....................................................262
8.2.4 Post-processingofEMImages......................................................264
8.3 ElectricalImpedanceTomography............................................................265
PartIIReferences.............................................................................................268
