Download or read book Mathematical Aspects of Computerized Tomography written by G.T. Herman and published by Springer Science & Business Media. This book was released on 2013-03-12 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Mathematical Aspects of Computerized Tomography written by G T Herman and published by . This book was released on 1981-01-01 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Aspects of Computerized Tomography written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Aspects of Computerized Tomography written by Gabor T. Herman and published by Springer. This book was released on 1981-01-01 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Mathematics of Computerized Tomography written by Frank Natterer and published by SIAM. This book was released on 2001-06-01 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a unified view of tomographic techniques and an in-depth treatment of reconstruction algorithms.
Download or read book Computed Tomography written by Lawrence A. Shepp and published by American Mathematical Soc.. This book was released on 1983 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this volume, the collection of articles by Shepp, Helgason, Radon, and others, gives mathematicians unfamiliar with applied mathematics a rather full spectrum of models of computed tomography. Included are nice problems both relevant and of intrinsic interest suggested by each of the papers.
Download or read book Mathematical aspects of computerized tomography written by and published by . This book was released on 1980 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Mathematics of Computerized Tomography written by F. Natterer and published by Springer-Verlag. This book was released on 2013-03-09 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Principles of Computerized Tomographic Imaging written by Avinash C. Kak and published by SIAM. This book was released on 2001-01-01 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive, tutorial-style introduction to the algorithms necessary for tomographic imaging.
Download or read book Mathematical Methods in Tomography written by Gabor T. Herman and published by Springer. This book was released on 2006-11-14 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: The conference was devoted to the discussion of present and future techniques in medical imaging, including 3D x-ray CT, ultrasound and diffraction tomography, and biomagnetic ima- ging. The mathematical models, their theoretical aspects and the development of algorithms were treated. The proceedings contains surveys on reconstruction in inverse obstacle scat- tering, inversion in 3D, and constrained least squares pro- blems.Research papers include besides the mentioned imaging techniques presentations on image reconstruction in Hilbert spaces, singular value decompositions, 3D cone beam recon- struction, diffuse tomography, regularization of ill-posed problems, evaluation reconstruction algorithms and applica- tions in non-medical fields. Contents: Theoretical Aspects: J.Boman: Helgason' s support theorem for Radon transforms-a newproof and a generalization -P.Maass: Singular value de- compositions for Radon transforms- W.R.Madych: Image recon- struction in Hilbert space -R.G.Mukhometov: A problem of in- tegral geometry for a family of rays with multiple reflec- tions -V.P.Palamodov: Inversion formulas for the three-di- mensional ray transform - Medical Imaging Techniques: V.Friedrich: Backscattered Photons - are they useful for a surface - near tomography - P.Grangeat: Mathematical frame- work of cone beam 3D reconstruction via the first derivative of the Radon transform -P.Grassin,B.Duchene,W.Tabbara: Dif- fraction tomography: some applications and extension to 3D ultrasound imaging -F.A.Gr}nbaum: Diffuse tomography: a re- fined model -R.Kress,A.Zinn: Three dimensional reconstruc- tions in inverse obstacle scattering -A.K.Louis: Mathemati- cal questions of a biomagnetic imaging problem - Inverse Problems and Optimization: Y.Censor: On variable block algebraic reconstruction techniques -P.P.Eggermont: On Volterra-Lotka differential equations and multiplicative algorithms for monotone complementary problems
Download or read book Fundamentals of Computerized Tomography written by Gabor T. Herman and published by Springer Science & Business Media. This book was released on 2009-07-14 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Computed Tomography written by Per Christian Hansen and published by SIAM. This book was released on 2021-09-25 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Introduction to the Mathematics of Medical Imaging written by Charles L. Epstein and published by SIAM. This book was released on 2008-01-01 with total page 794 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Mathematics of Computerized Tomography written by and published by . This book was released on 1986 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Mathematics of Medical Imaging written by Timothy G. Feeman and published by Springer Science & Business Media. This book was released on 2010-03-10 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Computer Modelling in Tomography and Ill Posed Problems written by Mikhail M. Lavrent'ev and published by Walter de Gruyter GmbH & Co KG. This book was released on 2014-07-24 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Computerized Tomography written by M. M. Lavrent'ev and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-05-18 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: No detailed description available for "Computerized Tomography".
