The Resource The Mathematics of Medical Imaging : A Beginner’s Guide, by Timothy G. Feeman, (electronic resource)

The Mathematics of Medical Imaging : A Beginner’s Guide, by Timothy G. Feeman, (electronic resource)

Label
The Mathematics of Medical Imaging : A Beginner’s Guide
Title
The Mathematics of Medical Imaging
Title remainder
A Beginner’s Guide
Statement of responsibility
by Timothy G. Feeman
Creator
Contributor
Author
Provider
Subject
Language
eng
Summary
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 X-ray imaging, Kacmarz’s method and least squares approximation, spectral filtering, and more. Copious examples and exercises, several 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 t o 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.” –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 well-written book dealing with mathematical techniques that support recent ground-breaking discoveries in biomedical technology both to students...and to specialists.” –Zentralblatt MATH, Vol. 1191, 2010
Member of
http://library.link/vocab/creatorName
Feeman, Timothy G
Image bit depth
0
LC call number
QA319-329.9
Literary form
non fiction
http://library.link/vocab/relatedWorkOrContributorName
SpringerLink
Series statement
Springer Undergraduate Texts in Mathematics and Technology,
http://library.link/vocab/subjectName
  • Mathematics
  • Radiology
  • Computer science
  • Computer graphics
  • Functional analysis
  • Integral transforms
  • Operational calculus
  • Biomedical engineering
  • Mathematics
  • Functional Analysis
  • Imaging / Radiology
  • Computer Imaging, Vision, Pattern Recognition and Graphics
  • Biomedical Engineering
  • Integral Transforms, Operational Calculus
  • Math Applications in Computer Science
Label
The Mathematics of Medical Imaging : A Beginner’s Guide, by Timothy G. Feeman, (electronic resource)
Instantiates
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
txt
Content type MARC source
rdacontent
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 -- Bibliography -- Index
Dimensions
unknown
Edition
2nd ed. 2015.
Extent
XIV, 197 p. 38 illus.
File format
multiple file formats
Form of item
electronic
Isbn
9783319226651
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other control number
10.1007/978-3-319-22665-1
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-3-319-22665-1
Label
The Mathematics of Medical Imaging : A Beginner’s Guide, by Timothy G. Feeman, (electronic resource)
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
txt
Content type MARC source
rdacontent
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 -- Bibliography -- Index
Dimensions
unknown
Edition
2nd ed. 2015.
Extent
XIV, 197 p. 38 illus.
File format
multiple file formats
Form of item
electronic
Isbn
9783319226651
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other control number
10.1007/978-3-319-22665-1
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-3-319-22665-1

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