The Universality Of The Radon Transform

Author : Leon Ehrenpreis
Publisher : OUP Oxford
ISBN 13 : 9780198509783
Total Pages : 746 pages
Book Rating : 4.82/5 ( download)

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Download or read book The Universality of the Radon Transform written by Leon Ehrenpreis and published by OUP Oxford. This book was released on 2003 with total page 746 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by a leading scholar in mathematics, this monograph discusses the Radon transform, a field that has wide ranging applications to X-ray technology, partial differential equations, nuclear magnetic resonance scanning and tomography. In this book, Ehrenpreis focuses on recent research and highlights the strong relationship between high-level pure mathematics and applications of the Radon transform to areas such as medical imaging.

Author : Gestur Ólafsson
Publisher : American Mathematical Soc.
ISBN 13 : 0821843273
Total Pages : 282 pages
Book Rating : 4.77/5 ( download)

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Download or read book Radon Transforms, Geometry, and Wavelets written by Gestur Ólafsson and published by American Mathematical Soc.. This book was released on 2008 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is based on two special sessions held at the AMS Annual Meeting in New Orleans in January 2007, and a satellite workshop held in Baton Rouge on January 4-5, 2007. It consists of invited expositions that together represent a broad spectrum of fields, stressing surprising interactions and connections between areas that are normally thought of as disparate. The main topics are geometry and integral transforms. On the one side are harmonic analysis, symmetric spaces,representation theory (the groups include continuous and discrete, finite and infinite, compact and non-compact), operator theory, PDE, and mathematical probability. Moving in the applied direction we encounter wavelets, fractals, and engineering topics such as frames and signal and image processing.The subjects covered in this book form a unified whole, and they stand at the crossroads of pure and applied mathematics. The articles cover a broad range in harmonic analysis, with the main themes related to integral geometry, the Radon transform, wavelets and frame theory. These themes can loosely be grouped together as follows:Frame Theory and ApplicationsHarmonic Analysis and Function SpacesHarmonic Analysis and Number TheoryIntegral Geometry and Radon TransformsMultiresolution Analysis, Wavelets, and Applications

Author : Gestur Ólafsson
Publisher : American Mathematical Soc.
ISBN 13 : 0821839306
Total Pages : 176 pages
Book Rating : 4.00/5 ( download)

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Download or read book The Radon Transform, Inverse Problems, and Tomography written by Gestur Ólafsson and published by American Mathematical Soc.. This book was released on 2006 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Peter Kuchment
Publisher : SIAM
ISBN 13 : 1611973295
Total Pages : 238 pages
Book Rating : 4.97/5 ( download)

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Download or read book The Radon Transform and Medical Imaging written by Peter Kuchment and published by SIAM. This book was released on 2014-01-01 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book surveys the main mathematical ideas and techniques behind some well-established imaging modalities such as X-ray CT and emission tomography, as well as a variety of newly developing coupled-physics or hybrid techniques, including thermoacoustic tomography. The Radon Transform and Medical Imaging emphasizes mathematical techniques and ideas arising across the spectrum of medical imaging modalities and explains important concepts concerning inversion, stability, incomplete data effects, the role of interior information, and other issues critical to all medical imaging methods. For nonexperts, the author provides appendices that cover background information on notation, Fourier analysis, geometric rays, and linear operators. The vast bibliography, with over 825 entries, directs readers to a wide array of additional information sources on medical imaging for further study.

Author : Boris Rubin
Publisher : Cambridge University Press
ISBN 13 : 0521854598
Total Pages : 595 pages
Book Rating : 4.97/5 ( download)

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Download or read book Introduction to Radon Transforms written by Boris Rubin and published by Cambridge University Press. This book was released on 2015-11-12 with total page 595 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive introduction to basic operators of integral geometry and the relevant harmonic analysis for students and researchers.

Author : Hershel M. Farkas
Publisher : Springer Science & Business Media
ISBN 13 : 1461440750
Total Pages : 563 pages
Book Rating : 4.58/5 ( download)

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Download or read book From Fourier Analysis and Number Theory to Radon Transforms and Geometry written by Hershel M. Farkas and published by Springer Science & Business Media. This book was released on 2012-09-18 with total page 563 pages. Available in PDF, EPUB and Kindle. Book excerpt: ​​​A memorial conference for Leon Ehrenpreis was held at Temple University, November 15-16, 2010. In the spirit of Ehrenpreis’s contribution to mathematics, the papers in this volume, written by prominent mathematicians, represent the wide breadth of subjects that Ehrenpreis traversed in his career, including partial differential equations, combinatorics, number theory, complex analysis and a bit of applied mathematics. With the exception of one survey article, the papers in this volume are all new results in the various fields in which Ehrenpreis worked . There are papers in pure analysis, papers in number theory, papers in what may be called applied mathematics such as population biology and parallel refractors and papers in partial differential equations. The mature mathematician will find new mathematics and the advanced graduate student will find many new ideas to explore.​A biographical sketch of Leon Ehrenpreis by his daughter, a professional journalist, enhances the memorial tribute and gives the reader a glimpse into the life and career of a great mathematician.

