Statistics of Medical Imaging  book cover
1st Edition

Statistics of Medical Imaging

ISBN 9781138114746
Published June 14, 2017 by Chapman and Hall/CRC
438 Pages 50 B/W Illustrations

USD $84.95

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Book Description

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.

Table of Contents

Data Flow and Statistics
Imaging and Image Statistics
Statistical Image Analysis
Motivation and Organization

X-ray CT Physics and Mathematics
Photon Emission, Attenuation, and Detection
Attenuation Coefficient
Mathematical Foundation of Image Reconstruction
Fourier Slice theorem
Image Reconstruction

MRI Physics and Mathematics
Nuclear Spin and Magnetic Moment
Alignment and Precession
Macroscopic Magnetization
Resonance and Relaxation
Bloch Equation and Its Solution
k-Space and k-Space Sample
Image Reconstruction
Echo Signal

Non-diffraction Computed Tomography
Interaction between EM Wave and Object
Inverse Scattering Problem
Non-diffraction Computed Tomography

Statistics of X-ray CT Imaging
Statistics of Photon Measurements
Statistics of Projections
Statistical Interpretation of X-ray CT Image Reconstruction

Statistics of X-ray CT Image
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
Statistics of Macroscopic Magnetizations
Statistics of MR Signals
Statistics of k-Space Samples
Statistical Interpretation of MR Image Reconstruction

Statistics of MR Image
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
Stochastic Model I
Stochastic Model II

Statistical Image Analysis – I
Detection of Number of Image Regions
Estimation of Image Parameters
Classification of Pixels
Statistical Image Analysis

Statistical Image Analysis – II
Detection of the Number of Image Regions
Estimation of Image Parameters
Classification of Pixels
Statistical Image Analysis

Performance Evaluation of Image Analysis Methods
Performance of the iFNM Model-Based Image Analysis Method
Performance of the cFNM Model-Based Image Analysis Method


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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.


"Statistics of Medical Imaging is an in-depth and mathematical account of the statistics associated with medical imaging technologies, particularly x-ray CT and MR imaging. The text is logically structured into a review of mathematics and imaging principles, and then it transitions to describing the statistics of CT and MR imaging and images and image analysis models. … the text is successful at developing a structured argument for the statistical properties with supporting background physics, mathematical proofs, and integrated statistical models for both x-ray CT and MRI."
—Camille Palmer, Health Physics-The Radiation Protection Journal, March 2013

"… a welcome addition to the important interface of statistics and medical imaging. … The book fills a relatively long-standing gap in engineering literature, which is useful in understanding the statistical properties of medical images. This hopefully leads to a better understanding and interpretation, both qualitative and quantitative, of the resulting images that are useful to medical practitioners. In addition, this is expected to point to the design of better imaging systems by a closer scrutiny of the flaws in the existing systems. … it can be used both as a textbook for students in medical physics and biomedical engineering as well as a research reference for Ph.D. students engaged in designing imaging systems."
Technometrics, February 2013

"This is a good reference for graduate students and researchers in signal processing and electrical and systems engineering. … The author has demonstrated a mastery and thorough knowledge of this subject and has done a superb job of describing CT and MR image and imaging statistics systematically. The book is unique in the targeted signal processing literature, rationally illustrating the steps of analyzing CT and MR images statistically and providing an evaluation tool. The equation derivations are written in a rigorous way so that researchers and students in signal processing can understand the basic principles. With some background knowledge, researchers can also perform statistical analysis and evaluate the statistics on CT and MR images and imaging processes."
—Teh Lin, Doody’s Review Service, 2013

"… a well-organized and well-thought out physics-based textbook … Dr. Lei has done a fine job in emphasizing the statistical aspects of medical imaging, specifically analysis and synthesis methods. … this book would be very well received by [the] intended target audience. I recommend that interested members of the author’s target population obtain a copy of Statistics of Medical Imaging."
—Robert D. Stoffey, American Journal of Roentgenology, November 2012