Introduction to Inverse Problems in Imaging

Author: M. Bertero,P. Boccacci

Publisher: CRC Press

ISBN: 9781439822067

Category: Technology & Engineering

Page: 352

View: 2622

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This is a graduate textbook on the principles of linear inverse problems, methods of their approximate solution, and practical application in imaging. The level of mathematical treatment is kept as low as possible to make the book suitable for a wide range of readers from different backgrounds in science and engineering. Mathematical prerequisites are first courses in analysis, geometry, linear algebra, probability theory, and Fourier analysis. The authors concentrate on presenting easily implementable and fast solution algorithms. With examples and exercised throughout, the book will provide the reader with the appropriate background for a clear understanding of the essence of inverse problems (ill-posedness and its cure) and, consequently, for an intelligent assessment of the rapidly growing literature on these problems.
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An Introduction to Data Analysis and Uncertainty Quantification for Inverse Problems

Author: Luis Tenorio

Publisher: SIAM

ISBN: 1611974917

Category: Mathematics

Page: 269

View: 3098

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Inverse problems are found in many applications, such as medical imaging, engineering, astronomy, and geophysics, among others. To solve an inverse problem is to recover an object from noisy, usually indirect observations. Solutions to inverse problems are subject to many potential sources of error introduced by approximate mathematical models, regularization methods, numerical approximations for efficient computations, noisy data, and limitations in the number of observations; thus it is important to include an assessment of the uncertainties as part of the solution. Such assessment is interdisciplinary by nature, as it requires, in addition to knowledge of the particular application, methods from applied mathematics, probability, and statistics. This book bridges applied mathematics and statistics by providing a basic introduction to probability and statistics for uncertainty quantification in the context of inverse problems, as well as an introduction to statistical regularization of inverse problems. The author covers basic statistical inference, introduces the framework of ill-posed inverse problems, and explains statistical questions that arise in their applications. An Introduction to Data Analysis and Uncertainty Quantification for Inverse Problems÷includes many examples that explain techniques which are useful to address general problems arising in uncertainty quantification, Bayesian and non-Bayesian statistical methods and discussions of their complementary roles, and analysis of a real data set to illustrate the methodology covered throughout the book.
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Nonlinear Inverse Problems in Imaging

Author: Jin Keun Seo,Eung Je Woo

Publisher: John Wiley & Sons

ISBN: 1118478150

Category: Technology & Engineering

Page: 376

View: 592

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This book provides researchers and engineers in the imaging field with the skills they need to effectively deal with nonlinear inverse problems associated with different imaging modalities, including impedance imaging, optical tomography, elastography, and electrical source imaging. Focusing on numerically implementable methods, the book bridges the gap between theory and applications, helping readers tackle problems in applied mathematics and engineering. Complete, self-contained coverage includes basic concepts, models, computational methods, numerical simulations, examples, and case studies. Provides a step-by-step progressive treatment of topics for ease of understanding. Discusses the underlying physical phenomena as well as implementation details of image reconstruction algorithms as prerequisites for finding solutions to non linear inverse problems with practical significance and value. Includes end of chapter problems, case studies and examples with solutions throughout the book. Companion website will provide further examples and solutions, experimental data sets, open problems, teaching material such as PowerPoint slides and software including MATLAB m files. Essential reading for Graduate students and researchers in imaging science working across the areas of applied mathematics, biomedical engineering, and electrical engineering and specifically those involved in nonlinear imaging techniques, impedance imaging, optical tomography, elastography, and electrical source imaging
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Optical Imaging and Metrology

Advanced Technologies

Author: Wolfgang Osten,Nadya Reingand

Publisher: John Wiley & Sons

ISBN: 3527648461

Category: Science

Page: 502

View: 4681

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A comprehensive review of the state of the art and advances in the field, while also outlining the future potential and development trends of optical imaging and optical metrology, an area of fast growth with numerous applications in nanotechnology and nanophysics. Written by the world's leading experts in the field, it fills the gap in the current literature by bridging the fields of optical imaging and metrology, and is the only up-to-date resource in terms of fundamental knowledge, basic concepts, methodologies, applications, and development trends.
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Introduction to the Mathematics of Medical Imaging

Second Edition

Author: Charles L. Epstein

Publisher: SIAM

ISBN: 9780898717792

Category: Diagnostic imaging

Page: 761

View: 495

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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.
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Modeling and Inverse Problems in Imaging Analysis

