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Image Reconstruction From Projections
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Book Synopsis Fundamentals of Computerized Tomography by : Gabor T. Herman
Download or read book Fundamentals of Computerized Tomography written by Gabor T. Herman and published by Springer Science & Business Media. This book was released on 2009-07-14 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: This revised and updated second edition – now with two new chapters - is the only book to give a comprehensive overview of computer algorithms for image reconstruction. It covers the fundamentals of computerized tomography, including all the computational and mathematical procedures underlying data collection, image reconstruction and image display. Among the new topics covered are: spiral CT, fully 3D positron emission tomography, the linogram mode of backprojection, and state of the art 3D imaging results. It also includes two new chapters on comparative statistical evaluation of the 2D reconstruction algorithms and alternative approaches to image reconstruction.
Book Synopsis Fundamentals of Computerized Tomography by : Gabor T. Herman
Download or read book Fundamentals of Computerized Tomography written by Gabor T. Herman and published by Springer. This book was released on 2012-03-14 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This revised and updated second edition – now with two new chapters - is the only book to give a comprehensive overview of computer algorithms for image reconstruction. It covers the fundamentals of computerized tomography, including all the computational and mathematical procedures underlying data collection, image reconstruction and image display. Among the new topics covered are: spiral CT, fully 3D positron emission tomography, the linogram mode of backprojection, and state of the art 3D imaging results. It also includes two new chapters on comparative statistical evaluation of the 2D reconstruction algorithms and alternative approaches to image reconstruction.
Book Synopsis Image Reconstruction from Projections by : Gabor T. Herman
Download or read book Image Reconstruction from Projections written by Gabor T. Herman and published by . This book was released on 1980 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Image reconstruction from projections. Probability and random variables. An overview of the process of CT. Physical problems associated with data collection in CT. Computer simulation of data collection in CT. Data collection and reconstruction of the head phantom under various assumptions. Basic concepts of reconstruction algorithms. Backprojection. Convolution method for parallel beams. Other transform methods for parallel beams. Convolution methods for divergent beams. The algebraic reconstruction techniques. Quadratic optimization methods. Noniterative series expansion methods. Truly three-dimensional reconstruction. Three-dimensional display of organs. Mathematical background.
Book Synopsis Image Reconstruction by : Gengsheng Lawrence Zeng
Download or read book Image Reconstruction written by Gengsheng Lawrence Zeng and published by Walter de Gruyter GmbH & Co KG. This book was released on 2017-03-20 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Medical Image Reconstruction by : Gengsheng Zeng
Download or read book Medical Image Reconstruction written by Gengsheng Zeng and published by Springer Science & Business Media. This book was released on 2010-12-28 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Medical Image Reconstruction: A Conceptual Tutorial" introduces the classical and modern image reconstruction technologies, such as two-dimensional (2D) parallel-beam and fan-beam imaging, three-dimensional (3D) parallel ray, parallel plane, and cone-beam imaging. This book presents both analytical and iterative methods of these technologies and their applications in X-ray CT (computed tomography), SPECT (single photon emission computed tomography), PET (positron emission tomography), and MRI (magnetic resonance imaging). Contemporary research results in exact region-of-interest (ROI) reconstruction with truncated projections, Katsevich's cone-beam filtered backprojection algorithm, and reconstruction with highly undersampled data with l0-minimization are also included. This book is written for engineers and researchers in the field of biomedical engineering specializing in medical imaging and image processing with image reconstruction. Gengsheng Lawrence Zeng is an expert in the development of medical image reconstruction algorithms and is a professor at the Department of Radiology, University of Utah, Salt Lake City, Utah, USA.
