Introduction To The Mathematics Of Medical Imaging
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Introduction To The Mathematics Of Medical Imaging
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Author : Charles L. Epstein
language : en
Publisher: SIAM
Release Date : 2008-01-01
Introduction To The Mathematics Of Medical Imaging written by Charles L. Epstein and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-01 with Mathematics categories.
At the heart of every medical imaging technology is a sophisticated mathematical model of the measurement process and an algorithm to reconstruct an image from the measured data. This book provides a firm foundation in the mathematical tools used to model the measurements and derive the reconstruction algorithms used in most imaging modalities in current use. In the process, it also covers many important analytic concepts and techniques used in Fourier analysis, integral equations, sampling theory, and noise analysis.This text uses X-ray computed tomography as a "pedagogical machine" to illustrate important ideas and incorporates extensive discussions of background material making the more advanced mathematical topics accessible to readers with a less formal mathematical education. The mathematical concepts are illuminated with over 200 illustrations and numerous exercises.New to the second edition are a chapter on magnetic resonance imaging (MRI), a revised section on the relationship between the continuum and discrete Fourier transforms, a new section on Grangreat's formula, an improved description of the gridding method, and a new section on noise analysis in MRI. Audience The book is appropriate for one- or two-semester courses at the advanced undergraduate or beginning graduate level on the mathematical foundations of modern medical imaging technologies. The text assumes an understanding of calculus, linear algebra, and basic mathematical analysis. Contents Preface to the Second Edition; Preface; How to Use This Book; Notational Conventions; Chapter 1: Measurements and Modeling; Chapter 2: Linear Models and Linear Equations; Chapter 3: A Basic Model for Tomography; Chapter 4: Introduction to the Fourier Transform; Chapter 5: Convolution; Chapter 6: The Radon Transform; Chapter 7: Introduction to Fourier Series; Chapter 8: Sampling; Chapter 9: Filters; Chapter 10: Implementing Shift Invariant Filters; Chapter 11: Reconstruction in X-Ray Tomography; Chapter 12: Imaging Artifacts in X-Ray Tomography; Chapter 13: Algebraic Reconstruction Techniques; Chapter 14: Magnetic Resonance Imaging; Chapter 15: Probability and Random Variables; Chapter 16: Applications of Probability; Chapter 17: Random Processes; Appendix A: Background Material; Appendix B: Basic Analysis; Index.
Introduction To The Mathematics Of Medical Imaging
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Author : Charles L. Epstein
language : en
Publisher: SIAM
Release Date : 2008-01-01
Introduction To The Mathematics Of Medical Imaging written by Charles L. Epstein and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-01 with Mathematics categories.
At the heart of every medical imaging technology is a sophisticated mathematical model of the measurement process and an algorithm to reconstruct an image from the measured data. This book provides a firm foundation in the mathematical tools used to model the measurements and derive the reconstruction algorithms used in most of these modalities. The text uses X-ray computed tomography (X-ray CT) as a 'pedagogical machine' to illustrate important ideas and its extensive discussion of background material makes the more advanced mathematical topics accessible to people with a less formal mathematical education. This new edition contains a chapter on magnetic resonance imaging (MRI), a revised section on the relationship between the continuum and discrete Fourier transforms, an improved description of the gridding method, and new sections on both Grangreat's formula and noise analysis in MR-imaging. Mathematical concepts are illuminated with over 200 illustrations and numerous exercises.
The Mathematics Of Medical Imaging
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Author : Timothy G. Feeman
language : en
Publisher: Springer Science & Business Media
Release Date : 2010
The Mathematics Of Medical Imaging written by Timothy G. Feeman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Computers categories.
Medical imaging is a major part of twenty-first century health care. This introduction explores the mathematical aspects of imaging in medicine to explain approximation methods in addition to computer implementation of inversion algorithms.
The Mathematics Of Medical Imaging
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Author : Timothy G. Feeman
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-03-10
The Mathematics Of Medical Imaging written by Timothy G. Feeman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-03-10 with Mathematics categories.
