The Mathematics of Medical Imaging - Softcover

From the reviews:

“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, 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. ... 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, February, 2010)

“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, Vol. 1191, 2010)

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.