Integral Geometry And Tomography

Download Integral Geometry And Tomography full books in PDF, epub, and Kindle. Read online Integral Geometry And Tomography ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!

Integral Geometry and Tomography

Author : Andrew Markoe
Publisher : American Mathematical Soc.
ISBN 13 : 0821837559
Total Pages : 155 pages
Book Rating : 4.8/5 (218 download)

DOWNLOAD NOW!

Book Synopsis Integral Geometry and Tomography by : Andrew Markoe

Download or read book Integral Geometry and Tomography written by Andrew Markoe and published by American Mathematical Soc.. This book was released on 2006 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 geometric structure 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 of interest to a wide spectrum of researchers both in mathematics and in other fields.

Integral Geometry and Tomography

Author : Eric Grinberg
Publisher : American Mathematical Soc.
ISBN 13 : 0821851209
Total Pages : 249 pages
Book Rating : 4.8/5 (218 download)

DOWNLOAD NOW!

Book Synopsis Integral Geometry and Tomography by : Eric Grinberg

Download or read book Integral Geometry and Tomography written by Eric Grinberg and published by American Mathematical Soc.. This book was released on 1990 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book 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. The papers collected here represent current research in these two interrelated fields. The articles in pure mathematics range over such diverse areas as combinatorics, geometric inequalities, micro-local analysis, group theory, and harmonic analysis. The interplay between Lie group theory, geometry, harmonic analysis, and Radon transforms is well covered.The papers on tomography reflect current research on X-ray computed tomography, as well as radiation dose planning, radar, and partial differential equations. In addition to describing current research, this book provides a useful perspective on the interplay between the fields. For example, abstract theorems about Radon transforms are used to understand applied mathematics, while applied mathematics motivates some of the results in pure mathematics. Though directed at specialists in the field, the book would also be of interest to others who wish to understand current research in these areas and to witness how they relate to other branches of mathematics.

Geometric Tomography

Author : Richard J. Gardner
Publisher : Cambridge University Press
ISBN 13 : 0521866804
Total Pages : 7 pages
Book Rating : 4.5/5 (218 download)

DOWNLOAD NOW!

Book Synopsis Geometric Tomography by : Richard J. Gardner

Download or read book Geometric Tomography written by Richard J. Gardner and published by Cambridge University Press. This book was released on 2006-06-19 with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Tomography, Impedance Imaging, and Integral Geometry

Author : Eric Todd Quinto
Publisher : American Mathematical Soc.
ISBN 13 : 9780821896990
Total Pages : 300 pages
Book Rating : 4.8/5 (969 download)

DOWNLOAD NOW!

Book Synopsis Tomography, Impedance Imaging, and Integral Geometry by : Eric Todd Quinto

Download or read book Tomography, Impedance Imaging, and Integral Geometry written by Eric Todd Quinto and published by American Mathematical Soc.. This book was released on 1991 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Integral Geometry and Radon Transforms

Author : Sigurdur Helgason
Publisher : Springer Science & Business Media
ISBN 13 : 1441960546
Total Pages : 309 pages
Book Rating : 4.4/5 (419 download)

DOWNLOAD NOW!

Book Synopsis Integral Geometry and Radon Transforms by : Sigurdur Helgason

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

Tomography, impedance imaging, and integral geometry : June 7 - 18, 1993, Mount Holyoke College, Massachusetts

Author : Eric Todd Quinto
Publisher :
ISBN 13 : 9780821803370
Total Pages : 287 pages
Book Rating : 4.8/5 (33 download)

DOWNLOAD NOW!

Book Synopsis Tomography, impedance imaging, and integral geometry : June 7 - 18, 1993, Mount Holyoke College, Massachusetts by : Eric Todd Quinto

Download or read book Tomography, impedance imaging, and integral geometry : June 7 - 18, 1993, Mount Holyoke College, Massachusetts written by Eric Todd Quinto and published by . This book was released on 1994 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Integral Geometry of Tensor Fields

Author : V. A. Sharafutdinov
Publisher : Walter de Gruyter
ISBN 13 : 3110900092
Total Pages : 277 pages
Book Rating : 4.1/5 (19 download)

DOWNLOAD NOW!

Book Synopsis Integral Geometry of Tensor Fields by : V. A. Sharafutdinov

Download or read book Integral Geometry of Tensor Fields written by V. A. Sharafutdinov and published by Walter de Gruyter. This book was released on 2012-01-02 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Tomography

Author : Eric Grinberg
Publisher : American Mathematical Soc.
ISBN 13 : 9780821854464
Total Pages : 270 pages
Book Rating : 4.8/5 (544 download)

DOWNLOAD NOW!

