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Fundamental Mathematics and Physics of Medical Imaging

Author: Jack Lancaster

Publisher: CRC Press

Published: 2016-10-14

Total Pages: 322

ISBN-13: 1498751628

Authored by a leading educator, this book teaches the fundamental mathematics and physics concepts associated with medical imaging systems. Going beyond mere description of imaging modalities, this book delves into the mechanisms of image formation and image quality common to all imaging systems: contrast mechanisms, noise, and spatial and temporal resolution, making it an important reference for medical physicists and biomedical engineering students. This is an extensively revised new edition of The Physics of Medical X-Ray Imaging by Bruce Hasegawa (Medical Physics Publishing, 1991), and includes a wide range of modalities such as X-ray CT, MRI and SPECT.

Fundamentals of Medical Imaging

Author: Paul Suetens

Publisher: Cambridge University Press

Published: 2009-08-06

Total Pages: 265

ISBN-13: 1139479881

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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.

Fundamental Mathematics and Physics of Medical Imaging

Author: Jack Lancaster

Publisher: CRC Press

Published: 2016-10-14

Total Pages: 468

ISBN-13: 1498751644

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Introduction to the Mathematics of Medical Imaging

Author: Charles L. Epstein

Publisher: SIAM

Published: 2008-01-01

Total Pages: 794

ISBN-13: 9780898717792

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Mathematics and Physics of Emerging Biomedical Imaging

Author: National Research Council

Publisher: National Academies Press

Published: 1996-03-28

Total Pages: 261

ISBN-13: 0309053870

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This cross-disciplinary book documents the key research challenges in the mathematical sciences and physics that could enable the economical development of novel biomedical imaging devices. It is hoped that the infusion of new insights from mathematical scientists and physicists will accelerate progress in imaging. Incorporating input from dozens of biomedical researchers who described what they perceived as key open problems of imaging that are amenable to attack by mathematical scientists and physicists, this book introduces the frontiers of biomedical imaging, especially the imaging of dynamic physiological functions, to the educated nonspecialist. Ten imaging modalities are covered, from the well-established (e.g., CAT scanning, MRI) to the more speculative (e.g., electrical and magnetic source imaging). For each modality, mathematics and physics research challenges are identified and a short list of suggested reading offered. Two additional chapters offer visions of the next generation of surgical and interventional techniques and of image processing. A final chapter provides an overview of mathematical issues that cut across the various modalities.

Introduction to the Mathematics of Medical Imaging

Author: Charles L. Epstein

Publisher: SIAM

Published: 2008-01-01

Total Pages: 782

ISBN-13: 089871642X

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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.

The Mathematics of Medical Imaging

Author: Timothy G. Feeman

Publisher: Springer Science & Business Media

Published: 2010

Total Pages: 150

ISBN-13: 0387927115

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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.

The Physics and Mathematics of MRI

Author: Richard Ansorge

Publisher: Morgan & Claypool Publishers

Published: 2016-11-01

Total Pages: 188

ISBN-13: 1681740680

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Magnetic Resonance Imaging is a very important clinical imaging tool. It combines different fields of physics and engineering in a uniquely complex way. MRI is also surprisingly versatile, 'pulse sequences' can be designed to yield many different types of contrast. This versatility is unique to MRI. This short book gives both an in depth account of the methods used for the operation and construction of modern MRI systems and also the principles of sequence design and many examples of applications. An important additional feature of this book is the detailed discussion of the mathematical principles used in building optimal MRI systems and for sequence design. The mathematical discussion is very suitable for undergraduates attending medical physics courses. It is also more complete than usually found in alternative books for physical scientists or more clinically orientated works.

Fundamentals of MRI

Author: Elizabeth Berry

Publisher: CRC Press

Published: 2008-12-22

Total Pages: 320

ISBN-13: 1584889020

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Fundamentals of MRI: An Interactive Learning Approach explores the physical principles that underpin the technique of magnetic resonance imaging (MRI).After covering background mathematics, physics, and digital imaging, the book presents fundamental physical principles, including magnetization and rotating reference frame. It describes how relaxati

The Essential Physics of Medical Imaging

Author: Jerold T. Bushberg

Publisher: Lippincott Williams & Wilkins

Published: 2020-11-24

Total Pages: 1688

ISBN-13: 1975103246

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Widely regarded as the cornerstone text in the field, the successful series of editions continues to follow the tradition of a clear and comprehensive presentation of the physical principles and operational aspects of medical imaging. The Essential Physics of Medical Imaging, 4th Edition, is a coherent and thorough compendium of the fundamental principles of the physics, radiation protection, and radiation biology that underlie the practice and profession of medical imaging. Distinguished scientists and educators from the University of California, Davis, provide up-to-date, readable information on the production, characteristics, and interactions of non-ionizing and ionizing radiation, magnetic fields and ultrasound used in medical imaging and the imaging modalities in which they are used, including radiography, mammography, fluoroscopy, computed tomography, magnetic resonance, ultrasound, and nuclear medicine. This vibrant, full-color text is enhanced by more than 1,000 images, charts, and graphs, including hundreds of new illustrations. This text is a must-have resource for medical imaging professionals, radiology residents who are preparing for Core Exams, and teachers and students in medical physics and biomedical engineering.