Statistics of Medical Imaging: 1st Edition (Paperback) book cover

Statistics of Medical Imaging

1st Edition

By Tianhu Lei

Chapman and Hall/CRC

438 pages | 50 B/W Illus.

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pub: 2011-12-19
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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.


"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

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


About the Author

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.

About the Series

Chapman & Hall/CRC Interdisciplinary Statistics

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Subject Categories

BISAC Subject Codes/Headings:
MATHEMATICS / Probability & Statistics / General
MEDICAL / Biotechnology
SCIENCE / Biotechnology