Download or read book The Radon Transform written by Sigurdur Helgason and published by Springer Science & Business Media. This book was released on 1999-08-01 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Radon transform is an important topic in integral geometry which deals with the problem of expressing a function on a manifold in terms of its integrals over certain submanifolds. Solutions to such problems have a wide range of applications, namely to partial differential equations, group representations, X-ray technology, nuclear magnetic resonance scanning, and tomography. This second edition, significantly expanded and updated, presents new material taking into account some of the progress made in the field since 1980. Aimed at beginning graduate students, this monograph will be useful in the classroom or as a resource for self-study. Readers will find here an accessible introduction to Radon transform theory, an elegant topic in integral geometry.
Download or read book The Radon Transform and Some of Its Applications written by Stanley R. Deans and published by Courier Corporation. This book was released on 2007-10-01 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Radon Transform and Medical Imaging written by Peter Kuchment and published by SIAM. This book was released on 2014-03-20 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.
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 348 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.
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.
Download or read book The Radon Transform written by Ronny Ramlau and published by de Gruyter. This book was released on 2019 with total page 0 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
Download or read book The Radon Transform and Local Tomography written by Alexander G. Ramm and published by CRC Press. This book was released on 2020-07-16 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the past decade, the field of image processing has made tremendous advances. One type of image processing that is currently of particular interest is "tomographic imaging," a technique for computing the density function of a body, or discontinuity surfaces of this function. Today, tomography is widely used, and has applications in such fields as medicine, engineering, physics, geophysics, and security. The Radon Transform and Local Tomography clearly explains the theoretical, computational, and practical aspects of applied tomography. It includes sufficient background information to make it essentially self-contained for most readers.
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
Download or read book Integral Geometry Radon Transforms and Complex Analysis written by Carlos A. Berenstein and published by Springer. This book was released on 2006-11-14 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the notes of five short courses delivered at the "Centro Internazionale Matematico Estivo" session "Integral Geometry, Radon Transforms and Complex Analysis" held in Venice (Italy) in June 1996: three of them deal with various aspects of integral geometry, with a common emphasis on several kinds of Radon transforms, their properties and applications, the other two share a stress on CR manifolds and related problems. All lectures are accessible to a wide audience, and provide self-contained introductions and short surveys on the subjects, as well as detailed expositions of selected results.
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.
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.
Download or read book X ray Phase Contrast Imaging Using Near Field Speckles written by Marie-Christine Zdora and published by Springer Nature. This book was released on 2021-02-16 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis presents research on novel X-ray imaging methods that improve the study of specimens with small density differences, revealing their inner structure and density distribution. Exploiting the phase shift of X-rays in a material can significantly increase the image contrast compared to conventional absorption imaging. This thesis provides a practical guide to X-ray phase-contrast imaging with a strong focus on X-ray speckle-based imaging, the most recently developed phase-sensitive method. X-ray speckle-based imaging only requires a piece of abrasive paper in addition to the standard X-ray imaging setup. Its simplicity and robustness combined with the compatibility with laboratory X-ray sources, make it an ideal candidate for wide user uptake in a range of fields. An in-depth overview of the state of the art of X-ray speckle-based imaging and its latest developments is given in this thesis. It, furthermore, explores a broad range of applications, from X-ray optics characterisation, to biomedical imaging for 3D virtual histology and geological studies of volcanic rocks, demonstrating is promising potential. Moreover, the speckle-based technique is placed in the context of other phase-sensitive X-ray imaging methods to assist in the choice of a suitable method, hence serving as a guide and reference work for future users.
