Mathematical Methods In Image Reconstruction
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Mathematical Methods In Image Reconstruction
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Author : Frank Natterer
language : en
Publisher: SIAM
Release Date : 2001-01-01
Mathematical Methods In Image Reconstruction written by Frank Natterer and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-01-01 with Computers categories.
This book provides readers with a superior understanding of the mathematical principles behind imaging.
Mathematical Methods In Image Processing And Inverse Problems
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Author : Xue-Cheng Tai
language : en
Publisher: Springer Nature
Release Date : 2021-09-25
Mathematical Methods In Image Processing And Inverse Problems written by Xue-Cheng Tai and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-25 with Mathematics categories.
This book contains eleven original and survey scientific research articles arose from presentations given by invited speakers at International Workshop on Image Processing and Inverse Problems, held in Beijing Computational Science Research Center, Beijing, China, April 21–24, 2018. The book was dedicated to Professor Raymond Chan on the occasion of his 60th birthday. The contents of the book cover topics including image reconstruction, image segmentation, image registration, inverse problems and so on. Deep learning, PDE, statistical theory based research methods and techniques were discussed. The state-of-the-art developments on mathematical analysis, advanced modeling, efficient algorithm and applications were presented. The collected papers in this book also give new research trends in deep learning and optimization for imaging science. It should be a good reference for researchers working on related problems, as well as for researchers working on computer vision and visualization, inverse problems, image processing and medical imaging.
Mathematical Methods In Image Reconstruction
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Author : Frank Natterer
language : en
Publisher: SIAM
Release Date : 2001-01-01
Mathematical Methods In Image Reconstruction written by Frank Natterer and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-01-01 with Computers categories.
This book describes the state of the art of the mathematical theory and numerical analysis of imaging. Some of the applications covered in the book include computerized tomography, magnetic resonance imaging, emission tomography, electron microscopy, ultrasound transmission tomography, industrial tomography, seismic tomography, impedance tomography, and NIR imaging.
Image Processing
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Author : Artyom M. Grigoryan
language : en
Publisher: CRC Press
Release Date : 2018-09-03
Image Processing written by Artyom M. Grigoryan and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-03 with Technology & Engineering categories.
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.
Digital Image Processing
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Author : J M Blackledge
language : en
Publisher: Elsevier
Release Date : 2005-11-30
Digital Image Processing written by J M Blackledge and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-11-30 with Computers categories.
This authoritative text (the second part of a complete MSc course) provides mathematical methods required to describe images, image formation and different imaging systems, coupled with the principle techniques used for processing digital images. It is based on a course for postgraduates reading physics, electronic engineering, telecommunications engineering, information technology and computer science. This book relates the methods of processing and interpreting digital images to the 'physics' of imaging systems. Case studies reinforce the methods discussed, with examples of current research themes. - Provides mathematical methods required to describe images, image formation and different imaging systems - Outlines the principle techniques used for processing digital images - Relates the methods of processing and interpreting digital images to the 'physics' of imaging systems
Handbook Of Mathematical Methods In Imaging
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Author : Otmar Scherzer
language : en
Publisher: Springer
Release Date : 2015-05-30
Handbook Of Mathematical Methods In Imaging written by Otmar Scherzer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-05-30 with Mathematics categories.
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. This expanded and revised second edition contains updates to existing chapters and 16 additional entries on important mathematical methods such as graph cuts, morphology, discrete geometry, PDEs, conformal methods, to name a few. 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 200 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.
Introduction To The Mathematics Of Medical Imaging
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Author : Charles L. Epstein
language : en
Publisher: SIAM
Release Date : 2008-01-01
Introduction To The Mathematics Of Medical Imaging written by Charles L. Epstein and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-01 with Mathematics categories.
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.
Image Processing And Analysis
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Author : Tony F. Chan
language : en
Publisher: SIAM
Release Date : 2005-09-01
Image Processing And Analysis written by Tony F. Chan and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-09-01 with Computers categories.
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.
Variational Methods In Image Processing
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Author : Luminita A. Vese
language : en
Publisher: CRC Press
Release Date : 2015-11-18
Variational Methods In Image Processing written by Luminita A. Vese and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-18 with Computers categories.
Variational Methods in Image Processing presents the principles, techniques, and applications of variational image processing. The text focuses on variational models, their corresponding Euler–Lagrange equations, and numerical implementations for image processing. It balances traditional computational models with more modern techniques that solve the latest challenges introduced by new image acquisition devices. The book addresses the most important problems in image processing along with other related problems and applications. Each chapter presents the problem, discusses its mathematical formulation as a minimization problem, analyzes its mathematical well-posedness, derives the associated Euler–Lagrange equations, describes the numerical approximations and algorithms, explains several numerical results, and includes a list of exercises. MATLAB® codes are available online. Filled with tables, illustrations, and algorithms, this self-contained textbook is primarily for advanced undergraduate and graduate students in applied mathematics, scientific computing, medical imaging, computer vision, computer science, and engineering. It also offers a detailed overview of the relevant variational models for engineers, professionals from academia, and those in the image processing industry.