Book Synopsis Tensor Transform Based Method of Image Reconstruction by Projections by : Nan Du
Download or read book Tensor Transform Based Method of Image Reconstruction by Projections written by Nan Du and published by . This book was released on 2013 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: Methods of the Fourier transform are widely used for practical applications of image reconstruction from projections, such as the computerized tomography. We mention the well known methods of back-projection and methods based on the Fourier slice theorem, which requires a crude interpolation when transforming the Fourier projections from the polar grid to the traditional Cartesian grid. The solution of this complex problem is very important in medical diagnoses, where projections data for reconstructing two- and three-dimensional images are obtained by means of the roentgen radiation with an investigated part of the body. In this work, we analyze solutions of the problem of reconstruction of the discrete image on the Cartesian grid from projections of the image on the spatial domain, which are based on the concept of the two-dimensional discrete tensor transformation. In the framework of the constructed model, we show a way of using the line-integrals of the image, or real projections data for exact reconstructing the discrete image. The model of image reconstruction proposed in this research is described for the cases, when the size of the Cartesian grid are primes and power of two. The problem we focus on is formulated as follows. For a given image f(x, y) on the bounded region (such as the square [0, 1] × [0, 1]) and the N × N Cartesian grid placed on the region, reconstruct exactly the discrete image fn,m from the line-integrals of the image f(x, y) calculated in a finite number of projections. The solution of this problem is based on the new approach proposed by Grigoryan, which allows to transfer uniquely the geometry of the projections from the image plane to the geometry of projections onto the Cartesian grid. This transformation allows calculating the tensor representation of the discrete image, where the image is described by one-dimensional splitting-signals carrying the spectral information about the image at frequency-points of different subsets covering the Cartesian lattice. When the size of the image is a power of two, these subsets are intersected and this property can be used effectively for solution of the well known problem of image reconstruction from limited angle range projections. Our preliminary results show that the proposed method of reconstruction is more accurate than the known projections onto convex sets algorithm. In addition, the simulations of our algorithm demonstrate good reconstructions when the projections are within a limited angular range. The proposed method of image reconstruction is robust relative to the additive signal-independent noise in projection data.
Book Synopsis Image Processing by : Artyom M. Grigoryan
Download or read book Image Processing written by Artyom M. Grigoryan and published by CRC Press. This book was released on 2018-09-03 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focusing on mathematical methods in computer tomography, Image Processing: Tensor Transform and Discrete Tomography with MATLAB® introduces novel approaches to help in solving the problem of image reconstruction on the Cartesian lattice. Specifically, it discusses methods of image processing along parallel rays to more quickly and accurately reconstruct images from a finite number of projections, thereby avoiding overradiation of the body during a computed tomography (CT) scan. The book presents several new ideas, concepts, and methods, many of which have not been published elsewhere. New concepts include methods of transferring the geometry of rays from the plane to the Cartesian lattice, the point map of projections, the particle and its field function, and the statistical model of averaging. The authors supply numerous examples, MATLAB®-based programs, end-of-chapter problems, and experimental results of implementation. The main approach for image reconstruction proposed by the authors differs from existing methods of back-projection, iterative reconstruction, and Fourier and Radon filtering. In this book, the authors explain how to process each projection by a system of linear equations, or linear convolutions, to calculate the corresponding part of the 2-D tensor or paired transform of the discrete image. They then describe how to calculate the inverse transform to obtain the reconstruction. The proposed models for image reconstruction from projections are simple and result in more accurate reconstructions. Introducing a new theory and methods of image reconstruction, this book provides a solid grounding for those interested in further research and in obtaining new results. It encourages readers to develop effective applications of these methods in CT.