In 1979, the Nobel Prize for Medicine and Physiology was awarded jointly to Allan McLeod Cormack and Godfrey Newbold Houns eld, the two pioneering scienti- engineers primarily responsible for the development, in the 1960s and early 1970s, of computerized axial tomography, popularly known as the CAT or CT scan. In his papers [13], Cormack, then a Professor at Tufts University, in Massachusetts, dev- oped certain mathematical algorithms that, he envisioned, could be used to create an image from X-ray data. Working completely independently of Cormack and at about the same time, Houns eld, a research scientist at EMI Central Research Laboratories in the United Kingdom, designed the rst operational CT scanner as well as the rst commercially available model. (See [22] and [23]. ) Since 1980, the number of CT scans performed each year in the United States has risen from about 3 million to over 67 million. What few people who have had CT scans probably realize is that the fundamental problem behind this procedure is essentially mathematical: If we know the values of the integral of a two- or three-dimensional fu- tion along all possible cross-sections, then how can we reconstruct the function itself? This particular example of what is known as an inverse problem was studied by Johann Radon, an Austrian mathematician, in the early part of the twentieth century.
Fundamentals Of Medical Imaging
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Author : Paul Suetens
language : en
Publisher: Cambridge University Press
Release Date : 2017-05-11
Fundamentals Of Medical Imaging written by Paul Suetens and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-11 with Medical categories.
An up-to-date, concise, profound and generously illustrated survey of the complete field of medical imaging and image computing.
Medical Imaging Concepts Methodologies Tools And Applications
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Author : Management Association, Information Resources
language : en
Publisher: IGI Global
Release Date : 2016-07-18
Medical Imaging Concepts Methodologies Tools And Applications written by Management Association, Information Resources and has been published by IGI Global this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-18 with Medical categories.
Medical imaging has transformed the ways in which various conditions, injuries, and diseases are identified, monitored, and treated. As various types of digital visual representations continue to advance and improve, new opportunities for their use in medical practice will likewise evolve. Medical Imaging: Concepts, Methodologies, Tools, and Applications presents a compendium of research on digital imaging technologies in a variety of healthcare settings. This multi-volume work contains practical examples of implementation, emerging trends, case studies, and technological innovations essential for using imaging technologies for making medical decisions. This comprehensive publication is an essential resource for medical practitioners, digital imaging technologists, researchers, and medical students.
An Introduction To The Principles Of Medical Imaging
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Author : Chris Guy
language : en
Publisher: World Scientific
Release Date : 2005
An Introduction To The Principles Of Medical Imaging written by Chris Guy and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Diagnostic imaging categories.
Quantification Of Biophysical Parameters In Medical Imaging
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Author : Ingolf Sack
language : en
Publisher: Springer Nature
Release Date : 2024-11-05
Quantification Of Biophysical Parameters In Medical Imaging written by Ingolf Sack and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-05 with Medical categories.
The second edition of this book offers six new chapters covering the latest developments in quantitative medical imaging, including artificial intelligence, MRI mapping, sonography, elastography and cardiac CT. All the other existing chapters have been updated and expanded, many with new text and figures, to reflect the rapid translation and advancement of technology in this exciting area of biomedical research. This updated edition presents fundamental knowledge on the imaging quantification of biophysical parameters for clinical diagnostic purposes. Clinical imaging scanners are considered by the authors as physical measurement systems capable of quantifying intrinsic parameters for the representation of the constitution and biophysical properties of tissues in vivo. In one respect, this approach fosters the development of new imaging methods for highly reproducible, system-independent, and quantitative biomarkers. These methods are greatly detailed in the book. Alternatively, this new edition equips the reader with a better understanding of how the physical properties of tissues interact with signal generation in medical imaging, opening up new insights into the complex and fascinating relationship between structure and function in living tissues. This updated edition is of interest to all those who recognize the limitations of clinical diagnosis based primarily on visual inspection of images, and who wish to learn more about the diagnostic potential of quantitative, biophysically-based medical imaging markers, as well as the challenges posed by the scarcity of such markers for next-generation imaging technologies.
Introduction To The Science Of Medical Imaging
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Author : R. Nick Bryan
language : en
Publisher: Cambridge University Press
Release Date : 2010
Introduction To The Science Of Medical Imaging written by R. Nick Bryan and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Medical categories.
This landmark text from world-leading radiologist describes and illustrates how imaging techniques are created, analyzed and applied to biomedical problems.
Medical Imaging Physics
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Author : William R. Hendee
language : en
Publisher: John Wiley & Sons
Release Date : 2003-04-14
Medical Imaging Physics written by William R. Hendee and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-04-14 with Science categories.
This comprehensive publication covers all aspects of image formation in modern medical imaging modalities, from radiography, fluoroscopy, and computed tomography, to magnetic resonance imaging and ultrasound. It addresses the techniques and instrumentation used in the rapidly changing field of medical imaging. Now in its fourth edition, this text provides the reader with the tools necessary to be comfortable with the physical principles, equipment, and procedures used in diagnostic imaging, as well as appreciate the capabilities and limitations of the technologies.