Introduction To The Mathematics Of Medical Imaging

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Introduction to the Mathematics of Medical Imaging

Author : Charles L. Epstein
Publisher : SIAM
ISBN 13 : 9780898717792
Total Pages : 794 pages
Book Rating : 4.7/5 (177 download)

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Book Synopsis Introduction to the Mathematics of Medical Imaging by : Charles L. Epstein

The Mathematics of Medical Imaging

Author : Timothy G. Feeman
Publisher : Springer Science & Business Media
ISBN 13 : 0387927115
Total Pages : 150 pages
Book Rating : 4.3/5 (879 download)

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Book Synopsis The Mathematics of Medical Imaging by : Timothy G. Feeman

Download or read book The Mathematics of Medical Imaging written by Timothy G. Feeman and published by Springer Science & Business Media. This book was released on 2010 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: Medical imaging is a major part of twenty-first century health care. This introduction explores the mathematical aspects of imaging in medicine to explain approximation methods in addition to computer implementation of inversion algorithms.

Introduction to the Mathematics of Medical Imaging

Author : Charles L. Epstein
Publisher : SIAM
ISBN 13 : 089871642X
Total Pages : 782 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Introduction to the Mathematics of Medical Imaging by : Charles L. Epstein

Download or read book Introduction to the Mathematics of Medical Imaging written by Charles L. Epstein and published by SIAM. This book was released on 2008-01-01 with total page 782 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Introduction to Medical Imaging

Author : Nadine Barrie Smith
Publisher : Cambridge University Press
ISBN 13 : 1139492047
Total Pages : pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Introduction to Medical Imaging by : Nadine Barrie Smith

Download or read book Introduction to Medical Imaging written by Nadine Barrie Smith and published by Cambridge University Press. This book was released on 2010-11-18 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Covering the basics of X-rays, CT, PET, nuclear medicine, ultrasound, and MRI, this textbook provides senior undergraduate and beginning graduate students with a broad introduction to medical imaging. Over 130 end-of-chapter exercises are included, in addition to solved example problems, which enable students to master the theory as well as providing them with the tools needed to solve more difficult problems. The basic theory, instrumentation and state-of-the-art techniques and applications are covered, bringing students immediately up-to-date with recent developments, such as combined computed tomography/positron emission tomography, multi-slice CT, four-dimensional ultrasound, and parallel imaging MR technology. Clinical examples provide practical applications of physics and engineering knowledge to medicine. Finally, helpful references to specialised texts, recent review articles, and relevant scientific journals are provided at the end of each chapter, making this an ideal textbook for a one-semester course in medical imaging.

An Introduction to Mathematics of Emerging Biomedical Imaging

Author : Habib Ammari
Publisher : Springer Science & Business Media
ISBN 13 : 3540795537
Total Pages : 198 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis An Introduction to Mathematics of Emerging Biomedical Imaging by : Habib Ammari

Download or read book An Introduction to Mathematics of Emerging Biomedical Imaging written by Habib Ammari and published by Springer Science & Business Media. This book was released on 2008-05-21 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: Biomedical imaging is a fascinating research area to applied mathematicians. Challenging imaging problems arise and they often trigger the investigation of fundamental problems in various branches of mathematics. This is the first book to highlight the most recent mathematical developments in emerging biomedical imaging techniques. The main focus is on emerging multi-physics and multi-scales imaging approaches. For such promising techniques, it provides the basic mathematical concepts and tools for image reconstruction. Further improvements in these exciting imaging techniques require continued research in the mathematical sciences, a field that has contributed greatly to biomedical imaging and will continue to do so. The volume is suitable for a graduate-level course in applied mathematics and helps prepare the reader for a deeper understanding of research areas in biomedical imaging.

