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Introduction to the Mathematics of Medical Imaging

Introduction to the Mathematics of Medical Imaging

2nd Edition

£80.00

  • Date Published: November 2007
  • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
  • format: Paperback
  • isbn: 9780898716429

£ 80.00
Paperback

This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
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About the Authors
  • At the heart of every medical imaging technology is a sophisticated mathematical model of the measurement process and an algorithm to reconstruct an image from the measured data. This book provides a firm foundation in the mathematical tools used to model the measurements and derive the reconstruction algorithms used in most of these modalities. The text uses X-ray computed tomography (X-ray CT) as a 'pedagogical machine' to illustrate important ideas and its extensive discussion of background material makes the more advanced mathematical topics accessible to people with a less formal mathematical education. This new edition contains a chapter on magnetic resonance imaging (MRI), a revised section on the relationship between the continuum and discrete Fourier transforms, an improved description of the gridding method, and new sections on both Grangreat's formula and noise analysis in MR-imaging. Mathematical concepts are illuminated with over 200 illustrations and numerous exercises.

    • Now includes a chapter on magnetic resonance imaging (MRI), a section on Grangreat's formula and an improved description of the gridding method
    • Teaches mathematical analysis applied to specific problems in medical imaging, sacrificing neither rigour nor relevance
    • Contains over 200 illustrations, numerous exercises and extensive background material to introduce advanced mathematical concepts
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    Product details

    • Edition: 2nd Edition
    • Date Published: November 2007
    • format: Paperback
    • isbn: 9780898716429
    • length: 796 pages
    • dimensions: 255 x 179 x 40 mm
    • weight: 1.318kg
    • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
  • Table of Contents

    Preface to the second edition
    Preface
    How to use this nook
    Notational conventions
    1. Measurements and modeling
    2. Linear models and linear equations
    3. A basic model for tomography
    4. Introduction to the Fourier transform
    5. Convolution
    6. The radon transform
    7. Introduction to Fourier series
    8. Sampling
    9. Filters
    10. Implementing shift invariant filters
    11. Reconstruction in X-ray tomography
    12. Imaging artifacts in X-ray tomography
    13. Algebraic reconstruction techniques
    14. Magnetic resonance imaging
    15. Probability and random variables
    16. Applications of probability
    17. Random processes
    A. Background material
    B. Basic analysis
    Bibliography
    Index.

  • Author

    Charles L. Epstein, University of Pennsylvania
    Charles L. Epstein is a Professor at the University of Pennsylvania with appointments in Mathematics and Radiology.

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