大葉大學圖書館 |

The mathematics of medical imaging[electronic resource] :a beginner's guide /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
杜威分類號:	616.0754
書名/作者:	The mathematics of medical imaging : a beginner's guide // by Timothy G. Feeman.
作者:	Feeman, Timothy G.
出版者:	Cham : : Springer International Publishing :, 2015.
面頁冊數:	xiv, 197 p. : : ill., digital ;; 24 cm.
Contained By:	Springer eBooks
標題:	Diagnostic imaging - Mathematics.
標題:	Mathematics.
標題:	Radiology.
標題:	Computer science - Mathematics.
標題:	Computer graphics.
標題:	Functional analysis.
標題:	Integral transforms.
標題:	Calculus, Operational.
標題:	Biomedical engineering.
標題:	Imaging / Radiology.
標題:	Computer Imaging, Vision, Pattern Recognition and Graphics.
標題:	Integral Transforms, Operational Calculus.
標題:	Math Applications in Computer Science.
ISBN:	9783319226651
ISBN:	9783319226644
內容註:	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.
摘要、提要註:	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.
電子資源:	http://dx.doi.org/10.1007/978-3-319-22665-1

The mathematics of medical imaging[electronic resource] :a beginner's guide /
Feeman, Timothy G.

The mathematics of medical imaginga beginner's guide /[electronic resource] :by Timothy G. Feeman. - 2nd ed. - Cham :Springer International Publishing :2015. - xiv, 197 p. :ill., digital ;24 cm. - Springer undergraduate texts in mathematics and technology,1867-5506. - Springer undergraduate texts in mathematics and technology..

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.

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.

ISBN: 9783319226651

Standard No.: 10.1007/978-3-319-22665-1doiSubjects--Topical Terms:

635711
Diagnostic imaging
--Mathematics.

LC Class. No.: RC78.7.D53

Dewey Class. No.: 616.0754

The mathematics of medical imaging[electronic resource] :a beginner's guide /
LDR:03908nam a2200337 a 4500 001 444289
003 DE-He213
005 20160414140400.0
006 m d
007 cr nn 008maaau
008 160715s2015 gw s 0 eng d
020 $a 9783319226651 $q (electronic bk.)
020 $a 9783319226644 $q (paper)
024 7 $a 10.1007/978-3-319-22665-1 $2 doi
035 $a 978-3-319-22665-1
040 $a GP $c GP
041 0 $a eng
050 4 $a RC78.7.D53
072 7 $a PBKF $2 bicssc
072 7 $a MAT037000 $2 bisacsh
082 0 4 $a 616.0754 $2 23
090 $a RC78.7.D53 $b F295 2015
100 1 $a Feeman, Timothy G. $3 635710
245 1 4 $a The mathematics of medical imaging $h [electronic resource] : $b a beginner's guide / $c by Timothy G. Feeman.
250 $a 2nd ed.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2015.
300 $a xiv, 197 p. : $b ill., digital ; $c 24 cm.
490 1 $a Springer undergraduate texts in mathematics and technology, $x 1867-5506
505 0 $a 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.
520 $a 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.
650 0 $a Diagnostic imaging $x Mathematics. $3 635711
650 0 $a Mathematics. $3 172349
650 0 $a Radiology. $3 489264
650 0 $a Computer science $x Mathematics. $3 382369
650 0 $a Computer graphics. $3 172147
650 0 $a Functional analysis. $3 403818
650 0 $a Integral transforms. $3 610755
650 0 $a Calculus, Operational. $3 556839
650 0 $a Biomedical engineering. $3 218538
650 2 4 $a Imaging / Radiology. $3 463785
650 2 4 $a Computer Imaging, Vision, Pattern Recognition and Graphics. $3 465964
650 2 4 $a Integral Transforms, Operational Calculus. $3 602459
650 2 4 $a Math Applications in Computer Science. $3 466204
710 2 $a SpringerLink (Online service) $3 463450
773 0 $t Springer eBooks
830 0 $a Springer undergraduate texts in mathematics and technology. $3 512262
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-22665-1
950 $a Mathematics and Statistics (Springer-11649)