Author : Gaik Ambartsoumian
Publisher : World Scientific
ISBN 13 : 9811242453
Total Pages : 248 pages
Book Rating : 4.58/5 ( download)

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Download or read book Generalized Radon Transforms And Imaging By Scattered Particles: Broken Rays, Cones, And Stars In Tomography written by Gaik Ambartsoumian and published by World Scientific. This book was released on 2023-03-14 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: A generalized Radon transform (GRT) maps a function to its weighted integrals along a family of curves or surfaces. Such operators appear in mathematical models of various imaging modalities. The GRTs integrating along smooth curves and surfaces (lines, planes, circles, spheres, amongst others) have been studied at great lengths for decades, but relatively little attention has been paid to transforms integrating along non-smooth trajectories. Recently, an interesting new class of GRTs emerged at the forefront of research in integral geometry. The two common features of these transforms are the presence of a 'vertex' in their paths of integration (broken rays, cones, and stars) and their relation to imaging techniques based on physics of scattered particles (Compton camera imaging, single scattering tomography, etc).This book covers the relevant imaging modalities, their mathematical models, and the related GRTs. The discussion of the latter comprises a thorough exploration of their known mathematical properties, including injectivity, inversion, range description and microlocal analysis. The mathematical background required for reading most of the book is at the level of an advanced undergraduate student, which should make its content attractive for a large audience of specialists interested in imaging. Mathematicians may appreciate certain parts of the theory that are particularly elegant with connections to functional analysis, PDEs and algebraic geometry.

Author : Chwee Teck Lim
Publisher : Springer Science & Business Media
ISBN 13 : 3540928413
Total Pages : 2355 pages
Book Rating : 4.16/5 ( download)

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Download or read book 13th International Conference on Biomedical Engineering written by Chwee Teck Lim and published by Springer Science & Business Media. This book was released on 2009-03-15 with total page 2355 pages. Available in PDF, EPUB and Kindle. Book excerpt: th On behalf of the organizing committee of the 13 International Conference on Biomedical Engineering, I extend our w- mest welcome to you. This series of conference began in 1983 and is jointly organized by the YLL School of Medicine and Faculty of Engineering of the National University of Singapore and the Biomedical Engineering Society (Singapore). First of all, I want to thank Mr Lim Chuan Poh, Chairman A*STAR who kindly agreed to be our Guest of Honour to give th the Opening Address amidst his busy schedule. I am delighted to report that the 13 ICBME has more than 600 participants from 40 countries. We have received very high quality papers and inevitably we had to turndown some papers. We have invited very prominent speakers and each one is an authority in their field of expertise. I am grateful to each one of them for setting aside their valuable time to participate in this conference. For the first time, the Biomedical Engineering Society (USA) will be sponsoring two symposia, ie “Drug Delivery S- tems” and “Systems Biology and Computational Bioengineering”. I am thankful to Prof Tom Skalak for his leadership in this initiative. I would also like to acknowledge the contribution of Prof Takami Yamaguchi for organizing the NUS-Tohoku’s Global COE workshop within this conference. Thanks also to Prof Fritz Bodem for organizing the symposium, “Space Flight Bioengineering”. This year’s conference proceedings will be published by Springer as an IFMBE Proceedings Series.

Author : Sigurdur Helgason
Publisher : Springer Science & Business Media
ISBN 13 : 1441960546
Total Pages : 309 pages
Book Rating : 4.42/5 ( download)

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Download or read book Integral Geometry and Radon Transforms written by Sigurdur Helgason and published by Springer Science & Business Media. This book was released on 2010-11-17 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this text, integral geometry deals with Radon’s problem of representing a function on a manifold in terms of its integrals over certain submanifolds—hence the term the Radon transform. Examples and far-reaching generalizations lead to fundamental problems such as: (i) injectivity, (ii) inversion formulas, (iii) support questions, (iv) applications (e.g., to tomography, partial di erential equations and group representations). For the case of the plane, the inversion theorem and the support theorem have had major applications in medicine through tomography and CAT scanning. While containing some recent research, the book is aimed at beginning graduate students for classroom use or self-study. A number of exercises point to further results with documentation. From the reviews: “Integral Geometry is a fascinating area, where numerous branches of mathematics meet together. the contents of the book is concentrated around the duality and double vibration, which is realized through the masterful treatment of a variety of examples. the book is written by an expert, who has made fundamental contributions to the area.” —Boris Rubin, Louisiana State University

Author : Ronny Ramlau
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110560852
Total Pages : 347 pages
Book Rating : 4.55/5 ( download)

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Download or read book The Radon Transform written by Ronny Ramlau and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-06-17 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1917, Johann Radon published his fundamental work, where he introduced what is now called the Radon transform. Including important contributions by several experts, this book reports on ground-breaking developments related to the Radon transform throughout these years, and also discusses novel mathematical research topics and applications for the next century.