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The mathematics of medical imaging : a beginner's guide

Author: Timothy G Feeman
Publisher: Cham : Springer, 2015.
Series: Springer undergraduate texts in mathematics and technology
Edition/Format:   eBook : Document : English : 2nd edView all editions and formats
Summary:
The basic mathematics of computerized tomography, the CT scan, ℗ℓare 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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Printed edition:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Timothy G Feeman
ISBN: 9783319226651 3319226657
OCLC Number: 932168517
Description: 1 online resource (xiv, 197 pages) : illustrations.
Contents: 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.
Series Title: Springer undergraduate texts in mathematics and technology
Responsibility: Timothy G. Feeman.

Abstract:

The basic mathematics of computerized tomography, the CT scan, are aptly presented for an audience of undergraduates in mathematics and engineering.  Read more...

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"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 Read more...

 
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    schema:description "The basic mathematics of computerized tomography, the CT scan, ℗ℓare 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, Kacmarzℓ́ℓs method and least squares approximation, spectral filtering, ℗ℓ and more.℗ℓ℗ℓCopious examples and exercises, several new computer-based exercises, and additional graphics have been added to further delineate concepts. ℗ℓThe 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: ℓ́ℓThis book is valuable, for it addresses with care and rigor the relevance of a variety of mathematical topics t o a real-world problem. ℓ́ŒThis 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.ℓ́ℓ ℓ́ℓThe Journal of Nuclear Medicine, Vol. 51 (12), December, 2010 ℗ℓ ℓ́ℓThis new book by Timothy Feeman, truly intended to be a beginnerℓ́ℓs guide, makes the subject accessible to undergraduates with a working knowledge of multivariable calculus and some experience with vectors and matrix methods. ℓ́Œauthor handles the material with clarity and graceℓ́Œℓ́ℓ ℓ́ℓThe Mathematical Association of America, February, 2010 ℗ℓ ℓ́ℓAll theoretical material is illustrated with carefully selected examples which are easy to follow. ℓ́ŒI 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 studentsℓ́Œand to specialists.ℓ́ℓ ℓ́ℓZentralblatt MATH, Vol. 1191, 2010."@en ;
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