Mathematical Problems Of Tomography

Author : Izrailʹ Moiseevich Gelʹfand,Semen Grigorʹevich Gindikin
Publisher : American Mathematical Society(RI)
Page : 280 pages
File Size : 51,5 Mb
Release : 1990
Category : Medical
ISBN : UOM:39015021877462

Get Book

Mathematical Problems of Tomography by Izrailʹ Moiseevich Gelʹfand,Semen Grigorʹevich Gindikin Pdf

As early as 1917, Radon derived an explicit formula for the reconstruction of a function on the plane, given its integrals over all lines. In the late 1960s, the first applications of the Radon formula appeared, in radio astronomy and then in electron micrography. The use of the Radon formula for constructing tomograms, made possible by the advent of the computer, saw its first use in clinical medicine in 1970 and earned its developers the Nobel Prize in medicine.

Author : F. Natterer
Publisher : Springer-Verlag
Page : 235 pages
File Size : 52,8 Mb
Release : 2013-03-09
Category : Technology & Engineering
ISBN : 9783663014096

Get Book

The Mathematics of Computerized Tomography by F. Natterer Pdf

Author : Alexander G. Ramm
Publisher : Springer Science & Business Media
Page : 262 pages
File Size : 45,8 Mb
Release : 2013-11-11
Category : Technology & Engineering
ISBN : 9781402079757

Get Book

Inverse Problems, Tomography, and Image Processing by Alexander G. Ramm Pdf

Proceedings of Sessions from the First Congress of the International Society for Analysis, Applications, and Computind held in Newark, Delaware, June 2-6, 1997

Author : Gestur Ólafsson,Eric Todd Quinto
Publisher : American Mathematical Soc.
Page : 176 pages
File Size : 48,9 Mb
Release : 2006
Category : Imagerie médicale - Congrès
ISBN : 9780821839300

Get Book

The Radon Transform, Inverse Problems, and Tomography by Gestur Ólafsson,Eric Todd Quinto Pdf

Since their emergence in 1917, tomography and inverse problems remain active and important fields that combine pure and applied mathematics and provide strong interplay between diverse mathematical problems and applications. The applied side is best known for medical and scientific use, in particular, medical imaging, radiotherapy, and industrial non-destructive testing. Doctors use tomography to see the internal structure of the body or to find functional information, such asmetabolic processes, noninvasively. Scientists discover defects in objects, the topography of the ocean floor, and geological information using X-rays, geophysical measurements, sonar, or other data. This volume, based on the lectures in the Short Course The Radon Transform and Applications to InverseProblems at the American Mathematical Society meeting in Atlanta, GA, January 3-4, 2005, brings together articles on mathematical aspects of tomography and related inverse problems. The articles cover introductory material, theoretical problems, and practical issues in 3-D tomography, impedance imaging, local tomography, wavelet methods, regularization and approximate inverse, sampling, and emission tomography. All contributions are written for a general audience, and the authors have includedreferences for further reading.

Author : Mikhail M. Lavrent'ev,Sergei M. Zerkal,Oleg E. Trofimov
Publisher : Walter de Gruyter GmbH & Co KG
Page : 136 pages
File Size : 48,7 Mb
Release : 2014-07-24
Category : Mathematics
ISBN : 9783110940930

Get Book

Computer Modelling in Tomography and Ill-Posed Problems by Mikhail M. Lavrent'ev,Sergei M. Zerkal,Oleg E. Trofimov Pdf

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 : Per Christian Hansen,Jakob Jorgensen,William R. B. Lionheart
Publisher : SIAM
Page : 355 pages
File Size : 53,9 Mb
Release : 2021-09-25
Category : Mathematics
ISBN : 9781611976670

Get Book

Computed Tomography by Per Christian Hansen,Jakob Jorgensen,William R. B. Lionheart Pdf

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 : Esam M A Hussein
Publisher : Elsevier
Page : 303 pages
File Size : 42,6 Mb
Release : 2011-06-01
Category : Science
ISBN : 9780123877789

Get Book

Computed Radiation Imaging by Esam M A Hussein Pdf

Computer-assisted imaging with radiation (x- and gamma rays) is an integral part of modern medical-diagnostic practice. This imaging technology is also slowly finding its way into industrial applications. Although the technology is well developed, there is a need for further improvement to enhance image quality, reduce artifacts, minimize patient radiation exposure, compete with and complement other imaging methods (such as magnetic resonance imaging and ultrasonics), and accommodate dense and large objects encountered in industrial applications.Scientists and engineers, attempting to progress this technology, are faced with an enormous amount of literature, addressing the imaging problem from various view points. This book provides a single source that addresses both the physical and mathematical aspects of the imaging problem in a consistent and comprehensive manner. Discusses the inherent physical and numerical capabilities and limitations of the methods presented for both the forward and inverse problems Provides information on available Internet resources and software Written in a manner that makes it readable by physicists, mathematicians, engineers and computer scientists – avoids, as much as possible, the use of specialized terminology without clear introduction and definition

