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The Mathematics of Medical Imaging

A Beginner’s Guide

  • Timothy G. Feeman

Table of contents

  1. Front Matter
    Pages i-x
  2. Timothy G. Feeman
    Pages 1-10
  3. Timothy G. Feeman
    Pages 11-18
  4. Timothy G. Feeman
    Pages 19-24
  5. Timothy G. Feeman
    Pages 25-31
  6. Timothy G. Feeman
    Pages 33-46
  7. Timothy G. Feeman
    Pages 47-52
  8. Timothy G. Feeman
    Pages 53-66
  9. Timothy G. Feeman
    Pages 67-100
  10. Timothy G. Feeman
    Pages 101-114
  11. Timothy G. Feeman
    Pages 115-128
  12. Back Matter
    Pages 1-12

About this book

Introduction

A Beginner's Guide to the Mathematics of Medical Imaging presents the basic mathematics of computerized tomography – the CT scan – for an audience of undergraduates in mathematics and engineering. Assuming no prior background in advanced mathematical analysis, topics such as the Fourier transform, sampling, and discrete approximation algorithms are introduced from scratch and are developed within the context of medical imaging. A chapter on magnetic resonance imaging focuses on manipulation of the Bloch equation, the system of differential equations that is the foundation of this important technology.

The text is self-contained with a range of practical exercises, topics for further study, and an ample bibliography, making it ideal for use in an undergraduate course in applied or engineering mathematics, or by practitioners in radiology who want to know more about the mathematical foundations of their field.

Keywords

Fourier transform convolution discrete Fourier transform fast Fourier transform fast Fourier transform (FFT) ultrasound

Authors and affiliations

  • Timothy G. Feeman
    • 1
  1. 1.Dept. Mathematical SciencesVillanova UniversityVillanovaU.S.A.

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-387-92712-1
  • Copyright Information Springer Science+Business Media, LLC 2010
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-387-92711-4
  • Online ISBN 978-0-387-92712-1
  • Series Print ISSN 1867-5506
  • Series Online ISSN 1867-5514
  • Buy this book on publisher's site
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