Introduction To Inverse Problems In Imaging

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Introduction to Inverse Problems in Imaging

M. Bertero,P. Boccacci
Introduction to Inverse Problems in Imaging Book PDF

Author : M. Bertero,P. Boccacci
Publisher : CRC Press
Page : 364 pages
File Size : 46,6 Mb
Release : 2020-08-30
Category : Technology & Engineering
ISBN : 9781439822067

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Introduction to Inverse Problems in Imaging by M. Bertero,P. Boccacci Pdf

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 exercises 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.

Introduction to Inverse Problems in Imaging

M. Bertero,P. Boccacci,Christine De Mol
Introduction to Inverse Problems in Imaging Book PDF

Author : M. Bertero,P. Boccacci,Christine De Mol
Publisher : CRC Press
Page : 358 pages
File Size : 46,9 Mb
Release : 2021-12-20
Category : Science
ISBN : 9781000516357

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Introduction to Inverse Problems in Imaging by M. Bertero,P. Boccacci,Christine De Mol Pdf

Fully updated throughout and with several new chapters, this second edition of Introduction to Inverse Problems in Imaging guides advanced undergraduate and graduate students in physics, computer science, mathematics and engineering through the principles of linear inverse problems, in addition to methods of their approximate solution and their practical applications in imaging. This second edition contains new chapters on edge-preserving and sparsity-enforcing regularization in addition to maximum likelihood methods and Bayesian regularization for Poisson data. The level of mathematical treatment is kept as low as possible to make the book suitable for a wide range of students from different backgrounds, with readers needing just a rudimentary understanding of analysis, geometry, linear algebra, probability theory, and Fourier analysis. The authors concentrate on presenting easily implementable and fast solution algorithms, and this second edition is accompanied by numerical examples throughout. It will provide readers with the appropriate background needed 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. Key features: Provides an accessible introduction to the topic while keeping mathematics to a minimum Interdisciplinary topic with growing relevance and wide-ranging applications Accompanied by numerical examples throughout

Introduction to Inverse Problems in Imaging

M. Bertero,P. Boccacci
Introduction to Inverse Problems in Imaging Book PDF

Author : M. Bertero,P. Boccacci
Publisher : CRC Press
Page : 366 pages
File Size : 52,7 Mb
Release : 2020-08-30
Category : Technology & Engineering
ISBN : 1439822069

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Introduction to Inverse Problems in Imaging by M. Bertero,P. Boccacci Pdf

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 exercises 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.

Handbook of Mathematical Methods in Imaging

Otmar Scherzer
Handbook of Mathematical Methods in Imaging Book PDF

Author : Otmar Scherzer
Publisher : Springer Science & Business Media
Page : 1626 pages
File Size : 55,5 Mb
Release : 2010-11-23
Category : Mathematics
ISBN : 9780387929194

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Handbook of Mathematical Methods in Imaging by Otmar Scherzer Pdf

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. 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 150 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.

Nonlinear Inverse Problems in Imaging

Jin Keun Seo,Eung Je Woo
Nonlinear Inverse Problems in Imaging Book PDF

Author : Jin Keun Seo,Eung Je Woo
Publisher : John Wiley & Sons
Page : 379 pages
File Size : 50,8 Mb
Release : 2012-11-16
Category : Technology & Engineering
ISBN : 9781118478158

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Nonlinear Inverse Problems in Imaging by Jin Keun Seo,Eung Je Woo Pdf

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

Inverse Problems and Imaging

Luis L. Bonilla
Inverse Problems and Imaging Book PDF

Author : Luis L. Bonilla
Publisher : Springer
Page : 200 pages
File Size : 45,7 Mb
Release : 2009-06-19
Category : Mathematics
ISBN : 9783540785477

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Inverse Problems and Imaging by Luis L. Bonilla Pdf

Nowadays we are facing numerous and important imaging problems: nondestructive testing of materials, monitoring of industrial processes, enhancement of oil production by efficient reservoir characterization, emerging developments in noninvasive imaging techniques for medical purposes - computerized tomography (CT), magnetic resonance imaging (MRI), positron emission tomography (PET), X-ray and ultrasound tomography, etc. In the CIME Summer School on Imaging (Martina Franca, Italy 2002), leading experts in mathematical techniques and applications presented broad and useful introductions for non-experts and practitioners alike to many aspects of this exciting field. The volume contains part of the above lectures completed and updated by additional contributions on other related topics.