Author : Regina Y. Liu,William E. Strawderman,Cun-Hui Zhang
Publisher : IMS
Page : 286 pages
File Size : 41,7 Mb
Release : 2007
Category : Computers
ISBN : 0940600706

Get Book

Complex Datasets and Inverse Problems by Regina Y. Liu,William E. Strawderman,Cun-Hui Zhang Pdf

Author : Alexander G. Ramm
Publisher : Unknown
Page : 272 pages
File Size : 50,5 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 148991899X

Get Book

Inverse Problems, Tomography, and Image Processing by Alexander G. Ramm Pdf

Author : Anthony J. Devaney
Publisher : Cambridge University Press
Page : 537 pages
File Size : 45,9 Mb
Release : 2012-06-21
Category : Science
ISBN : 9781139510141

Get Book

Mathematical Foundations of Imaging, Tomography and Wavefield Inversion by Anthony J. Devaney Pdf

Inverse problems are of interest and importance across many branches of physics, mathematics, engineering and medical imaging. In this text, the foundations of imaging and wavefield inversion are presented in a clear and systematic way. The necessary theory is gradually developed throughout the book, progressing from simple wave equation based models to vector wave models. By combining theory with numerous MATLAB based examples, the author promotes a complete understanding of the material and establishes a basis for real world applications. Key topics of discussion include the derivation of solutions to the inhomogeneous and homogeneous Helmholtz equations using Green function techniques; the propagation and scattering of waves in homogeneous and inhomogeneous backgrounds; and the concept of field time reversal. Bridging the gap between mathematics and physics, this multidisciplinary book will appeal to graduate students and researchers alike. Additional resources including MATLAB codes and solutions are available online at www.cambridge.org/9780521119740.

Author : Gabor T. Herman
Publisher : Unknown
Page : 736 pages
File Size : 54,8 Mb
Release : 1987
Category : Geometric tomography
ISBN : UCSD:31822035099530

Get Book

Basic Methods of Tomography and Inverse Problems by Gabor T. Herman Pdf

Author : Gabor T. Herman,Attila Kuba
Publisher : Springer Science & Business Media
Page : 401 pages
File Size : 50,9 Mb
Release : 2008-01-19
Category : Technology & Engineering
ISBN : 9780817645434

Get Book

Advances in Discrete Tomography and Its Applications by Gabor T. Herman,Attila Kuba Pdf

The book provides a unified presentation of new methods, algorithms, and select applications that are the foundations of multidimensional image construction and reconstruction. The self-contained survey chapters, written by leading mathematicians, engineers, and computer scientists, present cutting-edge research and results in the field. Three main areas are covered: theoretical results, algorithms, and practical applications. Following an historical and introductory overview of the field, the book explores the various mathematical and computational problems of discrete tomography with an emphasis on new applications.

Author : Alexander G. Ramm
Publisher : Springer
Page : 0 pages
File Size : 44,7 Mb
Release : 1998-05-31
Category : Mathematics
ISBN : 0306458284

Get Book

Inverse Problems, Tomography, and Image Processing by Alexander G. Ramm Pdf

Proceedings of Sessions from the First Congress of the International Society for Analysis, Applications, and Computind held in Newark, Delaware, June 2-6, 1997

Author : Luis L. Bonilla
Publisher : Springer
Page : 200 pages
File Size : 51,5 Mb
Release : 2009-06-19
Category : Mathematics
ISBN : 9783540785477

Get Book

Inverse Problems and Imaging by Luis L. Bonilla Pdf

Nowadays we are facing numerous and important imaging problems: nondestructive testing of materials, monitoring of industrial processes, enhancement of oil production by efficient reservoir characterization, emerging developments in noninvasive imaging techniques for medical purposes - computerized tomography (CT), magnetic resonance imaging (MRI), positron emission tomography (PET), X-ray and ultrasound tomography, etc. In the CIME Summer School on Imaging (Martina Franca, Italy 2002), leading experts in mathematical techniques and applications presented broad and useful introductions for non-experts and practitioners alike to many aspects of this exciting field. The volume contains part of the above lectures completed and updated by additional contributions on other related topics.

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

Get Book

Mathematics and Physics of Emerging Biomedical Imaging by 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 Pdf

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.