The Mathematics of Medical Imaging

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

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

Autorentext
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.

Inhalt
Preface to Second Edition.-Preface.- 1. X-rays.- 2. The Radon Transform.- 3. Back Projection.- 4. Complex Numbers.- 5. The Fourier Transform.- 6. Two Big Theorems.- 7. Filters and Convolution.- 8. Discrete Image Reconstruction.- 9. Algebraic Reconstruction Techniques.- 10. MRIAn Overview.-Appendix A. Integrability.- Appendix B. Matrices, Transposes, and Factorization.- Appendix C.Topics for Further Study.- Bibliography.- Index.