Fundamentals of Medical Imaging

Author : Paul Suetens
Publisher : Cambridge University Press
ISBN 13 : 1139479881
Total Pages : 265 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Fundamentals of Medical Imaging by : Paul Suetens

Download or read book Fundamentals of Medical Imaging written by Paul Suetens and published by Cambridge University Press. This book was released on 2009-08-06 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fundamentals of Medical Imaging, second edition, is an invaluable technical introduction to each imaging modality, explaining the mathematical and physical principles and giving a clear understanding of how images are obtained and interpreted. Individual chapters cover each imaging modality – radiography, CT, MRI, nuclear medicine and ultrasound – reviewing the physics of the signal and its interaction with tissue, the image formation or reconstruction process, a discussion of image quality and equipment, clinical applications and biological effects and safety issues. Subsequent chapters review image analysis and visualization for diagnosis, treatment and surgery. New to this edition: • Appendix of questions and answers • New chapter on 3D image visualization • Advanced mathematical formulae in separate text boxes • Ancillary website containing 3D animations: www.cambridge.org/suetens • Full colour illustrations throughout Engineers, clinicians, mathematicians and physicists will find this an invaluable aid in understanding the physical principles of imaging and their clinical applications.

Mathematics and Computer Science in Medical Imaging

Author : Max A. Viergever
Publisher : Springer Science & Business Media
ISBN 13 : 3642833063
Total Pages : 535 pages
Book Rating : 4.6/5 (428 download)

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Book Synopsis Mathematics and Computer Science in Medical Imaging by : Max A. Viergever

Download or read book Mathematics and Computer Science in Medical Imaging written by Max A. Viergever and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 535 pages. Available in PDF, EPUB and Kindle. Book excerpt: Medical imaging is an important and rapidly expanding area in medical science. Many of the methods employed are essentially digital, for example computerized tomography, and the subject has become increasingly influenced by develop ments in both mathematics and computer science. The mathematical problems have been the concern of a relatively small group of scientists, consisting mainly of applied mathematicians and theoretical physicists. Their efforts have led to workable algorithms for most imaging modalities. However, neither the fundamentals, nor the limitations and disadvantages of these algorithms are known to a sufficient degree to the physicists, engineers and physicians trying to implement these methods. It seems both timely and important to try to bridge this gap. This book summarizes the proceedings of a NATO Advanced Study Institute, on these topics, that was held in the mountains of Tuscany for two weeks in the late summer of 1986. At another (quite different) earlier meeting on medical imaging, the authors noted that each of the speakers had given, there, a long introduction in their general area, stated that they did not have time to discuss the details of the new work, but proceeded to show lots of clinical results, while excluding any mathematics associated with the area.

Fundamentals of Digital Imaging in Medicine

Author : Roger Bourne
Publisher : Springer Science & Business Media
ISBN 13 : 1848820879
Total Pages : 209 pages
Book Rating : 4.8/5 (488 download)

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Book Synopsis Fundamentals of Digital Imaging in Medicine by : Roger Bourne

Download or read book Fundamentals of Digital Imaging in Medicine written by Roger Bourne and published by Springer Science & Business Media. This book was released on 2010-01-18 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: In general, image processing texts are intended for students of engineering and computer science, and there is little written at all on the specific requirements of medical image processing. Students of medical radiation science (Diagnostic radiography, Nuclear medicine, Radiation therapy) usually have minimal mathematical and computer science training and find the available texts incomprehensible. A text that explains the principles of image processing in minimally-mathematical language is needed for these students. Contrary to the claims of some textbook authors, the vast majority of technologists that process images do not need to understand the mathematics involved, but would nevertheless benefit from a thorough understanding of the general process.

An Introduction to the Principles of Medical Imaging

Author : Chris Guy
Publisher :
ISBN 13 : 9781860945021
Total Pages : 374 pages
Book Rating : 4.9/5 (45 download)

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Book Synopsis An Introduction to the Principles of Medical Imaging by : Chris Guy

Download or read book An Introduction to the Principles of Medical Imaging written by Chris Guy and published by . This book was released on 2005 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: - Covers the entire field of medical imaging at an introductory level - Provides a brief description of the clinical context of imaging for students with an engineering background - Provides a descriptive, non-mathematical background to the physics underpinning imaging for students with a medical background - Includes exercises and problems at the end of every chapter to test readers' understanding of the material

The Radon Transform and Medical Imaging

Author : Peter Kuchment
Publisher : SIAM
ISBN 13 : 1611973295
Total Pages : 238 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis The Radon Transform and Medical Imaging by : Peter Kuchment

Download or read book The Radon Transform and Medical Imaging written by Peter Kuchment and published by SIAM. This book was released on 2014-01-01 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.

