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Author: S. Azevedo
Publisher:
ISBN:
Category :
Languages : en
Pages : 7
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Author: S. Azevedo
Publisher:
ISBN:
Category :
Languages : en
Pages : 7
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Author: Stanley R. Deans
Publisher: Courier Corporation
ISBN: 0486462412
Category : Mathematics
Languages : en
Pages : 306
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Book Description
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.
Author: Sigurdur Helgason
Publisher: Springer Science & Business Media
ISBN: 9780817641092
Category : Mathematics
Languages : en
Pages : 214
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Book Description
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.
Author: Fouad Sabry
Publisher: One Billion Knowledgeable
ISBN:
Category : Computers
Languages : en
Pages : 153
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Book Description
What is Radon Transform In mathematics, the Radon transform is the integral transform which takes a function f defined on the plane to a function Rf defined on the (two-dimensional) space of lines in the plane, whose value at a particular line is equal to the line integral of the function over that line. The transform was introduced in 1917 by Johann Radon, who also provided a formula for the inverse transform. Radon further included formulas for the transform in three dimensions, in which the integral is taken over planes. It was later generalized to higher-dimensional Euclidean spaces and more broadly in the context of integral geometry. The complex analogue of the Radon transform is known as the Penrose transform. The Radon transform is widely applicable to tomography, the creation of an image from the projection data associated with cross-sectional scans of an object. How you will benefit (I) Insights, and validations about the following topics: Chapter 1: Radon transform Chapter 2: Fourier transform Chapter 3: Bessel function Chapter 4: Convolution theorem Chapter 5: Discrete Fourier transform Chapter 6: Fourier series Chapter 7: Integration by parts Chapter 8: Fractional Fourier transform Chapter 9: Mellin transform Chapter 10: Poisson kernel (II) Answering the public top questions about radon transform. (III) Real world examples for the usage of radon transform in many fields. Who this book is for Professionals, undergraduate and graduate students, enthusiasts, hobbyists, and those who want to go beyond basic knowledge or information for any kind of Radon Transform.
Author: Leon Ehrenpreis
Publisher: OUP Oxford
ISBN: 0191523267
Category : Mathematics
Languages : en
Pages : 740
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Book Description
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. The first part of the book discusses parametric and nonparametric Radon transforms, Harmonic Functions and Radon transform on Algebraic Varieties, nonlinear Radon and Fourier transforms, Radon transform on groups, and Radon transform as the interrelation of geometry and analysis. The later parts discuss the extension of solutions of differential equations, Periods of Eisenstein and Poincaré, and some problems of integral geometry arising in tomography. Examples and proofs are provided throughout the book to aid the reader's understanding. This is the latest title in the Oxford Mathematical Monographs, which includes texts and monographs covering many topics of current research interest in pure and applied mathematics. Other titles include: Carbone and Semmes: A graphic apology for symmetry and implicitness; Higson and Roe: Analytic K-Homology; Iwaniec and Martin: Geometric Function Theory and Nonlinear Analysis; Lyons and Qian: System Control and Rough Paths. Also new in paperback Johnson and Lapidus: The Feynman Integral and Feynman's Operational Calculus; Donaldson and Kronheimer: The geometry of four-manifolds.
Author: Paul Andrew Rattey
Publisher:
ISBN:
Category : Radon transforms
Languages : en
Pages : 254
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Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 6
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The amount of data generated by CT scanners is enormous, making the reconstruction operation slow, especially for 3-D and limited-data scans requiring iterative algorithms. The Radon transform and its inverse, commonly used for CT image reconstruction from projections, are computationally burdensome for today's single-processor computer architectures. If the processing times for the forward and inverse Radon transforms were comparatively small, a large set of new CT algorithms would become feasible, especially those for 3-D and iterative tomographic image reconstructions. In addition to image reconstruction, a fast Radon Transform Computer'' could be naturally applied in other areas of multidimensional signal processing including 2-D power spectrum estimation, modeling of human perception, Hough transforms, image representation, synthetic aperture radar processing, and others. A high speed processor for this operation is likely to motivate new algorithms for general multidimensional signal processing using the Radon transform. In the proposed workshop paper, we will first describe interpolation schemes useful in computation of the discrete Radon transform and backprojection and compare their errors and hardware complexities. We then will evaluate through statistical means the fixed-point number system required to accept and generate 12-bit input and output data with acceptable error using the linear interpolation scheme selected. These results set some of the requirements that must be met by our new VLSI chip architecture. Finally we will present a new unified architecture for a single-chip processor for computing both the forward Radon transform and backprojection at high data rates. 3 refs., 2 figs.
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 14
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Book Description
In this final report, we summarize some of our results from September 1989 to October 1990. The design, construction, and testing of a four-processor prototype multi-processor (RTP) board using TI TMS320C25 DSP chips has been completed. We are now finishing the extensive detailed final documentation of the RTP hardware and software. This extensive documentation will be provided to Steve Azevedo when we return the borrowed workstation and deliver the RTP to LLNL. A summary of the test results are in Section II. The design of our fully custom CMOS VLSI chip has been completed. The chip has been designed, the layout completed, and the chip is now going through its final pre-fabrication simulations. The present status of the custom chip design activity will be summarized in the separately submitted Final Report on the Real-Time Multi-Dimensional Processing Hardware Designs'' Project.'' Evaluations of the hardware requirements for fast filtering of data for filtered backprojection have been completed and are summarized. We briefly summarize the test results of the TMS320 multi-processor prototype RTP board evaluation.
Author: Eric Todd Quinto
Publisher: American Mathematical Soc.
ISBN: 9780821856147
Category : Mathematics
Languages : en
Pages : 276
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Book Description
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.
Author:
Publisher:
ISBN:
Category : Computer vision
Languages : en
Pages : 216
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