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Author: Max A. Viergever
Publisher: Springer Science & Business Media
ISBN: 3642833063
Category : Computers
Languages : en
Pages : 535
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Book Description
Medical imaging is an important and rapidly expanding area in medical science. Many of the methods employed are essentially digital, for example computerized tomography, and the subject has become increasingly influenced by develop ments in both mathematics and computer science. The mathematical problems have been the concern of a relatively small group of scientists, consisting mainly of applied mathematicians and theoretical physicists. Their efforts have led to workable algorithms for most imaging modalities. However, neither the fundamentals, nor the limitations and disadvantages of these algorithms are known to a sufficient degree to the physicists, engineers and physicians trying to implement these methods. It seems both timely and important to try to bridge this gap. This book summarizes the proceedings of a NATO Advanced Study Institute, on these topics, that was held in the mountains of Tuscany for two weeks in the late summer of 1986. At another (quite different) earlier meeting on medical imaging, the authors noted that each of the speakers had given, there, a long introduction in their general area, stated that they did not have time to discuss the details of the new work, but proceeded to show lots of clinical results, while excluding any mathematics associated with the area.
Author: Max A. Viergever
Publisher: Springer Science & Business Media
ISBN: 3642833063
Category : Computers
Languages : en
Pages : 535
Get Book Here
Book Description
Medical imaging is an important and rapidly expanding area in medical science. Many of the methods employed are essentially digital, for example computerized tomography, and the subject has become increasingly influenced by develop ments in both mathematics and computer science. The mathematical problems have been the concern of a relatively small group of scientists, consisting mainly of applied mathematicians and theoretical physicists. Their efforts have led to workable algorithms for most imaging modalities. However, neither the fundamentals, nor the limitations and disadvantages of these algorithms are known to a sufficient degree to the physicists, engineers and physicians trying to implement these methods. It seems both timely and important to try to bridge this gap. This book summarizes the proceedings of a NATO Advanced Study Institute, on these topics, that was held in the mountains of Tuscany for two weeks in the late summer of 1986. At another (quite different) earlier meeting on medical imaging, the authors noted that each of the speakers had given, there, a long introduction in their general area, stated that they did not have time to discuss the details of the new work, but proceeded to show lots of clinical results, while excluding any mathematics associated with the area.
Author: Timothy G. Feeman
Publisher: Springer Science & Business Media
ISBN: 0387927115
Category : Computers
Languages : en
Pages : 150
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Book Description
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.
Author: Charles L. Epstein
Publisher: SIAM
ISBN: 9780898717792
Category : Mathematics
Languages : en
Pages : 794
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Book Description
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.
Author: Timothy G. Feeman
Publisher: Springer Science & Business Media
ISBN: 0387927123
Category : Mathematics
Languages : en
Pages : 151
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Book Description
This text explores medical imaging, one of the most significant areas of recent mathematical applications, in a concise manner accessible to undergraduate students. The author emphasizes the mathematical aspects of medical imaging, including not only the theoretical background, but also the role of approximation methods and the computer implementation of the inversion algorithms. In twenty-first century health care, CAT scans, ultrasounds, and MRIs are commonplace. Significant computational advances, along with the development, design, and improvement of the machines themselves, can only occur in conjunction with a proper understanding of the mathematics. This book is inherently interdisciplinary in nature, and therefore is appropriate for students of engineering, physics, and computer science, in addition to mathematics.
Author: Roger Bourne
Publisher: Springer Science & Business Media
ISBN: 1848820879
Category : Medical
Languages : en
Pages : 209
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Book Description
In general, image processing texts are intended for students of engineering and computer science, and there is little written at all on the specific requirements of medical image processing. Students of medical radiation science (Diagnostic radiography, Nuclear medicine, Radiation therapy) usually have minimal mathematical and computer science training and find the available texts incomprehensible. A text that explains the principles of image processing in minimally-mathematical language is needed for these students. Contrary to the claims of some textbook authors, the vast majority of technologists that process images do not need to understand the mathematics involved, but would nevertheless benefit from a thorough understanding of the general process.
Author: Timothy G. Feeman
Publisher: Springer
ISBN: 3319226657
Category : Mathematics
Languages : en
Pages : 205
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Book Description
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
Author: National Library of Medicine (U.S.)
Publisher:
ISBN:
Category : Medicine
Languages : en
Pages : 1060
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Book Description
First multi-year cumulation covers six years: 1965-70.
Author: Otmar Scherzer
Publisher: Springer Science & Business Media
ISBN: 0387929193
Category : Mathematics
Languages : en
Pages : 1626
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Book Description
The Handbook of Mathematical Methods in Imaging provides a comprehensive treatment of the mathematical techniques used in imaging science. The material is grouped into two central themes, namely, Inverse Problems (Algorithmic Reconstruction) and Signal and Image Processing. Each section within the themes covers applications (modeling), mathematics, numerical methods (using a case example) and open questions. Written by experts in the area, the presentation is mathematically rigorous. The entries are cross-referenced for easy navigation through connected topics. Available in both print and electronic forms, the handbook is enhanced by more than 150 illustrations and an extended bibliography. It will benefit students, scientists and researchers in applied mathematics. Engineers and computer scientists working in imaging will also find this handbook useful.
Author: Jerry L. Prince
Publisher: Springer Science & Business Media
ISBN: 3642024971
Category : Computers
Languages : en
Pages : 744
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Book Description
This book constitutes the refeered proceedings of the 21st International Conference on Information Processing in Medical Imaging, IPMI 2009, held in Williamsburg, VA, USA, in July 2009 The 26 revised full papers and 33 revised poster papers presented were carefully reviewed and selected from 150 submissions. The papers are organized in topical sections on diffusion imaging, PET imaging, image registration, functional networks, space curves, tractography, microscopy, exploratory analyses, features and detection, image guided surgery, shape analysis, motion, and segmentation and validation.
Author: Yair Censor
Publisher: Oxford University Press, USA
ISBN: 9780195100624
Category : Computers
Languages : en
Pages : 574
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Book Description
This book offers a unique pathway to methods of parallel optimization by introducing parallel computing ideas into both optimization theory and into some numerical algorithms for large-scale optimization problems. The three parts of the book bring together relevant theory, careful study of algorithms, and modeling of significant real world problems such as image reconstruction, radiation therapy treatment planning, financial planning, transportation and multi-commodity network flow problems, planning under uncertainty, and matrix balancing problems.
