Timothy G. Feeman

The Mathematics of Medical Imaging (eBook, PDF)

A Beginner's Guide

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Springer New York
• Seitenzahl: 141
• Erscheinungstermin: 10. März 2010
• Englisch
• ISBN-13: 9780387927121
• Artikelnr.: 37289029

Autorenporträt

Dr. Timothy G. Feeman, veteran mathematics professor at Villanova University, has been published in all of the leading mathematics journals and has received an award for expository writing from the Mathematical Association of America. In 2002, the American Mathematical Society published his first book, Portraits of the Earth: A Mathematician Looks at Maps.

Inhaltsangabe

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. MRI-An Overview.-Appendix A. Integrability.- Appendix B. Matrices, Transposes, and Factorization.- Appendix C.Topics for Further Study.- Bibliography.- Index.

Rezensionen

"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)