The Mathematics of Medical Imaging: A Beginner's Guide (Springer Undergraduate Texts in Mathematics and Technology)
暫譯: 醫學影像的數學：初學者指南 (Springer 大學數學與技術系列)
Timothy G. G. Feeman
- 出版商: Springer
- 出版日期: 2016-10-29
- 售價: $2,660
- 貴賓價: 9.5 折 $2,527
- 語言: 英文
- 頁數: 212
- 裝訂: Paperback
- ISBN: 3319331078
- ISBN-13: 9783319331072
海外代購書籍(需單獨結帳)
商品描述
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 adeed 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, 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 to a real-world problem. …T
his 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
商品描述(中文翻譯)
電腦斷層掃描（CT掃描）的基本數學內容，適合數學和工程學的本科生閱讀。假設讀者沒有高級數學分析的背景，書中從零開始介紹傅立葉變換、取樣和離散近似演算法等主題，並在醫學影像的背景下進行發展。一章關於磁共振成像的內容專注於布洛赫方程的操作，這是該重要技術的基礎微分方程系統。
在備受讚譽的第一版基礎上，新增的材料使這本教科書對於課程使用更加易於理解。本版包括對拉東變換、狄拉克δ函數及其在X射線成像中的角色、Kacmarz方法和最小二乘近似、頻譜濾波等的新討論。大量的範例和練習、新的電腦基礎練習以及額外的圖形被添加進來，以進一步闡明概念。整體上，技術的使用經過重新設計，並結合開源程式設計環境R來說明範例和圖形的組成。所有R代碼作為額外的來源材料可在SpringerLink上獲得。
來自第一版的評價：
“這本書非常有價值，因為它仔細且嚴謹地探討了各種數學主題與現實世界問題的相關性。……這本書寫得很好。它達到了將多種數學主題聚焦於一個本質上是數學的現實應用的目的。”
–核醫學期刊，第51卷（12），2010年12月
“這本由Timothy Feeman撰寫的新書，真正旨在成為初學者的指南，使得這個主題對於具備多變量微積分基礎知識和一些向量及矩陣方法經驗的本科生變得可接觸。……作者以清晰和優雅的方式處理這些材料……”
–美國數學協會，2010年2月