Book Synopsis Integral Geometry and Tomography by : Eric Grinberg

Download or read book Integral Geometry and Tomography written by Eric Grinberg and published by American Mathematical Soc.. This book was released on 1991-01-18 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book 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. The papers collected here represent current research in these two interrelated fields. The articles in pure mathematics range over such diverse areas as combinatorics, geometric inequalities, micro-local analysis, group theory, and harmonic analysis. The interplay between Lie group theory, geometry, harmonic analysis, and Radon transforms is well covered. The papers on tomography reflect current research on X-ray computed tomography, as well as radiation dose planning, radar, and partial differential equations. In addition to describing current research, this book provides a useful perspective on the interplay between the fields. For example, abstract theorems about Radon transforms are used to understand applied mathematics, while applied mathematics motivates some of the results in pure mathematics. Though directed at specialists in the field, the book would also be of interest to others who wish to understand current research in these areas and to witness how they relate to other branches of mathematics.

Selected Topics in Integral Geometry

Author : Izrailʹ Moiseevich Gelʹfand
Publisher : American Mathematical Soc.
ISBN 13 : 9780821829325
Total Pages : 136 pages
Book Rating : 4.8/5 (293 download)

DOWNLOAD NOW!

Book Synopsis Selected Topics in Integral Geometry by : Izrailʹ Moiseevich Gelʹfand

Download or read book Selected Topics in Integral Geometry written by Izrailʹ Moiseevich Gelʹfand and published by American Mathematical Soc.. This book was released on 2003 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: The miracle of integral geometry is that it is often possible to recover a function on a manifold just from the knowledge of its integrals over certain submanifolds. The founding example is the Radon transform, introduced at the beginning of the 20th century. Since then, many other transforms were found, and the general theory was developed. Moreover, many important practical applications were discovered. The best known, but by no means the only one, being to medical tomography. This book is a general introduction to integral geometry, the first from this point of view for almost four decades. The authors, all leading experts in the field, represent one of the most influential schools in integral geometry. The book presents in detail basic examples of integral geometry problems, such as the Radon transform on the plane and in space, the John transform, the Minkowski-Funk transform, integral geometry on the hyperbolic plane and in the hyperbolic space, the horospherical transform and its relation to representations of $SL(2,\mathbb C)$, integral geometry on quadrics, etc. The study of these examples allows the authors to explain important general topics of integral geometry, such as the Cavalieri conditions, local and nonlocal inversion formulas, and overdetermined problems in integral geometry. Many of the results in the book were obtained by the authors in the course of their career-long work in integral geometry. This book is suitable for graduate students and researchers working in integral geometry and its applications.

Selected Topics in Integral Geometry

Author : Izrail_ Moiseevich Gel_fand
Publisher : American Mathematical Soc.
ISBN 13 : 9780821898048
Total Pages : 192 pages
Book Rating : 4.8/5 (98 download)

DOWNLOAD NOW!

Book Synopsis Selected Topics in Integral Geometry by : Izrail_ Moiseevich Gel_fand

Download or read book Selected Topics in Integral Geometry written by Izrail_ Moiseevich Gel_fand and published by American Mathematical Soc.. This book was released on 2003-09-02 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: The miracle of integral geometry is that it is often possible to recover a function on a manifold just from the knowledge of its integrals over certain submanifolds. The founding example is the Radon transform, introduced at the beginning of the 20th century. Since then, many other transforms were found, and the general theory was developed. Moreover, many important practical applications were discovered, the best known, but by no means the only one, being to medical tomography. The present book is a general introduction to integral geometry, the first from this point of view for almost four decades. The authors, all leading experts in the field, represent one of the most influential schools in integral geometry. The book presents in detail basic examples of integral geometry problems, such as the Radon transform on the plane and in space, the John transform, the Minkowski-Funk transform, integral geometry on the hyperbolic plane and in the hyperbolic space, the horospherical transform and its relation to representations of $SL(2,\mathbb C)$, integral geometry on quadrics, etc. The study of these examples allows the authors to explain important general topics of integral geometry, such as the Cavalieri conditions, local and nonlocal inversion formulas, and overdetermined problems. Many of the results in the book were obtained by the authors in the course of their career-long work in integral geometry.

Reconstructive Integral Geometry

Author : Victor Palamodov
Publisher : Birkhäuser
ISBN 13 : 3034879415
Total Pages : 171 pages
Book Rating : 4.0/5 (348 download)

DOWNLOAD NOW!

Book Synopsis Reconstructive Integral Geometry by : Victor Palamodov

Download or read book Reconstructive Integral Geometry written by Victor Palamodov and published by Birkhäuser. This book was released on 2012-12-06 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers facts and methods for the reconstruction of a function in a real affine or projective space from data of integrals, particularly over lines, planes, and spheres. Recent results stress explicit analytic methods. Coverage includes the relations between algebraic integral geometry and partial differential equations. The first half of the book includes the ray, the spherical mean transforms in the plane or in 3-space, and inversion from incomplete data.

