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Author: F. Natterer
Publisher: Springer-Verlag
ISBN: 3663014096
Category : Technology & Engineering
Languages : de
Pages : 235
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Book Description
Author: F. Natterer
Publisher: Springer-Verlag
ISBN: 3663014096
Category : Technology & Engineering
Languages : de
Pages : 235
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Book Description
Author:
Publisher:
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Category :
Languages : en
Pages :
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Book Description
Author: Avinash C. Kak
Publisher: SIAM
ISBN: 089871494X
Category : Mathematics
Languages : en
Pages : 335
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Book Description
A comprehensive, tutorial-style introduction to the algorithms necessary for tomographic imaging.
Author: Gabor T. Herman
Publisher: Springer Science & Business Media
ISBN: 1846287235
Category : Computers
Languages : en
Pages : 302
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Book Description
This revised and updated second edition – now with two new chapters - is the only book to give a comprehensive overview of computer algorithms for image reconstruction. It covers the fundamentals of computerized tomography, including all the computational and mathematical procedures underlying data collection, image reconstruction and image display. Among the new topics covered are: spiral CT, fully 3D positron emission tomography, the linogram mode of backprojection, and state of the art 3D imaging results. It also includes two new chapters on comparative statistical evaluation of the 2D reconstruction algorithms and alternative approaches to image reconstruction.
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: G.T. Herman
Publisher: Springer Science & Business Media
ISBN: 364293157X
Category : Mathematics
Languages : en
Pages : 317
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Book Description
G.T. Herman F. Natterer Universitat des Saarlandes Medical Image Processing Group Department of Computer Science Angewandte Mathematik und State University of New York at Informatik 66 Saarbrucken Buffalo Germany 4226 Ridge Lea Road Amherst, N.Y. 14226 USA In August 1978 we have attended a working conference on Computer Aided Tomography and Ultrasonics in Medicine which was held in Haifa, Israel under the auspices of the International Federation for Information Pro cessing [1]. That meeting, in common with other meetings relating to computerized tomography, concentrated on the physical, engineering and clinical aspects of the topic, with little attention paid to the under lying mathematics, and no attention paid to recent developments in ma thematics inspired by computerized tomography (although not necessarily) useful for computerized tomography). We both felt that it would be worthwhile to organize a meeting of mathematicians which would concen trate on the mathematical aspects of computerized tomography. This vol ume (and the meeting on which it is based) is the outcome of our decision in August 1978 to attempt to bring together such a meeting. In the meantime much has been published on the topic of computerized to mography.
Author: Timothy G. Feeman
Publisher: Springer
ISBN: 3319226657
Category : Mathematics
Languages : en
Pages : 197
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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: 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: Frank Natterer
Publisher: SIAM
ISBN: 0898716225
Category : Computers
Languages : en
Pages : 226
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Book Description
This book provides readers with a superior understanding of the mathematical principles behind imaging.
Author: Thorsten M. Buzug
Publisher: Springer Science & Business Media
ISBN: 3540394087
Category : Medical
Languages : en
Pages : 522
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Book Description
This volume provides an overview of X-ray technology and the historical development of modern CT systems. The main focus of the book is a detailed derivation of reconstruction algorithms in 2D and modern 3D cone-beam systems. A thorough analysis of CT artifacts and a discussion of practical issues such as dose considerations give further insight into current CT systems. Although written mainly for graduate students, practitioners will also benefit from this book.
