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Author : F. Natterer
Publisher : Springer-Verlag
Page : 235 pages
File Size : 53,7 Mb
Release : 2013-03-09
Category : Technology & Engineering
ISBN : 9783663014096
Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 51,7 Mb
Release : 1986
Category : Electronic
ISBN : OCLC:471879093
Author : Gabor T. Herman
Publisher : Springer Science & Business Media
Page : 302 pages
File Size : 42,6 Mb
Release : 2009-07-14
Category : Computers
ISBN : 9781846287237
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 : G.T. Herman,F. Natterer
Publisher : Springer Science & Business Media
Page : 317 pages
File Size : 43,9 Mb
Release : 2013-03-12
Category : Mathematics
ISBN : 9783642931574
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 : Avinash C. Kak,Malcolm Slaney
Publisher : SIAM
Page : 335 pages
File Size : 41,7 Mb
Release : 2001-01-01
Category : Mathematics
ISBN : 9780898714944
A comprehensive, tutorial-style introduction to the algorithms necessary for tomographic imaging.
Author : Committee on the Mathematics and Physics of Emerging Dynamic Biomedical Imaging,Commission on Physical Sciences, Mathematics, and Applications,Division on Engineering and Physical Sciences,National Research Council
Publisher : National Academies Press
Page : 261 pages
File Size : 47,7 Mb
Release : 1996-03-13
Category : Science
ISBN : 9780309552929
This cross-disciplinary book documents the key research challenges in the mathematical sciences and physics that could enable the economical development of novel biomedical imaging devices. It is hoped that the infusion of new insights from mathematical scientists and physicists will accelerate progress in imaging. Incorporating input from dozens of biomedical researchers who described what they perceived as key open problems of imaging that are amenable to attack by mathematical scientists and physicists, this book introduces the frontiers of biomedical imaging, especially the imaging of dynamic physiological functions, to the educated nonspecialist. Ten imaging modalities are covered, from the well-established (e.g., CAT scanning, MRI) to the more speculative (e.g., electrical and magnetic source imaging). For each modality, mathematics and physics research challenges are identified and a short list of suggested reading offered. Two additional chapters offer visions of the next generation of surgical and interventional techniques and of image processing. A final chapter provides an overview of mathematical issues that cut across the various modalities.
Author : Per Christian Hansen,Jakob Jorgensen,William R. B. Lionheart
Publisher : SIAM
Page : 355 pages
File Size : 51,9 Mb
Release : 2021-09-25
Category : Mathematics
ISBN : 9781611976670
This book describes fundamental computational methods for image reconstruction in computed tomography (CT) with a focus on a pedagogical presentation of these methods and their underlying concepts. Insights into the advantages, limitations, and theoretical and computational aspects of the methods are included, giving a balanced presentation that allows readers to understand and implement CT reconstruction algorithms. Unique in its emphasis on the interplay between modeling, computing, and algorithm development, Computed Tomography: Algorithms, Insight, and Just Enough Theory develops the mathematical and computational aspects of three main classes of reconstruction methods: classical filtered back-projection, algebraic iterative methods, and variational methods based on nonlinear numerical optimization algorithms. It spotlights the link between CT and numerical methods, which is rarely discussed in current literature, and describes the effects of incomplete data using both microlocal analysis and singular value decomposition (SVD). This book sets the stage for further exploration of CT algorithms. Readers will be able to grasp the underlying mathematical models to motivate and derive the basic principles of CT reconstruction and will gain basic understanding of fundamental computational challenges of CT, such as the influence of noisy and incomplete data, as well as the reconstruction capabilities and the convergence of the iterative algorithms. Exercises using MATLAB are included, allowing readers to experiment with the algorithms and making the book suitable for teaching and self-study. Computed Tomography: Algorithms, Insight, and Just Enough Theory is primarily aimed at students, researchers, and practitioners interested in the computational aspects of X-ray CT and is also relevant for anyone working with other forms of tomography, such as neutron and electron tomography, that share the same mathematical formulation. With its basis in lecture notes developed for a PhD course, it is appropriate as a textbook for courses on computational methods for X-ray CT and computational methods for inverse problems.
Author : Timothy G. Feeman
Publisher : Unknown
Page : 128 pages
File Size : 50,5 Mb
Release : 2015
Category : Electronic
ISBN : 3319226665
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 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.
Author : Timothy G. Feeman
Publisher : Springer Science & Business Media
Page : 150 pages
File Size : 42,9 Mb
Release : 2010
Category : Computers
ISBN : 9780387927114
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 : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 46,7 Mb
Release : 2024-07-02
Category : Electronic
ISBN : 0387102779
Author : Timothy G. Feeman
Publisher : Springer
Page : 197 pages
File Size : 47,6 Mb
Release : 2015-11-19
Category : Mathematics
ISBN : 9783319226651
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 : Frank Natterer
Publisher : SIAM
Page : 240 pages
File Size : 44,8 Mb
Release : 2001-06-01
Category : Mathematics
ISBN : 9780898714937
This book provides a unified view of tomographic techniques and an in-depth treatment of reconstruction algorithms.
Author : Mikhail M. Lavrent'ev,Sergei M. Zerkal,Oleg E. Trofimov
Publisher : Walter de Gruyter GmbH & Co KG
Page : 136 pages
File Size : 49,6 Mb
Release : 2014-07-24
Category : Mathematics
ISBN : 9783110940930
Comparatively weakly researched untraditional tomography problems are solved because of new achievements in calculation mathematics and the theory of ill-posed problems, the regularization process of solving ill-posed problems, and the increase of stability. Experiments show possibilities and applicability of algorithms of processing tomography data. This monograph is devoted to considering these problems in connection with series of ill-posed problems in tomography settings arising from practice.The book includes chapters to the following themes: Mathematical basis of the method of computerized tomography Cone-beam tomography reconstruction Inverse kinematic problem in the tomographic setting
Author : G T Herman,F Natterer
Publisher : Unknown
Page : 320 pages
File Size : 46,6 Mb
Release : 1981-01-01
Category : Electronic
ISBN : 3642931588
Author : Frank Natterer,Frank Wuebbeling
Publisher : SIAM
Page : 226 pages
File Size : 52,6 Mb
Release : 2001-01-01
Category : Computers
ISBN : 9780898716221
This book provides readers with a superior understanding of the mathematical principles behind imaging.