The Radon Transform, Inverse Problems, and Tomography

Author : Gestur Ólafsson
Publisher : American Mathematical Soc.
ISBN 13 : 0821839306
Total Pages : 176 pages
Book Rating : 4.8/5 (218 download)

DOWNLOAD NOW!

Book Synopsis The Radon Transform, Inverse Problems, and Tomography by : Gestur Ólafsson

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.

Analytic Tomography

Author : Andrew Markoe
Publisher : Cambridge University Press
ISBN 13 : 0521793475
Total Pages : 358 pages
Book Rating : 4.5/5 (217 download)

DOWNLOAD NOW!

Book Synopsis Analytic Tomography by : Andrew Markoe

Download or read book Analytic Tomography written by Andrew Markoe and published by Cambridge University Press. This book was released on 2006-01-23 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: This study contains elementary introductions to properties of the Radon transform plus coverage of more advanced topics.

Reconstruction from Integral Data

Author : Victor Palamodov
Publisher : CRC Press
ISBN 13 : 1498710115
Total Pages : 172 pages
Book Rating : 4.4/5 (987 download)

DOWNLOAD NOW!

Book Synopsis Reconstruction from Integral Data by : Victor Palamodov

Download or read book Reconstruction from Integral Data written by Victor Palamodov and published by CRC Press. This book was released on 2016-04-27 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reconstruction of a function from data of integrals is used for problems arising in diagnostics, including x-ray, positron radiography, ultrasound, scattering, sonar, seismic, impedance, wave tomography, crystallography, photo-thermo-acoustics, photoelastics, and strain tomography. Reconstruction from Integral Data presents both long-standing and recent mathematical results from this field in a uniform way. The book focuses on exact analytic formulas for reconstructing a function or a vector field from data of integrals over lines, rays, circles, arcs, parabolas, hyperbolas, planes, hyperplanes, spheres, and paraboloids. It also addresses range characterizations. Coverage is motivated by both applications and pure mathematics. The book first presents known facts on the classical and attenuated Radon transform. It then deals with reconstructions from data of ray (circle) integrals. The author goes on to cover reconstructions in classical and new geometries. The final chapter collects necessary definitions and elementary facts from geometry and analysis that are not always included in textbooks.

Generalized Radon Transforms And Imaging By Scattered Particles: Broken Rays, Cones, And Stars In Tomography

Author : Gaik Ambartsoumian
Publisher : World Scientific
ISBN 13 : 9811242453
Total Pages : 248 pages
Book Rating : 4.8/5 (112 download)

DOWNLOAD NOW!

Book Synopsis Generalized Radon Transforms And Imaging By Scattered Particles: Broken Rays, Cones, And Stars In Tomography by : Gaik Ambartsoumian

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.

Mathematical Problems of Tomography

Author : S. GINDIKIN. I. M. GELFAND
Publisher :
ISBN 13 : 9781470446666
Total Pages : 274 pages
Book Rating : 4.4/5 (466 download)

DOWNLOAD NOW!

Book Synopsis Mathematical Problems of Tomography by : S. GINDIKIN. I. M. GELFAND

Download or read book Mathematical Problems of Tomography written by S. GINDIKIN. I. M. GELFAND and published by . This book was released on 1990 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Uniqueness Questions in Reconstruction of Multidimensional Objects from Tomography-Type Projection Data

Author : V. P. Golubyatnikov
Publisher : VSP
ISBN 13 : 9789067643320
Total Pages : 136 pages
Book Rating : 4.6/5 (433 download)

DOWNLOAD NOW!

Book Synopsis Uniqueness Questions in Reconstruction of Multidimensional Objects from Tomography-Type Projection Data by : V. P. Golubyatnikov

Download or read book Uniqueness Questions in Reconstruction of Multidimensional Objects from Tomography-Type Projection Data written by V. P. Golubyatnikov and published by VSP. This book was released on 2000 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first part of this new volume in the Inverse and Ill-Posed Problems Series studies uniqeness questions for recovering the shapes of the convex and more complicated bodies from shapes of their projections onto planes of low dimension. Some stability estimates of the solutions to these inverse problems are given. The second part deals with inverse problems with projection data directly connected to tomography, in partcular to apparent contours of smooth surfaces, which have practical interpretations such as thin cracks in continuous media which are studied in industrial defectoscopy, caustic surfaces which are studies in wave optics, etc. New results on reconstruction of smooth surfaces from observations of the wave fronts generated by these surfaces are obtained.