Download or read book Ultrasonic Nondestructive Testing of Inhomogeneous Isotropic and Anisotropic Media Modeling and Imaging written by Chinta, Prashanth Kumar and published by kassel university press GmbH. This book was released on 2013-01-01 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis discusses ultrasonic testing by means of numerical modeling and image reconstruction techniques using elastic and acoustic wave fields. Numerical modeling of elastic waves (part one of the thesis) is used to understand the elastic wave scattering due to material defects and the propagation of surface waves in inhomogeneous isotropic and anisotropic media, with special emphasis on transversely isotropic and orthotropic media. Different imaging techniques (part two of the thesis) are investigated to develop a software, implemented in Matlab, which can give imaging results immediately after the measurement almost in real time as it can read and process the data obtained directly from the measurement. Acoustic wave scattering using analytical techniques and imaging techniques based on Radon transform are investigated. The data obtained from the Radon transform are subjected for imaging utilizing the filtered back projection algorithm and the Fourier slice theorem. The fundamentals of elastic wave propagation in solids are extensively elaborated. The point source synthesis to compute the Green’s functions for anisotropic media and the plane wave synthesis to compute slowness, phase and group velocity surfaces are studied. The elastic integral equations for the so called stretched coordinate system are derived. Based on these equations the numerical tool ’Three-dimensional Elastodynamic Finite Integration Technique’ (3D-EFIT) has been enhanced to treat not only isotropic media but also anisotropic media. For fast computation, the 3D-EFIT code using the Message Passing Interface (MPI) is used by which processing on massive parallel computers is made possible. In 3D-EFIT the Convolutional Perfectly Matched Layers (CPML) can also be applied to absorb the elastic body waves as well as the surface and evanescent waves. 3D-EFIT for homogeneous anisotropic media is validated by comparing computed Green’s functions with an analytical solution. After the validation, the applications of EFIT such as elastic wave modeling in inhomogeneous austenitic steel welds and inhomogeneous orthotropic wooden structures are presented. The results of the 2D-EFIT and 3D-EFIT modeling are compared against measurements performed at Federal Institute for Materials Research and Testing (BAM). After the modeling part of the thesis, inverse scattering techniques for fast imaging of inhomogeneities are studied. For three-dimensional imaging of defects in concrete, the Synthetic Aperture and Focusing Technique (SAFT) and Fourier Transformed Synthetic aperture Focusing Technique (FT-SAFT) are applied to data measured using a transducer array. The seismic Dip-Moveout (DMO) method has been utilized to convert measured bistatic data into monostatic data. A special treatment of SAFT as a technique for back propagation of the wave fields using time reversal, utilizing the knowledge of the geometry, is presented. Finally, time domain anisotropic SAFT (AnSAFT) is studied for image reconstruction of defects in inhomogeneous geometry with orthotropic crystal structure of the embedding medium.
Download or read book Radon Transforms and Tomography written by Eric Todd Quinto and published by American Mathematical Soc.. This book was released on 2001 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the most exciting features of the fields of Radon transforms and tomography is the strong relationship between high-level pure mathematics and applications to areas such as medical imaging and industrial nondestructive evaluation. The proceedings featured in this volume bring together fundamental research articles in the major areas of Radon transforms and tomography. This volume includes expository papers that are of special interest to beginners as well as advanced researchers. Topics include local tomography and wavelets, Lambda tomography and related methods, tomographic methods in RADAR, ultrasound, Radon transforms and differential equations, and the Pompeiu problem. The major themes in Radon transforms and tomography are represented among the research articles. Pure mathematical themes include vector tomography, microlocal analysis, twistor theory, Lie theory, wavelets, harmonic analysis, and distribution theory. The applied articles employ high-quality pure mathematics to solve important practical problems. Effective scanning geometries are developed and tested for a NASA wind tunnel. Algorithms for limited electromagnetic tomographic data and for impedance imaging are developed and tested. Range theorems are proposed to diagnose problems with tomography scanners. Principles are given for the design of X-ray tomography reconstruction algorithms, and numerical examples are provided. This volume offers readers a comprehensive source of fundamental research useful to both beginners and advanced researchers in the fields.
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
Download or read book Advances in Neural Networks ISNN 2013 written by Chengan Guo and published by Springer. This book was released on 2013-07-04 with total page 710 pages. Available in PDF, EPUB and Kindle. Book excerpt: The two-volume set LNCS 7951 and 7952 constitutes the refereed proceedings of the 10th International Symposium on Neural Networks, ISNN 2013, held in Dalian, China, in July 2013. The 157 revised full papers presented were carefully reviewed and selected from numerous submissions. The papers are organized in following topics: computational neuroscience, cognitive science, neural network models, learning algorithms, stability and convergence analysis, kernel methods, large margin methods and SVM, optimization algorithms, varational methods, control, robotics, bioinformatics and biomedical engineering, brain-like systems and brain-computer interfaces, data mining and knowledge discovery and other applications of neural networks.
Download or read book Harmonic Analysis and Integral Geometry written by Massimo Picardello and published by CRC Press. This book was released on 2019-04-15 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprising a selection of expository and research papers, Harmonic Analysis and Integral Geometry grew from presentations offered at the July 1998 Summer University of Safi, Morocco-an annual, advanced research school and congress. This lively and very successful event drew the attendance of many top researchers, who offered both individual lecture
