Introduction To Radon Transforms

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Introduction To Radon Transforms

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Author : Boris Rubin
language : en
Publisher: Cambridge University Press
Release Date : 2015-11-12

Introduction To Radon Transforms written by Boris Rubin 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 2015-11-12 with Mathematics categories.

A comprehensive introduction to basic operators of integral geometry and the relevant harmonic analysis for students and researchers.

The Mojette Transform

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Author : Jeanpierre Guédon
language : en
Publisher: John Wiley & Sons
Release Date : 2013-03-04

The Mojette Transform written by Jeanpierre Guédon and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-04 with Mathematics categories.

Applied sciences in the 20th century have developed and used unitary transforms for concentrating energy. Now, the challenge lies in the expression and use of redundancy to build redundant systems. The Mojette transform is a very simple transform using only additions but with strong properties that break this challenge. The first part of the book gives the basics of the Mojette transform both mathematically and the corresponding optimal algorithms. The second part exemplifies its use through different fields: image representation, watermarking, medical imaging, distributed storage, information and cryptography. This book about a discrete exact Radon transform explains how to usefully produce and cope with redundancy for solving 21st century problems

Integral Transforms And Their Applications

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Author : Lokenath Debnath
language : en
Publisher: CRC Press
Release Date : 2016-04-19

Integral Transforms And Their Applications written by Lokenath Debnath and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-19 with Mathematics categories.

Keeping the style, content, and focus that made the first edition a bestseller, Integral Transforms and their Applications, Second Edition stresses the development of analytical skills rather than the importance of more abstract formulation. The authors provide a working knowledge of the analytical methods required in pure and applied mathematics, physics, and engineering. The second edition includes many new applications, exercises, comments, and observations with some sections entirely rewritten. It contains more than 500 worked examples and exercises with answers as well as hints to selected exercises. The most significant changes in the second edition include: New chapters on fractional calculus and its applications to ordinary and partial differential equations, wavelets and wavelet transformations, and Radon transform Revised chapter on Fourier transforms, including new sections on Fourier transforms of generalized functions, Poissons summation formula, Gibbs phenomenon, and Heisenbergs uncertainty principle A wide variety of applications has been selected from areas of ordinary and partial differential equations, integral equations, fluid mechanics and elasticity, mathematical statistics, fractional ordinary and partial differential equations, and special functions A broad spectrum of exercises at the end of each chapter further develops analytical skills in the theory and applications of transform methods and a deeper insight into the subject A systematic mathematical treatment of the theory and method of integral transforms, the book provides a clear understanding of the subject and its varied applications in mathematics, applied mathematics, physical sciences, and engineering.

Integral Transforms And Their Applications Third Edition

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Author : Lokenath Debnath
language : en
Publisher: CRC Press
Release Date : 2014-11-07

Integral Transforms And Their Applications Third Edition written by Lokenath Debnath and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-07 with Mathematics categories.

Integral Transforms and Their Applications, Third Edition covers advanced mathematical methods for many applications in science and engineering. The book is suitable as a textbook for senior undergraduate and first-year graduate students and as a reference for professionals in mathematics, engineering, and applied sciences. It presents a systematic development of the underlying theory as well as a modern approach to Fourier, Laplace, Hankel, Mellin, Radon, Gabor, wavelet, and Z transforms and their applications. New to the Third Edition New material on the historical development of classical and modern integral transforms New sections on Fourier transforms of generalized functions, the Poisson summation formula, the Gibbs phenomenon, and the Heisenberg uncertainty principle Revised material on Laplace transforms and double Laplace transforms and their applications New examples of applications in mechanical vibrations, electrical networks, quantum mechanics, integral and functional equations, fluid mechanics, mathematical statistics, special functions, and more New figures that facilitate a clear understanding of physical explanations Updated exercises with solutions, tables of integral transforms, and bibliography Through numerous examples and end-of-chapter exercises, this book develops readers’ analytical and computational skills in the theory and applications of transform methods. It provides accessible working knowledge of the analytical methods and proofs required in pure and applied mathematics, physics, and engineering, preparing readers for subsequent advanced courses and research in these areas.