Book Synopsis Handbook of Image Engineering by : Yu-Jin Zhang
Download or read book Handbook of Image Engineering written by Yu-Jin Zhang and published by Springer Nature. This book was released on 2021-01-04 with total page 1963 pages. Available in PDF, EPUB and Kindle. Book excerpt: Image techniques have been developed and implemented for various purposes, and image engineering (IE) is a rapidly evolving, integrated discipline comprising the study of all the different branches of image techniques, and encompassing mathematics, physics, biology, physiology, psychology, electrical engineering, computer science and automation. Advances in the field are also closely related to the development of telecommunications, biomedical engineering, remote sensing, surveying and mapping, as well as document processing and industrial applications. IE involves three related and partially overlapping groups of image techniques: image processing (IP) (in its narrow sense), image analysis (IA) and image understanding (IU), and the integration of these three groups makes the discipline of image engineering an important part of the modern information era. This is the first handbook on image engineering, and provides a well-structured, comprehensive overview of this new discipline. It also offers detailed information on the various image techniques. It is a valuable reference resource for R&D professional and undergraduate students involved in image-related activities.
Book Synopsis Mathematical Methods in Image Reconstruction by : Frank Natterer
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.
Book Synopsis Image Reconstruction from Projections by : Behrouz Nobahar Shabestari
Download or read book Image Reconstruction from Projections written by Behrouz Nobahar Shabestari and published by . This book was released on 1988 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Principles of Computerized Tomographic Imaging by : Avinash C. Kak
Download or read book Principles of Computerized Tomographic Imaging written by Avinash C. Kak and published by SIAM. This book was released on 2001-01-01 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive, tutorial-style introduction to the algorithms necessary for tomographic imaging.
Book Synopsis Emission Tomography by : Miles N. Wernick
Download or read book Emission Tomography written by Miles N. Wernick and published by Elsevier. This book was released on 2004-12-07 with total page 597 pages. Available in PDF, EPUB and Kindle. Book excerpt: PET and SPECT are two of today’s most important medical-imaging methods, providing images that reveal subtle information about physiological processes in humans and animals. Emission Tomography: The Fundamentals of PET and SPECT explains the physics and engineering principles of these important functional-imaging methods. The technology of emission tomography is covered in detail, including historical origins, scientific and mathematical foundations, imaging systems and their components, image reconstruction and analysis, simulation techniques, and clinical and laboratory applications. The book describes the state of the art of emission tomography, including all facets of conventional SPECT and PET, as well as contemporary topics such as iterative image reconstruction, small-animal imaging, and PET/CT systems. This book is intended as a textbook and reference resource for graduate students, researchers, medical physicists, biomedical engineers, and professional engineers and physicists in the medical-imaging industry. Thorough tutorials of fundamental and advanced topics are presented by dozens of the leading researchers in PET and SPECT. SPECT has long been a mainstay of clinical imaging, and PET is now one of the world’s fastest growing medical imaging techniques, owing to its dramatic contributions to cancer imaging and other applications. Emission Tomography: The Fundamentals of PET and SPECT is an essential resource for understanding the technology of SPECT and PET, the most widely used forms of molecular imaging. *Contains thorough tutorial treatments, coupled with coverage of advanced topics *Three of the four holders of the prestigious Institute of Electrical and Electronics Engineers Medical Imaging Scientist Award are chapter contributors *Include color artwork
Download or read book Using OpenMP written by Barbara Chapman and published by MIT Press. This book was released on 2007-10-12 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive overview of OpenMP, the standard application programming interface for shared memory parallel computing—a reference for students and professionals. "I hope that readers will learn to use the full expressibility and power of OpenMP. This book should provide an excellent introduction to beginners, and the performance section should help those with some experience who want to push OpenMP to its limits." —from the foreword by David J. Kuck, Intel Fellow, Software and Solutions Group, and Director, Parallel and Distributed Solutions, Intel Corporation OpenMP, a portable programming interface for shared memory parallel computers, was adopted as an informal standard in 1997 by computer scientists who wanted a unified model on which to base programs for shared memory systems. OpenMP is now used by many software developers; it offers significant advantages over both hand-threading and MPI. Using OpenMP offers a comprehensive introduction to parallel programming concepts and a detailed overview of OpenMP. Using OpenMP discusses hardware developments, describes where OpenMP is applicable, and compares OpenMP to other programming interfaces for shared and distributed memory parallel architectures. It introduces the individual features of OpenMP, provides many source code examples that demonstrate the use and functionality of the language constructs, and offers tips on writing an efficient OpenMP program. It describes how to use OpenMP in full-scale applications to achieve high performance on large-scale architectures, discussing several case studies in detail, and offers in-depth troubleshooting advice. It explains how OpenMP is translated into explicitly multithreaded code, providing a valuable behind-the-scenes account of OpenMP program performance. Finally, Using OpenMP considers trends likely to influence OpenMP development, offering a glimpse of the possibilities of a future OpenMP 3.0 from the vantage point of the current OpenMP 2.5. With multicore computer use increasing, the need for a comprehensive introduction and overview of the standard interface is clear. Using OpenMP provides an essential reference not only for students at both undergraduate and graduate levels but also for professionals who intend to parallelize existing codes or develop new parallel programs for shared memory computer architectures.
