An Introduction to Mathematics of Emerging Biomedical Imaging

An Introduction to Mathematics of Emerging Biomedical Imaging

Author: Habib Ammari

Publisher: Springer Science & Business Media

Published: 2008-05-21

Total Pages: 198

ISBN-13: 3540795537

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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.


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.

Mathematics and Physics of Emerging Biomedical Imaging

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.


Book Synopsis Mathematics and Physics of Emerging Biomedical Imaging by : National Research Council

Download or read book Mathematics and Physics of Emerging Biomedical Imaging written by National Research Council and published by National Academies Press. This book was released on 1996-03-28 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

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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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.


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 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.

The Mathematics of Medical Imaging

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.


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.

Fundamental Mathematics and Physics of Medical Imaging

Fundamental Mathematics and Physics of Medical Imaging

Author: Jack Lancaster

Publisher: CRC Press

Published: 2016-10-14

Total Pages: 347

ISBN-13: 1498751628

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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.


Book Synopsis Fundamental Mathematics and Physics of Medical Imaging by : Jack Lancaster

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 347 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.

Introduction to Medical Imaging

Introduction to Medical Imaging

Author: Nadine Barrie Smith

Publisher: Cambridge University Press

Published: 2010-11-18

Total Pages:

ISBN-13: 1139492047

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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.


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.

Mathematical Modeling in Biomedical Imaging I

Mathematical Modeling in Biomedical Imaging I

Author: Habib Ammari

Publisher: Springer Science & Business Media

Published: 2009-10-21

Total Pages: 244

ISBN-13: 3642034438

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This volume gives an introduction to a fascinating research area to applied mathematicians. It is devoted to providing the exposition of promising analytical and numerical techniques for solving challenging biomedical imaging problems, which trigger the investigation of interesting issues in various branches of mathematics.


Book Synopsis Mathematical Modeling in Biomedical Imaging I by : Habib Ammari

Download or read book Mathematical Modeling in Biomedical Imaging I written by Habib Ammari and published by Springer Science & Business Media. This book was released on 2009-10-21 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume gives an introduction to a fascinating research area to applied mathematicians. It is devoted to providing the exposition of promising analytical and numerical techniques for solving challenging biomedical imaging problems, which trigger the investigation of interesting issues in various branches of mathematics.

Mathematics and Physics of Emerging Biomedical Imaging

Mathematics and Physics of Emerging Biomedical Imaging

Author: National Research Council

Publisher: National Academies Press

Published: 1996-02-28

Total Pages: 260

ISBN-13: 0309175976

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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.


Book Synopsis Mathematics and Physics of Emerging Biomedical Imaging by : National Research Council

Download or read book Mathematics and Physics of Emerging Biomedical Imaging written by National Research Council and published by National Academies Press. This book was released on 1996-02-28 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Mathematics of Medical Imaging

The Mathematics of Medical Imaging

Author: Timothy G. Feeman

Publisher: Springer

Published: 2015-11-19

Total Pages: 205

ISBN-13: 3319226657

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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


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. 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

Introduction to Biomedical Imaging

Introduction to Biomedical Imaging

Author: Andrew Webb

Publisher: John Wiley & Sons

Published: 2022-11-08

Total Pages: 388

ISBN-13: 1119867711

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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.


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.