Analytic Tomography

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Author : Andrew Markoe
language : en
Publisher: Cambridge University Press
Release Date : 2006-01-23

Analytic Tomography written by Andrew Markoe 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 2006-01-23 with Mathematics categories.

This study contains elementary introductions to properties of the Radon transform plus coverage of more advanced topics.

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.

Introduction To The Mathematics Of Medical Imaging

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Author : Charles L. Epstein
language : en
Publisher: SIAM
Release Date : 2008-01-01

Introduction To The Mathematics Of Medical Imaging written by Charles L. Epstein and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-01 with Mathematics categories.

At the heart of every medical imaging technology is a sophisticated mathematical model of the measurement process and an algorithm to reconstruct an image from the measured data. This book provides a firm foundation in the mathematical tools used to model the measurements and derive the reconstruction algorithms used in most imaging modalities in current use. In the process, it also covers many important analytic concepts and techniques used in Fourier analysis, integral equations, sampling theory, and noise analysis.This text uses X-ray computed tomography as a "pedagogical machine" to illustrate important ideas and incorporates extensive discussions of background material making the more advanced mathematical topics accessible to readers with a less formal mathematical education. The mathematical concepts are illuminated with over 200 illustrations and numerous exercises.New to the second edition are a chapter on magnetic resonance imaging (MRI), a revised section on the relationship between the continuum and discrete Fourier transforms, a new section on Grangreat's formula, an improved description of the gridding method, and a new section on noise analysis in MRI. Audience The book is appropriate for one- or two-semester courses at the advanced undergraduate or beginning graduate level on the mathematical foundations of modern medical imaging technologies. The text assumes an understanding of calculus, linear algebra, and basic mathematical analysis. Contents Preface to the Second Edition; Preface; How to Use This Book; Notational Conventions; Chapter 1: Measurements and Modeling; Chapter 2: Linear Models and Linear Equations; Chapter 3: A Basic Model for Tomography; Chapter 4: Introduction to the Fourier Transform; Chapter 5: Convolution; Chapter 6: The Radon Transform; Chapter 7: Introduction to Fourier Series; Chapter 8: Sampling; Chapter 9: Filters; Chapter 10: Implementing Shift Invariant Filters; Chapter 11: Reconstruction in X-Ray Tomography; Chapter 12: Imaging Artifacts in X-Ray Tomography; Chapter 13: Algebraic Reconstruction Techniques; Chapter 14: Magnetic Resonance Imaging; Chapter 15: Probability and Random Variables; Chapter 16: Applications of Probability; Chapter 17: Random Processes; Appendix A: Background Material; Appendix B: Basic Analysis; Index.

An Introduction To The Uncertainty Principle

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Author : Sundaram Thangavelu
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

An Introduction To The Uncertainty Principle written by Sundaram Thangavelu 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 2012-12-06 with Mathematics categories.

In 1932 Norbert Wiener gave a series of lectures on Fourier analysis at the Univer sity of Cambridge. One result of Wiener's visit to Cambridge was his well-known text The Fourier Integral and Certain of its Applications; another was a paper by G. H. Hardy in the 1933 Journalofthe London Mathematical Society. As Hardy says in the introduction to this paper, This note originates from a remark of Prof. N. Wiener, to the effect that "a f and g [= j] cannot both be very small". ... The theo pair of transforms rems which follow give the most precise interpretation possible ofWiener's remark. Hardy's own statement of his results, lightly paraphrased, is as follows, in which f is an integrable function on the real line and f is its Fourier transform: x 2 m If f and j are both 0 (Ix1e- /2) for large x and some m, then each is a finite linear combination ofHermite functions. In particular, if f and j are x2 x 2 2 2 both O(e- / ), then f = j = Ae- / , where A is a constant; and if one x 2 2 is0(e- / ), then both are null.

The Radon Transform

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Author : Sigurdur Helgason
language : en
Publisher: Springer Science & Business Media
Release Date : 1999-08-01

The Radon Transform 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 1999-08-01 with Mathematics categories.

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.

Image Processing And Transputers

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Author : Hugh C. Webber
language : en
Publisher: IOS Press
Release Date : 1992

Image Processing And Transputers written by Hugh C. Webber and has been published by IOS Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Computers categories.