医学图像重建

1BasicPrinciplesofTomography

1.1Tomography

1.2Projection

1.3ImageReconstruction

1.4Backprojection

*1.5MathematicalExpressions

1.5.1Projection

1.5.2Backprojection

1.5.3TheDiracδ-function

1.6WorkedExamples

1.7Summary

Problems

References

2Parallel-BeamImageReconstruction

2.1FourierTransform

2.2CentralSliceTheorem

2.3ReconstructionAlgorithms

2.3.1Method1

2.3.2Method2

2.3.3Method3

2.3.4Method4

2.3.5Method5

2.4AComputerSimulation

*2.5ROIReconstructionwithTruncatedProjections

*2.6MathematicalExpressions

2.6.1TheFourierTransformandConvolution

2.6.2TheHilbertTransformandtheFiniteHilbertTransform

2.6.3ProofoftheCentralSliceTheorem

2.6.4DerivationoftheFilteredBackprojectionAlgorithm

2.6.5ExpressionoftheConvolutionBackprojectionAlgorithm

2.6.6ExpressionoftheRadonInversionFormula

2.6.7DerivationoftheBackprojection-then-FilteringAlgorithm

2.7WorkedExamples

2.8Summary

Problems

References

3Fan-BeamImageReconstruction

3.1Fan-BeamGeometryandPointSpreadFunction

3.2Parallel-BeamtoFan-BeamAlgorithmConversion

3.3ShortScan

*3.4MathematicalExpressions

3.4.1DerivationofaFilteredBackprojectionFan-BeamAlgorithm

3.4.2AFan-BeamAlgorithmUsingtheDerivativeandtheHilbertTransform

3.5WorkedExamples

3.6Summary

Problems

References

4TransmissionandEmissionTomography

4.1X-RayComputedTomography

4.2PositronEmissionTomographyandSinglePhotonEmissionComputedTomography

4.3AttenuationCorrectionforEmissionTomography

*4.4MathematicalExpressions

4.5WorkedExamples

4.6Summary

Problems

References

53DImageReconstruction

5.1ParallelLine-IntegralData

5.1.1Backprojection-then-Filtering

5.1.2FilteredBackprojection

5.2ParallelPlane-IntegralData

5.3Cone-BeamData

5.3.1FeldkampsAlgorithm

5.3.2GrangeatsAlgorithm

5.3.3KatsevichsAlgorithm

*5.4MathematicalExpressions

5.4.1Backprojection-then-FilteringforParallelLine-IntegralData

5.4.2FilteredBackprojectionAlgorithmforParallelLine-IntegralData

5.4.33DRadonInversionFormula

5.4.43DBackprojection-then-FilteringAlgorithmforRadonData

5.4.5FeldkampsAlgorithm

5.4.6TuysRelationship

5.4.7GrangeatsRelationship

5.4.8KatseviehsAlgorithm

5.5WorkedExamples

5.6Summary

Problems

References

6IterativeReconstruction

6.1SolvingaSystemofLinearEquations

6.2AlgebraicReconstructionTechnique

6.3GradientDescentAlgorithms

6.4Maximum-LikelihoodExpectation-MaximizationAlgorithms

6.5Ordered-SubsetExpectation-MaximizationAlgorithm

6.6NoiseHandling

6.6.1AnalyticalMethods--Windowing

6.6.2IterativeMethods--StoppingEarly

6.6.3IterativeMethods--ChoosingPixels

6.6.4IterativeMethods--AccurateModeling

6.7NoiseModelingasaLikelihoodFunction

6.8IncludingPriorKnowledge

*6.9MathematicalExpressions

6.9.1ART

6.9.2ConjugateGradientAlgorithm

6.9.3ML-EM

6.9.4OS-EM

6.9.5GreensOne-StepLateAlgorithm

6.9.6MatchedandUnmatchedProjector/BackprojectorPairs

*6.10ReconstructionUsingHighlyUndersampledDatawith10Minimization

6.11WorkedExamples

6.12Summary

Problems

References

7MRIReconstruction

7.1The"M"

7.2The"R"

7.3The"T"

7.3.1ToObtainz-Information--SliceSelection

7.3.2ToObtainx-Information--FrequencyEncoding

7.3.3ToObtainy-Information--PhaseEncoding

*7.4MathematicalExpressions

7.5WorkedExamples

7.6Summary

Problems

References

Index

　　MedicalImageReconstructionAConceptualTutorialintroducestheclassicalandmodernimagereconstructiontechnologies,suchastwo-dimensional(2D)parallel-beamandfan-beamimaging,three-dimensional(3D)parallelray,parallelplane,andcone-beamimaging.ThisbookpresentsbothanalyticalanditerativemethodsofthesetechnologiesandtheirapplicationsinX-rayCT(computedtomography),SPECT(singlephotonemissioncomputedtomography),PET(positronemissiontomography),andMRI(magneticresonanceimaging).Contemporaryresearchresultsinexactregion-of-interest(ROI)reconstructionwithtruncatedprojections,Katsevichscone-beamfilteredbackprojectionalgorithm,andreconstructionwithhighlyundersampleddatawith/o-minimizationarealsoincluded.　　Thisbookiswrittenforengineersandresearchersinthefieldofbiomedicalengineeringspecializinginmedicalimagingandimageprocessingwithimagereconstruction.