LEADER 06088nam 22008055 450 001 9910300258103321 005 20200630024408.0 010 $a3-319-22665-7 024 7 $a10.1007/978-3-319-22665-1 035 $a(CKB)3710000000521699 035 $a(SSID)ssj0001585295 035 $a(PQKBManifestationID)16262903 035 $a(PQKBTitleCode)TC0001585295 035 $a(PQKBWorkID)14864052 035 $a(PQKB)11737774 035 $a(DE-He213)978-3-319-22665-1 035 $a(MiAaPQ)EBC5590735 035 $a(PPN)190536012 035 $a(EXLCZ)993710000000521699 100 $a20151119d2015 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 14$aThe Mathematics of Medical Imaging $eA Beginner?s Guide /$fby Timothy G. Feeman 205 $a2nd ed. 2015. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2015. 215 $a1 online resource (XIV, 197 p. 38 illus.) 225 1 $aSpringer Undergraduate Texts in Mathematics and Technology,$x1867-5506 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-319-22664-9 327 $aPreface 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. 330 $aThe 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. 410 0$aSpringer Undergraduate Texts in Mathematics and Technology,$x1867-5506 606 $aFunctional analysis 606 $aRadiology 606 $aOptical data processing 606 $aBiomedical engineering 606 $aIntegral transforms 606 $aCalculus, Operational 606 $aComputer science?Mathematics 606 $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066 606 $aImaging / Radiology$3https://scigraph.springernature.com/ontologies/product-market-codes/H29005 606 $aComputer Imaging, Vision, Pattern Recognition and Graphics$3https://scigraph.springernature.com/ontologies/product-market-codes/I22005 606 $aBiomedical Engineering and Bioengineering$3https://scigraph.springernature.com/ontologies/product-market-codes/T2700X 606 $aIntegral Transforms, Operational Calculus$3https://scigraph.springernature.com/ontologies/product-market-codes/M12112 606 $aMath Applications in Computer Science$3https://scigraph.springernature.com/ontologies/product-market-codes/I17044 615 0$aFunctional analysis. 615 0$aRadiology. 615 0$aOptical data processing. 615 0$aBiomedical engineering. 615 0$aIntegral transforms. 615 0$aCalculus, Operational. 615 0$aComputer science?Mathematics. 615 14$aFunctional Analysis. 615 24$aImaging / Radiology. 615 24$aComputer Imaging, Vision, Pattern Recognition and Graphics. 615 24$aBiomedical Engineering and Bioengineering. 615 24$aIntegral Transforms, Operational Calculus. 615 24$aMath Applications in Computer Science. 676 $a616.0754 700 $aFeeman$b Timothy G$4aut$4http://id.loc.gov/vocabulary/relators/aut$0451114 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300258103321 996 $aThe Mathematics of Medical Imaging$92494810 997 $aUNINA