Statistics of Medical Imaging

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