Integral Geometry And Tomography
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Integral Geometry And Tomography
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Author : Andrew Markoe
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
Integral Geometry And Tomography written by Andrew Markoe and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
This volume consists of a collection of papers that brings together fundamental research in Radon transforms, integral geometry, and tomography. It grew out of the Special Session at a Sectional Meeting of the American Mathematical Society in 2004. The book contains very recent work of some of the top researchers in the field. The articles in the book deal with the determination of properties of functions on a manifold by integral theoretic methods, or by determining the geometricstructure of subsets of a manifold by analytic methods. Of particular concern are ways of reconstructing an unknown function from some of its projections. Radon transforms were developed at the beginning of the twentieth century by researchers who were motivated by problems in differential geometry,mathematical physics, and partial differential equations. Later, medical applications of these transforms produced breakthroughs in imaging technology that resulted in the 1979 Nobel Prize in Physiology and Medicine for the development of computerized tomography. Today the subject boasts substantial cross-disciplinary interactions, both in pure and applied mathematics as well as medicine, engineering, biology, physics, geosciences, and industrial testing. Therefore, this volume should be ofinterest to a wide spectrum of researchers both in mathematics and in other fields.
Integral Geometry And Tomography
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Author : Eric Grinberg
language : en
Publisher: American Mathematical Soc.
Release Date : 1990
Integral Geometry And Tomography written by Eric Grinberg and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Mathematics categories.
Contains the proceedings of an AMS-IMS-SIAM Joint Summer Research Conference on Integral Geometry and Tomography, held in June 1989 at Humboldt State University in Arcata, California. This book features articles that range over such diverse areas as combinatorics, geometric inequalities, micro-local analysis, group theory, and harmonic analysis.
Geometric Tomography
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Author : Richard J. Gardner
language : en
Publisher: Cambridge University Press
Release Date : 2006-06-19
Geometric Tomography written by Richard J. Gardner and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-06-19 with Mathematics categories.
Geometric tomography deals with the retrieval of information about a geometric object from data concerning its projections (shadows) on planes or cross-sections by planes. It is a geometric relative of computerized tomography, which reconstructs an image from X-rays of a human patient. It overlaps with convex geometry, and employs many tools from that area including integral geometry. It also has connections to geometric probing in robotics and to stereology. The main text contains a rigorous treatment of the subject starting from basic concepts and moving up to the research frontier: seventy-two unsolved problems are stated. Each chapter ends with extensive notes, historical remarks, and some biographies. This comprehensive work will be invaluable to specialists in geometry and tomography; the opening chapters can also be read by advanced undergraduate students.
Integral Geometry And Radon Transforms
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Author : Sigurdur Helgason
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-11-17
Integral Geometry And Radon Transforms written by Sigurdur Helgason and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11-17 with Mathematics categories.
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
The Radon Transform And Some Of Its Applications
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Author : Stanley R. Deans
language : en
Publisher: Courier Corporation
Release Date : 2007-10-01
The Radon Transform And Some Of Its Applications written by Stanley R. Deans and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-10-01 with Mathematics categories.
Of value to mathematicians, physicists, and engineers, this excellent introduction to Radon transform covers both theory and applications, with a rich array of examples and literature that forms a valuable reference. This 1993 edition is a revised and updated version by the author of his pioneering work.
Microlocal Analysis And Inverse Problems In Tomography And Geometry
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Author : Eric Todd Quinto
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2024-09-23
Microlocal Analysis And Inverse Problems In Tomography And Geometry written by Eric Todd Quinto and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-23 with Mathematics categories.
Microlocal Analysis has proven to be a powerful tool for analyzing and solving inverse problems; including answering questions about stability, uniqueness, recovery of singularities, etc. This volume, presents several studies on microlocal methods in problems in tomography, integral geometry, geodesic transforms, travel time tomography, thermoacoustic tomography, Compton CT, cosmology, nonlinear inverse problems, and others.
Inverse Problems For Partial Differential Equations
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Author : Victor Isakov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Inverse Problems For Partial Differential Equations written by Victor Isakov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.
This book describes the contemporary state of the theory and some numerical aspects of inverse problems in partial differential equations. The topic is of sub stantial and growing interest for many scientists and engineers, and accordingly to graduate students in these areas. Mathematically, these problems are relatively new and quite challenging due to the lack of conventional stability and to nonlinearity and nonconvexity. Applications include recovery of inclusions from anomalies of their gravitational fields; reconstruction of the interior of the human body from exterior electrical, ultrasonic, and magnetic measurements, recovery of interior structural parameters of detail of machines and of the underground from similar data (non-destructive evaluation); and locating flying or navigated objects from their acoustic or electromagnetic fields. Currently, there are hundreds of publica tions containing new and interesting results. A purpose of the book is to collect and present many of them in a readable and informative form. Rigorous proofs are presented whenever they are relatively short and can be demonstrated by quite general mathematical techniques. Also, we prefer to present results that from our point of view contain fresh and promising ideas. In some cases there is no com plete mathematical theory, so we give only available results. We do not assume that a reader possesses an enormous mathematical technique. In fact, a moderate knowledge of partial differential equations, of the Fourier transform, and of basic functional analysis will suffice.
Integral Geometry Of Tensor Fields
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Author : V. A. Sharafutdinov
language : en
Publisher: VSP
Release Date : 1994
Integral Geometry Of Tensor Fields written by V. A. Sharafutdinov and has been published by VSP this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.
The Inverse and Ill-Posed Problems Series is a series of monographs publishing postgraduate level information on inverse and ill-posed problems for an international readership of professional scientists and researchers. The series aims to publish works which involve both theory and applications in, e.g., physics, medicine, geophysics, acoustics, electrodynamics, tomography, and ecology.
Integral Geometry And Convexity Proceedings Of The International Conference
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Author : Eric L Grinberg
language : en
Publisher: World Scientific
Release Date : 2006-04-20
Integral Geometry And Convexity Proceedings Of The International Conference written by Eric L Grinberg and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04-20 with Mathematics categories.
Integral geometry, known as geometric probability in the past, originated from Buffon's needle experiment. Remarkable advances have been made in several areas that involve the theory of convex bodies. This volume brings together contributions by leading international researchers in integral geometry, convex geometry, complex geometry, probability, statistics, and other convexity related branches. The articles cover both recent results and exciting directions for future research.
Tomography Impedance Imaging And Integral Geometry
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Author : Eric Todd Quinto
language : en
Publisher: American Mathematical Soc.
Release Date : 1991
Tomography Impedance Imaging And Integral Geometry written by Eric Todd Quinto and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Medical categories.
One of the most exciting features of tomography is the strong relationship between high-level pure mathematics (such as harmonic analysis, partial differential equations, microlocal analysis, and group theory) and applications to medical imaging, impedance imaging, radiotherapy, and industrial nondestructive evaluation. This book contains the refereed proceedings of the AMS-SIAM Summer Seminar on Tomography, Impedance Imaging, and Integral Geometry, held at Mount Holyoke College in June 1993. A number of common themes are found among the papers. Group theory is fundamental both to tomographic sampling theorems and to pure Radon transforms. Microlocal and Fourier analysis are important for research in all three fields. Differential equations and integral geometric techniques are useful in impedance imaging. In short, a common body of mathematics can be used to solve dramatically different problems in pure and applied mathematics. Radon transforms can be used to model impedance imaging problems. These proceedings include exciting results in all three fields represented at the conference.