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The Mathematics of Medical Imaging: A Beginner's Guide

The Mathematics of Medical Imaging: A Beginner's Guide - Free Ebook Download

Book Detail

Author/Editor(s): Timothy G. Feeman
Publication Date: November 20, 2015
ISBN-10: 3319226649
ISBN-13: 978-3319226644
Language: English
Edition: 2
Publisher: Springer
Size: 4.25 MB
Format: pdf

Book Description

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 added 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, several 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.

About the Author

Timothy G. Feeman is professor of mathematics, Villanova University, in Lancaster, Pennsylvania. His original area of research is the theory of operators on Hilbert spaces once described as "the field of mathematics that has the strongest interaction with the scientific and technological developments which are characteristic of the twentieth century." Since the mid- to late-1990s, his scholarly efforts have become more diversified.


It is a textbook that presents a compact, rigorous treatment of basic tomographic image reconstruction at a level suitable for an undergraduate who is strong in math. … This book is valuable, for it addresses with care and rigor the relevance of a variety of mathematical topics to a real-world problem. … This 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.

--Richard Wendt III, The Journal of Nuclear Medicine

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. … The current book begins with a description of the imaging problem in the simplest possible situation, where the physics and geometry are clearest. … author handles the material with clarity and grace. … Doing that in a system like MATLAB or Maple would make for a very nice independent project.

--William J. Satzer, The Mathematical Association of America

This concise and nicely written book grew out of a course offered by the author in 2008 to undergraduate mathematics majors and minors at Villanova University. … The book is well structured; the exposition is neat and transparent. All theoretical material is illustrated with carefully selected examples which are easy to follow. … I highly recommend this interesting, accessible to wide audience and well-written book dealing with mathematical techniques that support recent ground-breaking discoveries in biomedical technology both to students … and to specialists.

--Svitlana P. Rogovchenko, Zentralblatt MATH
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