Introduction to Biomedical Imaging

Author : Andrew Webb
Publisher : John Wiley & Sons
ISBN 13 : 1119867711
Total Pages : 388 pages
Book Rating : 4.1/5 (198 download)

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Book Synopsis Introduction to Biomedical Imaging by : Andrew Webb

Download or read book Introduction to Biomedical Imaging written by Andrew Webb and published by John Wiley & Sons. This book was released on 2022-11-08 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to BiomedicalImaging A state-of-the-art exploration of the foundations and latest developments in biomedical imaging technology In the newly revised second edition of Introduction to Biomedical Imaging, distinguished researcher Dr. Andrew Webb delivers a comprehensive description of the fundamentals and applications of the most important current medical imaging techniques: X-ray and computed tomography, nuclear medicine, ultrasound, magnetic resonance imaging, and various optical-based methods. Each chapter explains the physical principles, instrument design, data acquisition, image reconstruction, and clinical applications of its respective modality. This latest edition incorporates descriptions of recent developments in photon counting CT, total body PET, superresolution-based ultrasound, phased-array MRI technology, optical coherence tomography, and iterative and model-based image reconstruction techniques. The final chapter discusses the increasing role of artificial intelligence/deep learning in biomedical imaging. The text also includes a thorough introduction to general image characteristics, including discussions of signal-to-noise and contrast-to-noise. Perfect for graduate and senior undergraduate students of biomedical engineering, Introduction to Biomedical Imaging, 2nd Edition will also earn a place in the libraries of medical imaging professionals with an interest in medical imaging techniques.

Introduction to Functional Magnetic Resonance Imaging

Author : Richard B. Buxton
Publisher : Cambridge University Press
ISBN 13 : 0521899958
Total Pages : 479 pages
Book Rating : 4.5/5 (218 download)

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Book Synopsis Introduction to Functional Magnetic Resonance Imaging by : Richard B. Buxton

Download or read book Introduction to Functional Magnetic Resonance Imaging written by Richard B. Buxton and published by Cambridge University Press. This book was released on 2009-08-27 with total page 479 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second edition of a useful introductory book on a technique that has revolutionized neuroscience, specifically cognitive neuroscience. Functional magnetic resonance imaging (fMRI) has now become the standard tool for studying the brain systems involved in cognitive and emotional processing. It has also been a major factor in the consilience of the fields of neurobiology, cognitive psychology, social psychology, radiology, physics, mathematics, engineering, and even philosophy. Written and edited by a clinician-scientist in the field, this book remains an excellent user's guide to t

The Mathematics of Medical Imaging

Author : Timothy G. Feeman
Publisher :
ISBN 13 : 9783319226668
Total Pages : pages
Book Rating : 4.2/5 (266 download)

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Book Synopsis The Mathematics of Medical Imaging by : Timothy G. Feeman

Download or read book The Mathematics of Medical Imaging written by Timothy G. Feeman and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The basic mathematics of computerized tomography, the CT scan, are aptly presented for an audience of undergraduates in mathematics and engineering. Assuming no prior background in advanced mathematical analysis, topics such as the Fourier transform, sampling, and discrete approximation algorithms are introduced from scratch and are developed within the context of medical imaging. A chapter on magnetic resonance imaging focuses on manipulation of the Bloch equation, the system of differential equations that is the foundation of this important technology. Extending the ideas of the acclaimed first edition, new material has been added to render an even more accessible textbook for course usage. This edition includes new discussions of the Radon transform, the Dirac delta function and its role in X-ray imaging, Kacmarz's method and least squares approximation, spectral filtering, and more. Copious examples and exercises, several new computer-based exercises, and additional graphics have been added to further delineate concepts. The use of technology has been revamped throughout with the incorporation of the open source programming environment R to illustrate examples and composition of graphics. All R code is available as extra source material on SpringerLink. From the reviews of the first edition: "This book is valuable, for it addresses with care and rigor the relevance of a variety of mathematical topics t o a real-world problem. ...This book is well written. It serves its purpose of focusing a variety of mathematical topics onto a real-world application that is in its essence mathematics." -The Journal of Nuclear Medicine, Vol. 51 (12), December, 2010 "This new book by Timothy Feeman, truly intended to be a beginner's guide, makes the subject accessible to undergraduates with a working knowledge of multivariable calculus and some experience with vectors and matrix methods. ...author handles the material with clarity and grace..." -The Mathematical Association of America, February, 2010 "All theoretical material is illustrated with carefully selected examples which are easy to follow. ...I highly recommend this interesting, accessible to wide audience and well-written book dealing with mathematical techniques that support recent ground-breaking discoveries in biomedical technology both to students...and to specialists." -Zentralblatt MATH, Vol. 1191, 2010.