Author: Bernard Chalmond

Publisher: Springer Science & Business Media

ISBN: 9780387955476

Category: Computers

Page: 309

View: 5412

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More mathematics have been taking part in the development of digital image processing as a science, and the contributions are reflected in the increasingly important role modeling has played solving complex problems. This book is mostly concerned with energy-based models. Through concrete image analysis problems, the author develops consistent modeling, a know-how generally hidden in the proposed solutions. The book is divided into three main parts. The first two parts describe the theory behind the applications that are presented in the third part. These materials include splines (variational approach, regression spline, spline in high dimension) and random fields (Markovian field, parametric estimation, stochastic and deterministic optimization, continuous Gaussian field). Most of these applications come from industrial projects in which the author was involved in robot vision and radiography: tracking 3-D lines, radiographic image processing, 3-D reconstruction and tomography, matching and deformation learning. Numerous graphical illustrations accompany the text showing the performance of the proposed models. This book will be useful to researchers and graduate students in mathematics, physics, computer science, and engineering.
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Statistical and Computational Inverse Problems

Author: Jari Kaipio,E. Somersalo

Publisher: Springer Science & Business Media

ISBN: 0387271325

Category: Mathematics

Page: 340

View: 8918

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This book covers the statistical mechanics approach to computational solution of inverse problems, an innovative area of current research with very promising numerical results. The techniques are applied to a number of real world applications such as limited angle tomography, image deblurring, electical impedance tomography, and biomagnetic inverse problems. Contains detailed examples throughout and includes a chapter on case studies where such methods have been implemented in biomedical engineering.
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Encyclopedia of Nonlinear Science

Author: Alwyn Scott

Publisher: Routledge

ISBN: 1135455570

Category: Reference

Page: 1096

View: 4548

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In 438 alphabetically-arranged essays, this work provides a useful overview of the core mathematical background for nonlinear science, as well as its applications to key problems in ecology and biological systems, chemical reaction-diffusion problems, geophysics, economics, electrical and mechanical oscillations in engineering systems, lasers and nonlinear optics, fluid mechanics and turbulence, and condensed matter physics, among others.
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Inverse Problems in Scattering and Imaging

Author: Bertero

Publisher: CRC Press

ISBN: 9780750301435

Category: Technology & Engineering

Page: 550

View: 6769

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Inverse Problems in Scattering and Imaging is a collection of lectures from a NATO Advanced Research Workshop that integrates the expertise of physicists and mathematicians in different areas with a common interest in inverse problems. Covering a range of subjects from new developments on the applied mathematics/mathematical physics side to many areas of application, the book achieves a blend of research, review, and tutorial contributions. It is of interest to researchers in the areas of applied mathematics and mathematical physics as well as those working in areas where inverse problems can be applied.
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Geophysical Inverse Theory and Regularization Problems

Author: Michael S. Zhdanov

Publisher: Elsevier

ISBN: 9780080532509

Category: Science

Page: 633

View: 547

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This book presents state-of-the-art geophysical inverse theory developed in modern mathematical terminology. The book brings together fundamental results developed by the Russian mathematical school in regularization theory and combines them with the related research in geophysical inversion carried out in the West. It presents a detailed exposition of the methods of regularized solution of inverse problems based on the ideas of Tikhonov regularization, and shows the different forms of their applications in both linear and nonlinear methods of geophysical inversion. This text is the first to treat many kinds of inversion and imaging techniques in a unified mathematical manner. The book is divided in five parts covering the foundations of the inversion theory and its applications to the solution of different geophysical inverse problems, including potential field, electromagnetic, and seismic methods. The first part is an introduction to inversion theory. The second part contains a description of the basic methods of solution of the linear and nonlinear inverse problems using regularization. The following parts treat the application of regularization methods in gravity and magnetic, electromagnetic, and seismic inverse problems. The key connecting idea of these applied parts of the book is the analogy between the solutions of the forward and inverse problems in different geophysical methods. The book also includes chapters related to the modern technology of geophysical imaging, based on seismic and electromagnetic migration. This volume is unique in its focus on providing a link between the methods used in gravity, electromagnetic, and seismic imaging and inversion, and represents an exhaustive treatise on inversion theory.
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