版本 
Second edition 
說明 
1 online resource (xiv, 197 pages) : illustrations, digital ; 24 cm 

text txt rdacontent 

computer c rdamedia 

online resource cr rdacarrier 

text file PDF rda 
系列 
Springer undergraduate texts in mathematics and technology, 18675506


Springer undergraduate texts in mathematics and technology

附註 
Preface to Second Edition  Preface  1. Xrays  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 

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 Xray imaging, Kacmarz's method and least squares approximation, spectral filtering, and more. Copious examples and exercises, several new computerbased 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 t o a realworld problem. …This book is well written. It serves its purpose of focusing a variety of mathematical topics onto a realworld 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 the material with clarity and grace…" The Mathematical Association of America, February, 2010 "All theoretical material is illustrated with carefully selected examples which are easy to follow. …I highly recommend this interesting, accessible to wide audience and wellwritten book dealing with mathematical techniques that support recent groundbreaking discoveries in biomedical technology both to students…and to specialists." Zentralblatt MATH, Vol. 1191, 2010 
Host Item 
Springer eBooks

主題 
Diagnostic imaging  Mathematics


Mathematics


Radiology


Computer science  Mathematics


Computer graphics


Functional analysis


Integral transforms


Calculus, Operational


Biomedical engineering


Imaging / Radiology


Computer Imaging, Vision, Pattern Recognition and Graphics


Integral Transforms, Operational Calculus


Math Applications in Computer Science

Alt Author 
SpringerLink (Online service)

