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 the statistical aspects of these techniques. Statistics of Medical Imaging fills this gap and provides a theoretical framework for statistical investigation into medical imaging technologies.
Describes physical principles and mathematical procedures of two medical imaging techniques: X-ray CT and MRI
Presents statistical properties of imaging data (measurements) at each stage in the imaging processes of X-ray CT and MRI
Demonstrates image reconstruction as a transform from a set of random variables (imaging data) to another set of random variables (image data)
Presents statistical properties of image data (pixel intensities) at three levels: a single pixel, any two pixels, and a group of pixels (a region)
Provides two stochastic models for X-ray CT and MR image in terms of their statistics and two model-based statistical image analysis methods
Evaluates statistical image analysis methods in terms of their detection, estimation, and classification performances
Indicates that X-ray CT, MRI, PET and SPECT belong to a category of imaging: the non-diffraction computed tomography
Rather than offering detailed descriptions of statistics of basic imaging protocols of X-ray CT and MRI, this book provides 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.
Introduction Data Flow and Statistics Imaging and Image Statistics Statistical Image Analysis Motivation and Organization X-ray CT Physics and Mathematics Introduction Photon Emission, Attenuation, and Detection Attenuation Coefficient Projections Mathematical Foundation of Image Reconstruction Fourier Slice theorem Image Reconstruction MRI Physics and Mathematics Introduction Nuclear Spin and Magnetic Moment Alignment and Precession Macroscopic Magnetization Resonance and Relaxation Bloch Equation and Its Solution Excitation Induction k-Space and k-Space Sample Image Reconstruction Echo Signal Non-diffraction Computed Tomography Introduction Interaction between EM Wave and Object Inverse Scattering Problem Non-diffraction Computed Tomography Statistics of X-ray CT Imaging Introduction Statistics of Photon Measurements Statistics of Projections Statistical Interpretation of X-ray CT Image Reconstruction Statistics of X-ray CT Image Introduction Statistics of the Intensity of a Single Pixel Statistics of the Intensities of Two Pixels Statistics of the Intensities of a Group of Pixels Statistics of MR Imaging Introduction Statistics of Macroscopic Magnetizations Statistics of MR Signals Statistics of k-Space Samples Statistical Interpretation of MR Image Reconstruction Statistics of MR Image Introduction Statistics of the Intensity of a Single Pixel Statistics of the Intensities of Two Pixels Statistics of the Intensities of a Group of Pixels Discussion and Remarks Stochastic Image Models Introduction Stochastic Model I Stochastic Model II Discussion Statistical Image Analysis - I Introduction Detection of Number of Image Regions Estimation of Image Parameters Classification of Pixels Statistical Image Analysis Statistical Image Analysis - II Introduction Detection of the Number of Image Regions Estimation of Image Parameters Classification of Pixels Statistical Image Analysis Performance Evaluation of Image Analysis Methods Introduction Performance of the iFNM Model-Based Image Analysis Method Performance of the cFNM Model-Based Image Analysis Method Index