Statistics of Medical Imaging

Statistical investigation into technology not only provides a better understanding of the intrinsic features of the technology (analysis), but also leads to an improved design of the technology (synthesis). Physical principles and mathematical procedures of medical imaging technologies have been extensively studied during past decades. However, less work has been done on their statistical aspect. Filling this gap, this book provides a theoretical framework for statistical investigation into medical technologies. Rather than offer detailed descriptions of statistics of basic imaging protocols of X-ray CT and MRI, the book presents a method to conduct similar statistical investigations into more complicated imaging protocols.

Tianhu Lei is an associate professor at the University of Pittsburgh. He has previously worked at the University of Maryland, the University of Pennsylvania, and the Children’s Hospital of Philadelphia. He earned a Ph.D. in electric and system engineering from the University of Pennsylvania.

IntroductionData Flow and StatisticsImaging and Image StatisticsStatistical Image AnalysisMotivation and OrganizationX-ray CT Physics and MathematicsIntroductionPhoton Emission, Attenuation, and DetectionAttenuation CoefficientProjectionsMathematical Foundation of Image ReconstructionFourier Slice theoremImage ReconstructionMRI Physics and MathematicsIntroductionNuclear Spin and Magnetic MomentAlignment and PrecessionMacroscopic MagnetizationResonance and RelaxationBloch Equation and Its SolutionExcitationInductionk-Space and k-Space SampleImage ReconstructionEcho SignalNon-diffraction Computed TomographyIntroductionInteraction between EM Wave and ObjectInverse Scattering ProblemNon-diffraction Computed TomographyStatistics of X-ray CT ImagingIntroductionStatistics of Photon MeasurementsStatistics of ProjectionsStatistical Interpretation of X-ray CT Image ReconstructionStatistics of X-ray CT ImageIntroductionStatistics of the Intensity of a Single PixelStatistics of the Intensities of Two PixelsStatistics of the Intensities of a Group of PixelsStatistics of MR ImagingIntroductionStatistics of Macroscopic MagnetizationsStatistics of MR SignalsStatistics of k-Space SamplesStatistical Interpretation of MR Image ReconstructionStatistics of MR ImageIntroductionStatistics of the Intensity of a Single PixelStatistics of the Intensities of Two PixelsStatistics of the Intensities of a Group of PixelsDiscussion and RemarksStochastic Image ModelsIntroductionStochastic Model IStochastic Model IIDiscussion
Statistical Image Analysis – IIntroductionDetection of Number of Image RegionsEstimation of Image ParametersClassification of PixelsStatistical Image AnalysisStatistical Image Analysis – IIIntroductionDetection of the Number of Image RegionsEstimation of Image ParametersClassification of PixelsStatistical Image AnalysisPerformance Evaluation of Image Analysis MethodsIntroductionPerformance of the iFNM Model-Based Image Analysis MethodPerformance of the cFNM Model-Based Image Analysis MethodIndex