Book Synopsis Medical Imaging Systems by : Andreas Maier
Download or read book Medical Imaging Systems written by Andreas Maier and published by Springer. This book was released on 2018-08-02 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access book gives a complete and comprehensive introduction to the fields of medical imaging systems, as designed for a broad range of applications. The authors of the book first explain the foundations of system theory and image processing, before highlighting several modalities in a dedicated chapter. The initial focus is on modalities that are closely related to traditional camera systems such as endoscopy and microscopy. This is followed by more complex image formation processes: magnetic resonance imaging, X-ray projection imaging, computed tomography, X-ray phase-contrast imaging, nuclear imaging, ultrasound, and optical coherence tomography.
Book Synopsis The Theory and Practice of 3D PET by : B. Bendriem
Download or read book The Theory and Practice of 3D PET written by B. Bendriem and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: The application of 3D methodology has recently been receiving increasing attention at many PET centres, and this monograph is an attempt to provide a state-of-the-art review of this methodology, covering 3D reconstruction methods, quantitative procedures, current tomography performance, and clinical and research applications. No such review has been available until now to assist PET researchers in understanding and implementing 3D methodology, and in evaluating the performance of the available imaging technology. In all the chapters, the subject matter is treated in sufficient depth to appeal equally to the physicist or engineer who wishes to establish the methodology, and to PET investigators with experience in 2D PET who wish to familiarize themselves with the concepts and advantages of 3D, and to be made aware of the pitfalls.
Book Synopsis The Radon Transform and Medical Imaging by : Peter Kuchment
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.
Book Synopsis Questions of Uniqueness and Resolution in Reconstruction from Projections by : M. B. Katz
Download or read book Questions of Uniqueness and Resolution in Reconstruction from Projections written by M. B. Katz and published by Springer Science & Business Media. This book was released on 2013-03-13 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reconstruction from projections has revolutionized radiology and has now become one of the most important tools of medical diagnosis The E. M. I. Scanner is one example. In this text, some fundamental theoretical and practical questions are resolved. Despite recent research activity in the area, the crucial subject of the uniqueness of the reconstruction and the effect of noise in the data posed some unsettled fundamental questions. In particular, Kennan Smith proved that if we describe an object by a C^inf_o function, i.e., infinitely differentiable with compact support, then there are other objects with the same shape, i.e., support, which can differ almost arbitrarily and still have the same projections in finitely many directions. On the other hand, he proved that objects in finite dimensional function spaces are uniquely determined by a single projection for almost all angles, i.e., except on a set of measure zero. Along these lines, Herman and Rowland in "Three Methods for reconstructing objects from x-rays: a comparative study" (1973) showed that reconstructions obtained from the commonly used algorithms can grossly misrepresent the object and that the algorithm which produced the best reconstruction when using noiseless data gave unsatisfactory results with noisy data. Equally important are reports in Science, and personal communications by radiologists indicating that in medical practice failure rates of reconstruction vary from four to twenty percent. within this work, the mathematical dilemma posed by Kennan Smith's result is discussed and clarified.
