› › Mathematical Models And Techniques For Medical Imaging

Introduction to the Mathematics of Medical Imaging

Author : Charles L. Epstein

Publisher : SIAM

Page : 794 pages

File Size : 46,32 MB

Release : 2008-01-01

Category : Mathematics

ISBN : 9780898717792

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Book Description

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.



Mathematical Methods in Image Reconstruction

Author : Frank Natterer

Publisher : SIAM

Page : 226 pages

File Size : 36,73 MB

Release : 2001-01-01

Category : Computers

ISBN : 0898716225

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Book Description

This book provides readers with a superior understanding of the mathematical principles behind imaging.



Handbook of Mathematical Methods in Imaging

Author : Otmar Scherzer

Publisher : Springer Science & Business Media

Page : 1626 pages

File Size : 29,50 MB

Release : 2010-11-23

Category : Mathematics

ISBN : 0387929193

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Book Description

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.



Measurement of Cardiac Deformations from MRI: Physical and Mathematical Models

Author : A.A. Amini

Publisher : Springer Science & Business Media

Page : 352 pages

File Size : 42,44 MB

Release : 2001-12-31

Category : Medical

ISBN : 9781402002229

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Book Description

Measurement of Cardiac Deformations from MRI: Physical and Mathematical Models describes the latest imaging and imag analysis techniques that have been developed at leading centers for the visualization, analysis, and understanding of normal and abnormal cardiac motion with magnetic resonance imaging (MRI). The use of MRI in measuring cardiac motion is particularly important because MRI is non-invasive, and it is the only modality capable of imaging detailed intramural motion within the myocardium. Biomedical engineers, medical physicists, computer scientists, and physicians interested in learning about the latest advances in cardiovascular MRI should find this book to be a valuable educational resource. In particular, it is more tutorial in nature than most of the technical papers where the research was originally published. Practitioners and researchers working in the field of cardiovascular MRI will find the book to be filled with practical technical details and references to other work, enabling the implementation of existing methods and serving as a basis for further research in the area.



The Radon Transform and Medical Imaging

Author : Peter Kuchment

Publisher : SIAM

Page : 238 pages

File Size : 25,29 MB

Release : 2014-03-20

Category : Computers

ISBN : 1611973287

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Book Description

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.





Handbook of Mathematical Models in Computer Vision

Author : Nikos Paragios

Publisher : Springer Science & Business Media

Page : 612 pages

File Size : 36,18 MB

Release : 2006-01-16

Category : Computers

ISBN : 0387288317

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Book Description

Abstract Biological vision is a rather fascinating domain of research. Scientists of various origins like biology, medicine, neurophysiology, engineering, math ematics, etc. aim to understand the processes leading to visual perception process and at reproducing such systems. Understanding the environment is most of the time done through visual perception which appears to be one of the most fundamental sensory abilities in humans and therefore a significant amount of research effort has been dedicated towards modelling and repro ducing human visual abilities. Mathematical methods play a central role in this endeavour. Introduction David Marr's theory v^as a pioneering step tov^ards understanding visual percep tion. In his view human vision was based on a complete surface reconstruction of the environment that was then used to address visual subtasks. This approach was proven to be insufficient by neuro-biologists and complementary ideas from statistical pattern recognition and artificial intelligence were introduced to bet ter address the visual perception problem. In this framework visual perception is represented by a set of actions and rules connecting these actions. The emerg ing concept of active vision consists of a selective visual perception paradigm that is basically equivalent to recovering from the environment the minimal piece information required to address a particular task of interest.



Image Processing and Analysis

Author : Tony F. Chan

Publisher : SIAM

Page : 414 pages

File Size : 35,30 MB

Release : 2005-09-01

Category : Computers

ISBN : 089871589X

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Book Description

This book develops the mathematical foundation of modern image processing and low-level computer vision, bridging contemporary mathematics with state-of-the-art methodologies in modern image processing, whilst organizing contemporary literature into a coherent and logical structure. The authors have integrated the diversity of modern image processing approaches by revealing the few common threads that connect them to Fourier and spectral analysis, the machinery that image processing has been traditionally built on. The text is systematic and well organized: the geometric, functional, and atomic structures of images are investigated, before moving to a rigorous development and analysis of several image processors. The book is comprehensive and integrative, covering the four most powerful classes of mathematical tools in contemporary image analysis and processing while exploring their intrinsic connections and integration. The material is balanced in theory and computation, following a solid theoretical analysis of model building and performance with computational implementation and numerical examples.



The Mathematics of Medical Imaging

Author : Timothy G. Feeman

Publisher : Springer

Page : 205 pages

File Size : 34,21 MB

Release : 2015-11-19

Category : Mathematics

ISBN : 3319226657

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Book Description

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



Mathematical Methods for Signal and Image Analysis and Representation

Author : Luc Florack

Publisher : Springer Science & Business Media

Page : 321 pages

File Size : 32,48 MB

Release : 2012-01-12

Category : Mathematics

ISBN : 1447123530

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Book Description

Mathematical Methods for Signal and Image Analysis and Representation presents the mathematical methodology for generic image analysis tasks. In the context of this book an image may be any m-dimensional empirical signal living on an n-dimensional smooth manifold (typically, but not necessarily, a subset of spacetime). The existing literature on image methodology is rather scattered and often limited to either a deterministic or a statistical point of view. In contrast, this book brings together these seemingly different points of view in order to stress their conceptual relations and formal analogies. Furthermore, it does not focus on specific applications, although some are detailed for the sake of illustration, but on the methodological frameworks on which such applications are built, making it an ideal companion for those seeking a rigorous methodological basis for specific algorithms as well as for those interested in the fundamental methodology per se. Covering many topics at the forefront of current research, including anisotropic diffusion filtering of tensor fields, this book will be of particular interest to graduate and postgraduate students and researchers in the fields of computer vision, medical imaging and visual perception.