The Radon Transform And Medical Imaging

Author : Peter Kuchment
Publisher : SIAM
Page : 238 pages
File Size : 46,6 Mb
Release : 2014-01-01
Category : Computers
ISBN : 9781611973297

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The Radon Transform and Medical Imaging by Peter Kuchment Pdf

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.

Author : Ronny Ramlau,Otmar Scherzer
Publisher : Walter de Gruyter GmbH & Co KG
Page : 469 pages
File Size : 42,8 Mb
Release : 2019-06-17
Category : Mathematics
ISBN : 9783110559514

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The Radon Transform by Ronny Ramlau,Otmar Scherzer Pdf

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

Author : Andrew E. Todd-Pokropek,Max A. Viergever
Publisher : Springer Science & Business Media
Page : 700 pages
File Size : 45,6 Mb
Release : 2013-06-29
Category : Medical
ISBN : 9783642778889

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Medical Images: Formation, Handling and Evaluation by Andrew E. Todd-Pokropek,Max A. Viergever Pdf

Medical imaging is a very important area in diagnostic (and increasingly therapeutic) medicine. Many new techniques are being developed or extended which depend on digital methods. Although conventional x-radiographs still comprise the bulk of the medical images acquired in a hospital, digital methods such as computerized tomography and magnetic resonance imaging are now often claimed to have a more significant clinical impact. This book is concerned with three aspects of such digital images: their formation, or how they can be acquired; their handling, or how they may be manipulated to increase their clinical value; and their evaluation, or how their impact and value may be assessed. The book is divided into three parts. Part 1 comprises a series of reviews in the general subject area written by authorities in the field. Part 2 includes papers on theoretical aspects: 3D images, reconstruction, perception, and image processing. Part 3includes papers on applications in nuclear medicine, magnetic resonance, andradiology.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 52,7 Mb
Release : 2024-06-06
Category : Electronic
ISBN : 9789814476065

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Principles and Advanced Methods in Medical Imaging and Image Analysis by Anonim Pdf

Author : Charles L. Epstein
Publisher : SIAM
Page : 794 pages
File Size : 40,9 Mb
Release : 2008-01-01
Category : Mathematics
ISBN : 0898717795

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Introduction to the Mathematics of Medical Imaging by Charles L. Epstein Pdf

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.

Author : Pierre Grangeat,Jean-Louis Amans
Publisher : Springer Science & Business Media
Page : 313 pages
File Size : 40,7 Mb
Release : 2013-03-09
Category : Medical
ISBN : 9789401587495

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Three-Dimensional Image Reconstruction in Radiology and Nuclear Medicine by Pierre Grangeat,Jean-Louis Amans Pdf

This book contains a selection of communications presented at the Third International Meeting on Fully Three-Dimensional Image Reconstruction in Radiology and Nuclear Medicine, held 4-6 July 1995 at Domaine d' Aix-Marlioz, Aix-Ies-Bains, France. This nice resort provided an inspiring environment to hold discussions and presentations on new and developing issues. Roentgen discovered X-ray radiation in 1895 and Becquerel found natural radioactivity in 1896 : a hundred years later, this conference was focused on the applications of such radiations to explore the human body. If the physics is now fully understood, 3D imaging techniques based on ionising radiations are still progressing. These techniques include 3D Radiology, 3D X-ray Computed Tomography (3D-CT), Single Photon Emission Computed Tomography (SPECT), Positron Emission Tomography (PET). Radiology is dedicated to morphological imaging, using transmitted radiations from an external X-ray source, and nuclear medicine to functional imaging, using radiations emitted from an internal radioactive tracer. In both cases, new 3D tomographic systems will tend to use 2D detectors in order to improve the radiation detection efficiency. Taking a set of 2D acquisitions around the patient, 3D acquisitions are obtained. Then, fully 3D image reconstruction algorithms are required to recover the 3D image of the body from these projection measurements.