Computational Methods for Inverse Problems

Curtis R. Vogel
Computational Methods for Inverse Problems Book PDF

Author : Curtis R. Vogel
Publisher : SIAM
Page : 195 pages
File Size : 41,5 Mb
Release : 2002-01-01
Category : Mathematics
ISBN : 9780898717570

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Computational Methods for Inverse Problems by Curtis R. Vogel Pdf

Provides a basic understanding of both the underlying mathematics and the computational methods used to solve inverse problems.

An Introduction to Data Analysis and Uncertainty Quantification for Inverse Problems

Luis Tenorio
An Introduction to Data Analysis and Uncertainty Quantification for Inverse Problems Book PDF

Author : Luis Tenorio
Publisher : SIAM
Page : 275 pages
File Size : 48,7 Mb
Release : 2017-07-06
Category : Mathematics
ISBN : 9781611974911

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An Introduction to Data Analysis and Uncertainty Quantification for Inverse Problems by Luis Tenorio Pdf

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.

Inverse Problems in the Mathematical Sciences

Charles W. Groetsch
Inverse Problems in the Mathematical Sciences Book PDF

Author : Charles W. Groetsch
Publisher : Springer Science & Business Media
Page : 154 pages
File Size : 45,6 Mb
Release : 2013-12-14
Category : Technology & Engineering
ISBN : 9783322992024

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Inverse Problems in the Mathematical Sciences by Charles W. Groetsch Pdf

Inverse problems are immensely important in modern science and technology. However, the broad mathematical issues raised by inverse problems receive scant attention in the university curriculum. This book aims to remedy this state of affairs by supplying an accessible introduction, at a modest mathematical level, to the alluring field of inverse problems. Many models of inverse problems from science and engineering are dealt with and nearly a hundred exercises, of varying difficulty, involving mathematical analysis, numerical treatment, or modelling of inverse problems, are provided. The main themes of the book are: causation problem modeled as integral equations; model identification problems, posed as coefficient determination problems in differential equations; the functional analytic framework for inverse problems; and a survey of the principal numerical methods for inverse problems. An extensive annotated bibliography furnishes leads on the history of inverse problems and a guide to the frontiers of current research.

Inverse Problems in Scattering and Imaging

Bertero
Inverse Problems in Scattering and Imaging Book PDF

Author : Bertero
Publisher : CRC Press
Page : 454 pages
File Size : 54,8 Mb
Release : 1992-02-27
Category : Technology & Engineering
ISBN : 0750301430

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Inverse Problems in Scattering and Imaging by Bertero Pdf

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.

An Introduction to Inverse Scattering and Inverse Spectral Problems

Khosrow Chadan,David Colton,Lassi P?iv?rinta,William Rundell
An Introduction to Inverse Scattering and Inverse Spectral Problems Book PDF

Author : Khosrow Chadan,David Colton,Lassi P?iv?rinta,William Rundell
Publisher : SIAM
Page : 206 pages
File Size : 49,9 Mb
Release : 1997-01-01
Category : Mathematics
ISBN : 9780898713879

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An Introduction to Inverse Scattering and Inverse Spectral Problems by Khosrow Chadan,David Colton,Lassi P?iv?rinta,William Rundell Pdf

Here is a clearly written introduction to three central areas of inverse problems: inverse problems in electromagnetic scattering theory, inverse spectral theory, and inverse problems in quantum scattering theory. Inverse problems, one of the most attractive parts of applied mathematics, attempt to obtain information about structures by nondestructive measurements. Based on a series of lectures presented by three of the authors, all experts in the field, the book provides a quick and easy way for readers to become familiar with the area through a survey of recent developments in inverse spectral and inverse scattering problems.

Inverse Problems and Imaging

Luis L. Bonilla
Inverse Problems and Imaging Book PDF

Author : Luis L. Bonilla
Publisher : Springer
Page : 0 pages
File Size : 54,6 Mb
Release : 2008-04-18
Category : Mathematics
ISBN : 3540785450

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Inverse Problems and Imaging by Luis L. Bonilla Pdf

Nowadays we are facing numerous and important imaging problems: nondestructive testing of materials, monitoring of industrial processes, enhancement of oil production by efficient reservoir characterization, emerging developments in noninvasive imaging techniques for medical purposes - computerized tomography (CT), magnetic resonance imaging (MRI), positron emission tomography (PET), X-ray and ultrasound tomography, etc. In the CIME Summer School on Imaging (Martina Franca, Italy 2002), leading experts in mathematical techniques and applications presented broad and useful introductions for non-experts and practitioners alike to many aspects of this exciting field. The volume contains part of the above lectures completed and updated by additional contributions on other related topics.

