Overview
- Offers concise treatment of mathematics for undergraduates solely within the context of medical imaging
- Covers current medical imaging development and improvements regarding CT scans, ultrasounds, MRIs, and more
- Offers short computer-based assignments and more than 20 examples using R
- SpringerLink features R code used throughout the text
- Includes supplementary material: sn.pub/extras
Part of the book series: Springer Undergraduate Texts in Mathematics and Technology (SUMAT)
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Table of contents (10 chapters)
Keywords
- Bloch equation
- Fourier transform
- Kaczmarz's method
- MRI
- R code medical imaging
- RF field
- algebraic reconstruction techniques
- back projection
- complex numbers
- convolution
- discrete Fourier transform
- eigenvalue decomposition
- fast Fourier transform (FFT)
- integrability
- mathematics medical imaging
- mathematics medical imaging textbook adoption
- radon transform
- singular value decomposition
- ultrasound
About this book
The basic mathematics of computerized tomography, the CT scan, are aptly presented 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.
Extending the ideas of the acclaimed first edition, new material has been adeed to render an even more accessible textbook for course usage. This edition includes new discussions of the Radon transform, the Dirac delta function and its role in X-ray imaging, Kacmarz’s method and least squares approximation, spectral filtering, and more. Copious examples and exercises, new computer-based exercises, and additional graphics have been added to further delineate concepts. The use of technology has been revamped throughout with the incorporation of the open source programming environment R to illustrate examples and composition of graphics. All R code is available as extra source material on SpringerLink.
From the reviews of the first edition:
“This book is valuable, for it addresses with care and rigor the relevance of a variety of mathematical topics to a real-world problem. …T
his book is well written. It serves its purpose of focusing a variety of mathematical topics onto a real-world application that is in its essence mathematics.”–The Journal of Nuclear Medicine, Vol. 51 (12), December, 2010
“This new book by Timothy Feeman, truly intended to be a beginner’s guide, makes the subject accessible to undergraduates with a working knowledge of multivariable calculus and some experience with vectors and matrix methods. …author handles thematerial with clarity and grace…”
–The Mathematical Association of America, February, 2010
Reviews
“The text is concise, lucidly written and coherently structured. It is also self-contained and easily accessible to any undergraduate student having a solid command of mathematics at the level of some introductory courses in algebra and analysis. The code written in R is a genuine asset of high practical and educational value. Overall, this textbook provides good, highly informative, and useful material to students and all of those with interest in medical imaging.” (Witold Pedrycz, zbMATH 1351.92002, 2017)
“I believe that the book is a useful starting point for undergraduate students from mathematics, computer science, and related fields who want to learn how CT works; it also provides interesting reading for people from medical areas who want to find out the technical and mathematical background of the tools that they use.” (Kai Diethelm, Computing Reviews, computingreviews.com, May, 2016)
Authors and Affiliations
About the author
Bibliographic Information
Book Title: The Mathematics of Medical Imaging
Book Subtitle: A Beginner’s Guide
Authors: Timothy G. Feeman
Series Title: Springer Undergraduate Texts in Mathematics and Technology
DOI: https://doi.org/10.1007/978-3-319-22665-1
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2015
Hardcover ISBN: 978-3-319-22664-4Published: 28 November 2015
Softcover ISBN: 978-3-319-33107-2Published: 29 October 2016
eBook ISBN: 978-3-319-22665-1Published: 19 November 2015
Series ISSN: 1867-5506
Series E-ISSN: 1867-5514
Edition Number: 2
Number of Pages: XIV, 197
Number of Illustrations: 38 b/w illustrations
Topics: Functional Analysis, Imaging / Radiology, Computer Imaging, Vision, Pattern Recognition and Graphics, Biomedical Engineering and Bioengineering, Integral Transforms, Operational Calculus, Math Applications in Computer Science