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.

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 794 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 of these modalities. The text uses X-ray computed tomography (X-ray CT) as a 'pedagogical machine' to illustrate important ideas and its extensive discussion of background material makes the more advanced mathematical topics accessible to people with a less formal mathematical education. This new edition contains a chapter on magnetic resonance imaging (MRI), a revised section on the relationship between the continuum and discrete Fourier transforms, an improved description of the gridding method, and new sections on both Grangreat's formula and noise analysis in MR-imaging. Mathematical concepts are illuminated with over 200 illustrations and numerous exercises.

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 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.

Download or read book Statistics of Medical Imaging written by Tianhu Lei and published by CRC Press. This book was released on 2011-12-19 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: More work is being done in the statistical aspects of medical imaging, and this book fills the gap to provide a unified framework of study by presenting a complete look at medical imaging and statistics - from the statistical aspects of imaging technology to the statistical analysis of images. It provides technicians and students with the statistical principles that underlay medical imaging, as required reference material for researchers involved in the design of new technology. Illustrations are included throughout as are many real examples, and algorithms. The text also includes exercises developed out of the author's many years experience with studying the statistics of medical imaging.

Download or read book Fundamental Mathematics and Physics of Medical Imaging written by Jack Lancaster and published by CRC Press. This book was released on 2016-10-14 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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.

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.

Download or read book Handbook of Mathematical Methods in Imaging written by Otmar Scherzer and published by Springer Science & Business Media. This book was released on 2010-11-23 with total page 1626 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Mathematical Methods in Imaging provides a comprehensive treatment of the mathematical techniques used in imaging science. The material is grouped into two central themes, namely, Inverse Problems (Algorithmic Reconstruction) and Signal and Image Processing. Each section within the themes covers applications (modeling), mathematics, numerical methods (using a case example) and open questions. Written by experts in the area, the presentation is mathematically rigorous. The entries are cross-referenced for easy navigation through connected topics. Available in both print and electronic forms, the handbook is enhanced by more than 150 illustrations and an extended bibliography. It will benefit students, scientists and researchers in applied mathematics. Engineers and computer scientists working in imaging will also find this handbook useful.

Download or read book The Mathematics of Medical Imaging written by Timothy G. Feeman and published by Springer. This book was released on 2015-11-19 with total page 205 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 adeed 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, 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 to a real-world problem. ...T his 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

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.

Download or read book The Physics and Mathematics of MRI written by Richard Ansorge and published by Morgan & Claypool Publishers. This book was released on 2016-11-01 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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.

Download or read book The Physics of Medical Imaging written by S. Webb and published by CRC Press. This book was released on 1988-01-01 with total page 658 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Physics of Medical Imaging reviews the scientific basis and physical principles underpinning imaging in medicine. It covers the major imaging methods of x-radiology, nuclear medicine, ultrasound, and nuclear magnetic resonance, and considers promising new techniques. Following these reviews are several thematic chapters that cover the mathematics of medical imaging, image perception, computational requirements, and techniques. Throughout the book, the author encourages readers to consider key questions concerning imaging. This profusely illustrated and extensively indexed text is accessible to graduate physical scientists, advanced undergraduates, and research students. It logically complements books on applications of imaging techniques in medicine, making it useful for clinicians as well.

Download or read book Mathematical Methods in Image Reconstruction written by Frank Natterer and published by SIAM. This book was released on 2001-01-01 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides readers with a superior understanding of the mathematical principles behind imaging.

Download or read book Mathematical Foundations of Imaging Tomography and Wavefield Inversion written by Anthony J. Devaney and published by Cambridge University Press. This book was released on 2012-06-21 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inverse problems are of interest and importance across many branches of physics, mathematics, engineering and medical imaging. In this text, the foundations of imaging and wavefield inversion are presented in a clear and systematic way. The necessary theory is gradually developed throughout the book, progressing from simple wave equation based models to vector wave models. By combining theory with numerous MATLAB based examples, the author promotes a complete understanding of the material and establishes a basis for real world applications. Key topics of discussion include the derivation of solutions to the inhomogeneous and homogeneous Helmholtz equations using Green function techniques; the propagation and scattering of waves in homogeneous and inhomogeneous backgrounds; and the concept of field time reversal. Bridging the gap between mathematics and physics, this multidisciplinary book will appeal to graduate students and researchers alike. Additional resources including MATLAB codes and solutions are available online at www.cambridge.org/9780521119740.

Download or read book Medical Imaging Physics written by William R. Hendee and published by Wiley-Liss. This book was released on 2002 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt: William Hendee and Russell Ritenour's comprehensive text provides the tools necessary to be comfortable with the physical principles, technology concepts, equiment, and procedures used in diagnostic imaging, as well as to appreciate the technological capabilities and limitations of the discipline. Readers need not possess a background in physics. Broadly accessible, Medical Imaging Physics covers all aspects of image formation in modern medical imaging modalities, such as radiography, ultrasonography, computed tomopgraphy(CT), nuclear imaging, and magnetic resonance. Other topics covered include; Digital x-ray imaging Doppler ultrasound Helical CT scanning Accumulation and analysis of nuclear data Experimental radiobiology Radiation protection and safety