Point Source Geometric Tomography
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Geometric Tomography
| Author | : Richard J. Gardner |
| Publisher | : Cambridge University Press |
| Total Pages | : 448 |
| Release | : 1995-09-29 |
| Genre | : Art |
| ISBN | : 9780521451260 |
Develops the new field of retrieving information about geometric objects from projections on planes.
Geometric Tomography
| Author | : Richard J. Gardner |
| Publisher | : Cambridge University Press |
| Total Pages | : 7 |
| Release | : 2006-06-19 |
| Genre | : Mathematics |
| ISBN | : 0521866804 |
Geometric tomography deals with the retrieval of information about a geometric object from data concerning its projections (shadows) on planes or cross-sections by planes. It is a geometric relative of computerized tomography, which reconstructs an image from X-rays of a human patient. It overlaps with convex geometry, and employs many tools from that area including integral geometry. It also has connections to geometric probing in robotics and to stereology. The main text contains a rigorous treatment of the subject starting from basic concepts and moving up to the research frontier: seventy-two unsolved problems are stated. Each chapter ends with extensive notes, historical remarks, and some biographies. This comprehensive work will be invaluable to specialists in geometry and tomography; the opening chapters can also be read by advanced undergraduate students.
Image Reconstruction
| Author | : Gengsheng Lawrence Zeng |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 240 |
| Release | : 2017-03-20 |
| Genre | : Medical |
| ISBN | : 3110500590 |
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
Emission Tomography
| Author | : Miles N. Wernick |
| Publisher | : Elsevier |
| Total Pages | : 597 |
| Release | : 2004-12-07 |
| Genre | : Science |
| ISBN | : 0080521878 |
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
Biomedical Imaging
| Author | : Tim Salditt |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 437 |
| Release | : 2017-10-23 |
| Genre | : Science |
| ISBN | : 3110423510 |
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
Medical Image Reconstruction
| Author | : Gengsheng Lawrence Zeng |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 288 |
| Release | : 2023-07-04 |
| Genre | : Science |
| ISBN | : 311105540X |
This textbook introduces the essential concepts of tomography in the field of medical imaging. The medical imaging modalities include x-ray CT (computed tomography), PET (positron emission tomography), SPECT (single photon emission tomography) and MRI. In these modalities, the measurements are not in the image domain and the conversion from the measurements to the images is referred to as the image reconstruction. The work covers various image reconstruction methods, ranging from the classic analytical inversion methods to the optimization-based iterative image reconstruction methods. As machine learning methods have lately exhibited astonishing potentials in various areas including medical imaging the author devotes one chapter to applications of machine learning in image reconstruction. Based on college level in mathematics, physics, and engineering the textbook supports students in understanding the concepts. It is an essential reference for graduate students and engineers with electrical engineering and biomedical background due to its didactical structure and the balanced combination of methodologies and applications,
Tomography
| Author | : Pierre Grangeat |
| Publisher | : John Wiley & Sons |
| Total Pages | : 350 |
| Release | : 2013-03-04 |
| Genre | : Technology & Engineering |
| ISBN | : 1118617673 |
The principle of tomography is to explore the structure and composition of objects non-destructively along spatial and temporal dimensions, using penetrating radiation, such as X- and gamma-rays, or waves, such as electromagnetic and acoustic waves. Based on computer-assisted image reconstruction, tomography provides maps of parameters that characterize the emission of the employed radiation or waves, or their interaction with the examined objects, for one or several cross-sections. Thus, it gives access to the inner structure of inert objects and living organisms in their full complexity. In this book, multidisciplinary specialists explain the foundations and principles of tomographic imaging and describe a broad range of applications. The content is organized in five parts, which are dedicated to image reconstruction, microtomography, industrial tomography, morphological medical tomography and functional medical tomography.
Rapid Detection of Food Adulterants and Contaminants
| Author | : Shyam Narayan Jha |
| Publisher | : Academic Press |
| Total Pages | : 280 |
| Release | : 2015-12-23 |
| Genre | : Technology & Engineering |
| ISBN | : 0128004282 |
Rapid Detection of Food Adulterants and Contaminants: Theory and Practice contains solid information on common adulterants and contaminants in various foods, guidelines for different standards, permissible limits prescribed by food regulatory authorities, and related detection techniques. This is an essential reference for anyone interested in progressive research on detection methods for food safety, especially researchers engaged in developing fast, reliable, and often nondestructive methods for the evaluation of food safety. Reviews the most common detection methods of food adulterants and contaminants Includes supporting theory behind the latest techniques Presents case studies to better understand practical applications and resources for further research Addresses the safety standards of a variety of governments and serves as a reference for why government procedures are put in place
Advanced High-Resolution Tomography in Regenerative Medicine
| Author | : Alessandra Giuliani |
| Publisher | : Springer |
| Total Pages | : 232 |
| Release | : 2018-11-19 |
| Genre | : Science |
| ISBN | : 303000368X |
This book covers the state-of-the-art research on advanced high-resolution tomography, exploring its role in regenerative medicine. and also explores the 3D interactions between tissues, cells, and biomaterials. Various multidisciplinary paths in regenerative medicine are covered, including X-ray microtomography and its role in regenerative medicine, synchrotron radiation-based microtomography and phase contrast tomography, the challenge of the vascularization of regenerated tissues, lung and cartilage imaging, and more. This is an ideal book for biomedical engineers, biologists, physicists, clinicians, and students who want to pursue their studies in the field of regenerative medicine. This book also: Reviews in detail the algorithms and software used for the 3D exploration of regenerated tissue Covers the latest research on the use of X-ray microtomography for muscle diseases Details applications of synchrotron radiation tomography in orthopedics and dentistry