Introduction to Inverse Problems in Imaging

Author : M. Bertero
Publisher : CRC Press
ISBN 13 : 9781439822067
Total Pages : 366 pages
Book Rating : 4.8/5 (22 download)

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Book Synopsis Introduction to Inverse Problems in Imaging by : M. Bertero

Download or read book Introduction to Inverse Problems in Imaging written by M. Bertero and published by CRC Press. This book was released on 2020-08-30 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a graduate textbook on the principles of linear inverse problems, methods of their approximate solution, and practical application in imaging. The level of mathematical treatment is kept as low as possible to make the book suitable for a wide range of readers from different backgrounds in science and engineering. Mathematical prerequisites are first courses in analysis, geometry, linear algebra, probability theory, and Fourier analysis. The authors concentrate on presenting easily implementable and fast solution algorithms. With examples and exercises throughout, the book will provide the reader with the appropriate background for a clear understanding of the essence of inverse problems (ill-posedness and its cure) and, consequently, for an intelligent assessment of the rapidly growing literature on these problems.

Medical Imaging Technology

Author : Victor I. Mikla
Publisher : Elsevier
ISBN 13 : 0124170366
Total Pages : 154 pages
Book Rating : 4.1/5 (241 download)

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Book Synopsis Medical Imaging Technology by : Victor I. Mikla

Download or read book Medical Imaging Technology written by Victor I. Mikla and published by Elsevier. This book was released on 2013-08-23 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: Medical Imaging Technology reveals the physical and materials principles of medical imaging and image processing, from how images are obtained to how they are used. It covers all aspects of image formation in modern imaging modalities and addresses the techniques, instrumentation, and advanced materials used in this rapidly changing field. Covering conventional and modern medical imaging techniques, this book encompasses radiography, fluoroscopy, computed tomography, magnetic resonance imaging, ultrasound, and Raman spectroscopy in medicine. In addition to the physical principles of imaging techniques, the book also familiarizes you with the equipment and procedures used in diagnostic imaging. Addresses the techniques, instrumentation, and advanced materials used in medical imaging Provides practical insight into the skills, tools, and procedures used in diagnostic imaging Focuses on selenium imagers and chalcogenide glasses

The Radon Transform

Author : Ronny Ramlau
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 311055951X
Total Pages : 469 pages
Book Rating : 4.1/5 (15 download)

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Book Synopsis The Radon Transform by : Ronny Ramlau

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 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series is devoted to the publication of high-level monographs, surveys and proceedings which cover the whole spectrum of computational and applied mathematics. The books of this series are addressed to both specialists and advanced students. Interested authors may submit book proposals to the Managing Editor or to any member of the Editorial Board. Managing EditorUlrich Langer, Johannes Kepler University Linz, Austria Editorial BoardHansj rg Albrecher, University of Lausanne, SwitzerlandRonald H. W. Hoppe, University of Houston, USAKarl Kunisch, RICAM, Linz, Austria; University of Graz, AustriaHarald Niederreiter, RICAM, Linz, AustriaChristian Schmeiser, University of Vienna, Austria

A Practical Approach to Medical Image Processing

Author : Elizabeth Berry
Publisher : Taylor & Francis
ISBN 13 : 1584888253
Total Pages : 304 pages
Book Rating : 4.5/5 (848 download)

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Book Synopsis A Practical Approach to Medical Image Processing by : Elizabeth Berry

Download or read book A Practical Approach to Medical Image Processing written by Elizabeth Berry and published by Taylor & Francis. This book was released on 2007-12-07 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: The ability to manipulate and analyze pictorial information to improve medical diagnosis, monitoring, and therapy via imaging is a valuable tool that every professional working in radiography, medical imaging, and medical physics should utilize. However, previous texts on the subject have only approached the subject from a programming or computer s