Image Reconstruction

Applications in Medical Sciences

Author: Gengsheng Lawrence Zeng

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 3110500590

Category: Medical

Page: 240

View: 9995

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This book introduces the classical and modern image reconstruction technologies. It covers topics in two-dimensional (2D) parallel-beam and fan-beam imaging, three-dimensional (3D) parallel ray, parallel plane, and cone-beam imaging. Both analytical and iterative methods are presented. The applications in X-ray CT, SPECT (single photon emission computed tomography), PET (positron emission tomography), and MRI (magnetic resonance imaging) are discussed. Contemporary research results in exact region-of-interest (ROI) reconstruction with truncated projections, Katsevich’s cone-beam filtered backprojection algorithm, and reconstruction with highly under-sampled data are included. The last chapter of the book is devoted to the techniques of using a fast analytical algorithm to reconstruct an image that is equivalent to an iterative reconstruction. These techniques are the author’s most recent research results. This book is intended for students, engineers, and researchers who are interested in medical image reconstruction. Written in a non-mathematical way, this book provides an easy access to modern mathematical methods in medical imaging. Table of Content: Chapter 1 Basic Principles of Tomography 1.1 Tomography 1.2 Projection 1.3 Image Reconstruction 1.4 Backprojection 1.5 Mathematical Expressions Problems References Chapter 2 Parallel-Beam Image Reconstruction 2.1 Fourier Transform 2.2 Central Slice Theorem 2.3 Reconstruction Algorithms 2.4 A Computer Simulation 2.5 ROI Reconstruction with Truncated Projections 2.6 Mathematical Expressions (The Fourier Transform and Convolution , The Hilbert Transform and the Finite Hilbert Transform , Proof of the Central Slice Theorem, Derivation of the Filtered Backprojection Algorithm , Expression of the Convolution Backprojection Algorithm, Expression of the Radon Inversion Formula ,Derivation of the Backprojection-then-Filtering Algorithm Problems References Chapter 3 Fan-Beam Image Reconstruction 3.1 Fan-Beam Geometry and Point Spread Function 3.2 Parallel-Beam to Fan-Beam Algorithm Conversion 3.3 Short Scan 3.4 Mathematical Expressions (Derivation of a Filtered Backprojection Fan-Beam Algorithm, A Fan-Beam Algorithm Using the Derivative and the Hilbert Transform) Problems References Chapter 4 Transmission and Emission Tomography 4.1 X-Ray Computed Tomography 4.2 Positron Emission Tomography and Single Photon Emission Computed Tomography 4.3 Attenuation Correction for Emission Tomography 4.4 Mathematical Expressions Problems References Chapter 5 3D Image Reconstruction 5.1 Parallel Line-Integral Data 5.2 Parallel Plane-Integral Data 5.3 Cone-Beam Data (Feldkamp's Algorithm, Grangeat's Algorithm, Katsevich's Algorithm) 5.4 Mathematical Expressions (Backprojection-then-Filtering for Parallel Line-Integral Data, Filtered Backprojection Algorithm for Parallel Line-Integral Data, 3D Radon Inversion Formula, 3D Backprojection-then-Filtering Algorithm for Radon Data, Feldkamp's Algorithm, Tuy's Relationship, Grangeat's Relationship, Katsevich’s Algorithm) Problems References Chapter 6 Iterative Reconstruction 6.1 Solving a System of Linear Equations 6.2 Algebraic Reconstruction Technique 6.3 Gradient Descent Algorithms 6.4 Maximum-Likelihood Expectation-Maximization Algorithms 6.5 Ordered-Subset Expectation-Maximization Algorithm 6.6 Noise Handling (Analytical Methods, Iterative Methods, Iterative Methods) 6.7 Noise Modeling as a Likelihood Function 6.8 Including Prior Knowledge 6.9 Mathematical Expressions (ART, Conjugate Gradient Algorithm, ML-EM, OS-EM, Green’s One-Step Late Algorithm, Matched and Unmatched Projector/Backprojector Pairs ) 6.10 Reconstruction Using Highly Undersampled Data with l0 Minimization Problems References Chapter 7 MRI Reconstruction 7.1 The 'M' 7.2 The 'R' 7.3 The 'I'; (To Obtain z-Information, x-Information, y-Information) 7.4 Mathematical Expressions Problems References Indexing
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Close-Range Photogrammetry and 3D Imaging

Author: Thomas Luhmann,Stuart Robson,Stephen Kyle,Jan Boehm

Publisher: Walter de Gruyter

ISBN: 3110302780

Category: Science

Page: 702

View: 1923

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This is the second edition of the established guide to close-range photogrammetry which uses accurate imaging techniques to analyse the three-dimensional shape of a wide range of manufactured and natural objects. After more than 20 years of use, close-range photogrammetry, now for the most part entirely digital, has become an accepted, powerful and readily available technique for engineers, scientists and others who wish to utilise images to make accurate 3D measurements of complex objects. Here they will find the photogrammetric fundamentals, details of system hardware and software, and broad range of real-world applications in order to achieve this. Following the introduction, the book provides fundamental mathematics covering subjects such as image orientation, digital imaging processing and 3D reconstruction methods, as well as a discussion of imaging technology, including targeting and illumination, and its implementation in hardware and software. It concludes with an overview of photogrammetric solutions for typical applications in engineering, manufacturing, medical science, architecture, archaeology and other fields.
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Biomedical Imaging

Principles of Radiography, Tomography and Medical Physics

Author: Tim Salditt,Timo Aspelmeier,Sebastian Aeffner

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 3110426692

Category: Science

Page: 358

View: 4506

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Covering both physical as well as mathematical and algorithmic foundations, this graduate textbook provides the reader with an introduction into modern biomedical imaging and image processing and reconstruction. These techniques are not only based on advanced instrumentation for image acquisition, but equally on new developments in image processing and reconstruction to extract relevant information from recorded data. To this end, the present book offers a quantitative treatise of radiography, computed tomography, and medical physics. Contents Introduction Digital image processing Essentials of medical x-ray physics Tomography Radiobiology, radiotherapy, and radiation protection Phase contrast radiography Object reconstruction under nonideal conditions
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Blind Equalization in Neural Networks

Theory, Algorithms and Applications

Author: Liyi Zhang

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 3110450291

Category: Computers

Page: 268

View: 7986

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The book begins with an introduction of blind equalization theory and its application in neural networks, then discusses the algorithms in recurrent networks, fuzzy networks and other frequently-studied neural networks. Each algorithm is accompanied by derivation, modeling and simulation, making the book an essential reference for electrical engineers, computer intelligence researchers and neural scientists.
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Current Catalog

Author: National Library of Medicine (U.S.)

Publisher: N.A

ISBN: N.A

Category: Medicine

Page: N.A

View: 9573

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First multi-year cumulation covers six years: 1965-70.
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Books in Print

Author: N.A

Publisher: N.A

ISBN: N.A

Category: American literature

Page: N.A

View: 1219

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Books in print is the major source of information on books currently published and in print in the United States. The database provides the record of forthcoming books, books in-print, and books out-of-print.
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