Author : Roger L. Easton Jr.
Publisher : John Wiley & Sons
Page : 1005 pages
File Size : 49,9 Mb
Release : 2010-11-18
Category : Technology & Engineering
ISBN : 9781119991861

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Fourier Methods in Imaging by Roger L. Easton Jr. Pdf

Fourier Methods in Imaging introduces the mathematical tools for modeling linear imaging systems to predict the action of the system or for solving for the input. The chapters are grouped into five sections, the first introduces the imaging “tasks” (direct, inverse, and system analysis), the basic concepts of linear algebra for vectors and functions, including complex-valued vectors, and inner products of vectors and functions. The second section defines "special" functions, mathematical operations, and transformations that are useful for describing imaging systems. Among these are the Fourier transforms of 1-D and 2-D function, and the Hankel and Radon transforms. This section also considers approximations of the Fourier transform. The third and fourth sections examine the discrete Fourier transform and the description of imaging systems as linear "filters", including the inverse, matched, Wiener and Wiener-Helstrom filters. The final section examines applications of linear system models to optical imaging systems, including holography. Provides a unified mathematical description of imaging systems. Develops a consistent mathematical formalism for characterizing imaging systems. Helps the reader develop an intuitive grasp of the most common mathematical methods, useful for describing the action of general linear systems on signals of one or more spatial dimensions. Offers parallel descriptions of continuous and discrete cases. Includes many graphical and pictorial examples to illustrate the concepts. This book helps students develop an understanding of mathematical tools for describing general one- and two-dimensional linear imaging systems, and will also serve as a reference for engineers and scientists

Author : Stanley R. Deans
Publisher : Courier Corporation
Page : 306 pages
File Size : 44,8 Mb
Release : 2007-10-01
Category : Mathematics
ISBN : 9780486462417

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The Radon Transform and Some of Its Applications by Stanley R. Deans Pdf

Of value to mathematicians, physicists, and engineers, this excellent introduction to Radon transform covers both theory and applications, with a rich array of examples and literature that forms a valuable reference. This 1993 edition is a revised and updated version by the author of his pioneering work.

Author : Atam P. Dhawan,H. K. Huang,Dae-Shik Kim
Publisher : World Scientific
Page : 869 pages
File Size : 45,8 Mb
Release : 2008
Category : Medical
ISBN : 9789812705341

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Principles and Advanced Methods in Medical Imaging and Image Analysis by Atam P. Dhawan,H. K. Huang,Dae-Shik Kim Pdf

Computerized medical imaging and image analysis have been the central focus in diagnostic radiology. They provide revolutionarizing tools for visualization of physiology as well as the understanding and quantitative measurement of physiological parameters. This book provides a unique depth of knowledge from the principles to recent advanced methods in medical imaging instrumentation and techniques as well as multidimensional image analysis and classification methods for research, education and applications in computer-aided diagnostic radiology. Internationally renowned researchers and experts in their respective areas provide detailed description of the basic foundation as well as the most recent developments in medical imaging. This book helps readers to understand theoretical and advanced concepts for important research and clinical applications.

Author : Jiri Jan
Publisher : CRC Press
Page : 755 pages
File Size : 48,5 Mb
Release : 2005-11-02
Category : Medical
ISBN : 9781420030679

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Medical Image Processing, Reconstruction and Restoration by Jiri Jan Pdf

It is essential that differently oriented specialists and students involved in image processing have a firm grasp of the necessary concepts and principles. A single-source reference that can provide this foundation, as well as a thorough explanation of the techniques involved, particularly those found in medical image processing, would be an

Author : Eric Todd Quinto
Publisher : American Mathematical Soc.
Page : 274 pages
File Size : 46,6 Mb
Release : 2001
Category : Radon transforms
ISBN : 9780821821350

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Radon Transforms and Tomography by Eric Todd Quinto Pdf

One of the most exciting features of the fields of Radon transforms and tomography is the strong relationship between high-level pure mathematics and applications to areas such as medical imaging and industrial nondestructive evaluation. The proceedings featured in this volume bring together fundamental research articles in the major areas of Radon transforms and tomography. This volume includes expository papers that are of special interest to beginners as well as advanced researchers. Topics include local tomography and wavelets, Lambda tomography and related methods, tomographic methods in RADAR, ultrasound, Radon transforms and differential equations, and the Pompeiu problem. The major themes in Radon transforms and tomography are represented among the research articles. Pure mathematical themes include vector tomography, microlocal analysis, twistor theory, Lie theory, wavelets, harmonic analysis, and distribution theory. The applied articles employ high-quality pure mathematics to solve important practical problems. Effective scanning geometries are developed and tested for a NASA wind tunnel. Algorithms for limited electromagnetic tomographic data and for impedance imaging are developed and tested. Range theorems are proposed to diagnose problems with tomography scanners. Principles are given for the design of X-ray tomography reconstruction algorithms, and numerical examples are provided. This volume offers readers a comprehensive source of fundamental research useful to both beginners and advanced researchers in the fields.