Mathematical Modelling

Seppo Pohjolainen,Matti Heiliö,Timo Lähivaara,Erkki Laitinen,Timo Mantere,Jorma Merikoski,Kimmo Raivio,Risto Silvennoinen,Antti Suutala,Tanja Tarvainen,Timo Tiihonen,Jukka Tuomela,Esko Turunen,Marko Vauhkonen
Mathematical Modelling Book PDF

Author : Seppo Pohjolainen,Matti Heiliö,Timo Lähivaara,Erkki Laitinen,Timo Mantere,Jorma Merikoski,Kimmo Raivio,Risto Silvennoinen,Antti Suutala,Tanja Tarvainen,Timo Tiihonen,Jukka Tuomela,Esko Turunen,Marko Vauhkonen
Publisher : Springer
Page : 242 pages
File Size : 44,6 Mb
Release : 2016-07-14
Category : Mathematics
ISBN : 9783319278360

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Mathematical Modelling by Seppo Pohjolainen,Matti Heiliö,Timo Lähivaara,Erkki Laitinen,Timo Mantere,Jorma Merikoski,Kimmo Raivio,Risto Silvennoinen,Antti Suutala,Tanja Tarvainen,Timo Tiihonen,Jukka Tuomela,Esko Turunen,Marko Vauhkonen Pdf

This book provides a thorough introduction to the challenge of applying mathematics in real-world scenarios. Modelling tasks rarely involve well-defined categories, and they often require multidisciplinary input from mathematics, physics, computer sciences, or engineering. In keeping with this spirit of modelling, the book includes a wealth of cross-references between the chapters and frequently points to the real-world context. The book combines classical approaches to modelling with novel areas such as soft computing methods, inverse problems, and model uncertainty. Attention is also paid to the interaction between models, data and the use of mathematical software. The reader will find a broad selection of theoretical tools for practicing industrial mathematics, including the analysis of continuum models, probabilistic and discrete phenomena, and asymptotic and sensitivity analysis.

Discrete Inverse Problems

Per Christian Hansen
Discrete Inverse Problems Book PDF

Author : Per Christian Hansen
Publisher : SIAM
Page : 220 pages
File Size : 52,6 Mb
Release : 2010-01-01
Category : Mathematics
ISBN : 9780898718836

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Discrete Inverse Problems by Per Christian Hansen Pdf

This book gives an introduction to the practical treatment of inverse problems by means of numerical methods, with a focus on basic mathematical and computational aspects. To solve inverse problems, we demonstrate that insight about them goes hand in hand with algorithms.

Linear and Nonlinear Inverse Problems with Practical Applications

Jennifer L. Mueller,Samuli Siltanen
Linear and Nonlinear Inverse Problems with Practical Applications Book PDF

Author : Jennifer L. Mueller,Samuli Siltanen
Publisher : SIAM
Page : 349 pages
File Size : 45,8 Mb
Release : 2012-11-30
Category : Mathematics
ISBN : 9781611972337

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Linear and Nonlinear Inverse Problems with Practical Applications by Jennifer L. Mueller,Samuli Siltanen Pdf

Inverse problems arise in practical applications whenever there is a need to interpret indirect measurements. This book explains how to identify ill-posed inverse problems arising in practice and gives a hands-on guide to designing computational solution methods for them, with related codes on an accompanying website. The guiding linear inversion examples are the problem of image deblurring, x-ray tomography, and backward parabolic problems, including heat transfer. A thorough treatment of electrical impedance tomography is used as the guiding nonlinear inversion example which combines the analytic-geometric research tradition and the regularization-based school of thought in a fruitful manner. This book is complete with exercises and project topics, making it ideal as a classroom textbook or self-study guide for graduate and advanced undergraduate students in mathematics, engineering or physics who wish to learn about computational inversion. It also acts as a useful guide for researchers who develop inversion techniques in high-tech industry.