Author : Haim Azhari,John A. Kennedy,Noam Weiss,Lana Volokh
Publisher : Springer Nature
Page : 472 pages
File Size : 51,7 Mb
Release : 2020-05-29
Category : Technology & Engineering
ISBN : 9783030353261

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From Signals to Image by Haim Azhari,John A. Kennedy,Noam Weiss,Lana Volokh Pdf

This textbook, intended for advanced undergraduate and graduate students, is an introduction to the physical and mathematical principles used in clinical medical imaging. The first two chapters introduce basic concepts and useful terms used in medical imaging and the tools implemented in image reconstruction, while the following chapters cover an array of topics such as physics of x-rays and their implementation in planar and computed tomography (CT) imaging; nuclear medicine imaging and the methods of forming functional planar and single photon emission computed tomography (SPECT) images and Clinical imaging using positron emitters as radiotracers. The book also discusses the principles of MRI pulse sequencing and signal generation, gradient fields, and the methodologies implemented for image formation, form flow imaging and magnetic resonance angiography and the basic physics of acoustic waves, the different acquisition modes used in medical ultrasound, and the methodologies implemented for image formation and flow imaging using the Doppler Effect. By the end of the book, readers will know what is expected from a medical image, will comprehend the issues involved in producing and assessing the quality of a medical image, will be able to conceptually implement this knowledge in the development of a new imaging modality, and will be able to write basic algorithms for image reconstruction. Knowledge of calculus, linear algebra, regular and partial differential equations, and a familiarity with the Fourier transform and it applications is expected, along with fluency with computer programming. The book contains exercises, homework problems, and sample exam questions that are exemplary of the main concepts and formulae students would encounter in a clinical setting.

Author : Timothy G. Feeman
Publisher : Springer Science & Business Media
Page : 150 pages
File Size : 40,9 Mb
Release : 2010
Category : Computers
ISBN : 9780387927114

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The Mathematics of Medical Imaging by Timothy G. Feeman Pdf

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.

Author : Hong Yan
Publisher : CRC Press
Page : 666 pages
File Size : 50,7 Mb
Release : 2002-02-20
Category : Technology & Engineering
ISBN : 9780203908785

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Signal Processing for Magnetic Resonance Imaging and Spectroscopy by Hong Yan Pdf

This reference/text contains the latest signal processing techniques in magnetic resonance imaging (MRI) and magnetic resonance spectroscopy (MRS) for more efficient clinical diagnoses-providing ready-to-use algorithms for image segmentation and analysis, reconstruction and visualization, and removal of distortions and artifacts for increased detec

Author : George C. Kagadis,Steve G. Langer
Publisher : CRC Press
Page : 370 pages
File Size : 46,9 Mb
Release : 2011-10-17
Category : Science
ISBN : 9781439831243

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Informatics in Medical Imaging by George C. Kagadis,Steve G. Langer Pdf

Informatics in Medical Imaging provides a comprehensive survey of the field of medical imaging informatics. In addition to radiology, it also addresses other specialties such as pathology, cardiology, dermatology, and surgery, which have adopted the use of digital images. The book discusses basic imaging informatics protocols, picture archiving and communication systems, and the electronic medical record. It details key instrumentation and data mining technologies used in medical imaging informatics as well as practical operational issues, such as procurement, maintenance, teleradiology, and ethics. Highlights Introduces the basic ideas of imaging informatics, the terms used, and how data are represented and transmitted Emphasizes the fundamental communication paradigms: HL7, DICOM, and IHE Describes information systems that are typically used within imaging departments: orders and result systems, acquisition systems, reporting systems, archives, and information-display systems Outlines the principal components of modern computing, networks, and storage systems Covers the technology and principles of display and acquisition detectors, and rounds out with a discussion of other key computer technologies Discusses procurement and maintenance issues; ethics and its relationship to government initiatives like HIPAA; and constructs beyond radiology The technologies of medical imaging and radiation therapy are so complex and computer-driven that it is difficult for physicians and technologists responsible for their clinical use to know exactly what is happening at the point of care. Medical physicists are best equipped to understand the technologies and their applications, and these individuals are assuming greater responsibilities in the clinical arena to ensure that intended care is delivered in a safe and effective manner. Built on a foundation of classic and cutting-edge research, Informatics in Medical Imaging supports and updates medical physicists functioning at the intersection of radiology and radiation.