Optimization In Computational Imaging And Inverse Problems

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Computational Methods for Inverse Problems in Imaging

Author : Marco Donatelli
Publisher : Springer Nature
ISBN 13 : 3030328821
Total Pages : 171 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Computational Methods for Inverse Problems in Imaging by : Marco Donatelli

Download or read book Computational Methods for Inverse Problems in Imaging written by Marco Donatelli and published by Springer Nature. This book was released on 2019-11-26 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents recent mathematical methods in the area of inverse problems in imaging with a particular focus on the computational aspects and applications. The formulation of inverse problems in imaging requires accurate mathematical modeling in order to preserve the significant features of the image. The book describes computational methods to efficiently address these problems based on new optimization algorithms for smooth and nonsmooth convex minimization, on the use of structured (numerical) linear algebra, and on multilevel techniques. It also discusses various current and challenging applications in fields such as astronomy, microscopy, and biomedical imaging. The book is intended for researchers and advanced graduate students interested in inverse problems and imaging.

Computational Methods for Inverse Problems

Author : Curtis R. Vogel
Publisher : SIAM
ISBN 13 : 0898717574
Total Pages : 195 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Computational Methods for Inverse Problems by : Curtis R. Vogel

Download or read book Computational Methods for Inverse Problems written by Curtis R. Vogel and published by SIAM. This book was released on 2002-01-01 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides a basic understanding of both the underlying mathematics and the computational methods used to solve inverse problems.

Optimization in Computational Imaging and Inverse Problems

Author : Keith J. Dillon
Publisher :
ISBN 13 : 9781303818103
Total Pages : 160 pages
Book Rating : 4.8/5 (181 download)

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Book Synopsis Optimization in Computational Imaging and Inverse Problems by : Keith J. Dillon

Download or read book Optimization in Computational Imaging and Inverse Problems written by Keith J. Dillon and published by . This book was released on 2014 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: With modern optimization techniques it is generally possible to form some kind of image estimate using an arbitrary collection of views or sensor measurements of an unknown object. The question is what is the best result that one can get with that data and will it be acceptable? We use optimization theory to analyze inverse problems such as this and formulate strategies for understanding how much high resolution information is contained in the data and how to intelligently reconstruct the best image possible. We start by formulating the reconstruction problem for a variety of different imaging systems, which we can view as special cases or extensions of tomography. In order to understand the range of potential solutions to such inverse problems, we formulate the optimization problems of bounding the elements of the unknown. We proceed to develop a novel approach to investigating inverse problems by defining uniqueness as the case where the upper and lower bounds on possible values each element can take are equal. This allows us both to express uniqueness on an element-wise basis, e.g. some elements may be uniquely-reconstructed while others may not, and to formulate conditions for uniqueness. These conditions provide a generalization of known conditions for unique solutions to systems with sparse or non-negative unknowns. We use these uniqueness conditions to pose a novel approach to estimation of system resolution and to thereby find low-resolution approximations which provide as much resolution as possible while retaining the uniqueness of the solution. Finally we demonstrate the extension to noisy and regularized problems using a Bayesian formulation which allows us to form trade-offs between resolution and uncertainty.

Optimization in Computational Imaging and Inverse Problems

Author : Keith Dillon
Publisher : Lulu.com
ISBN 13 : 9781304969699
Total Pages : 154 pages
Book Rating : 4.9/5 (696 download)

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Book Synopsis Optimization in Computational Imaging and Inverse Problems by : Keith Dillon

Download or read book Optimization in Computational Imaging and Inverse Problems written by Keith Dillon and published by Lulu.com. This book was released on 2014-03-23 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: Doctoral Dissertation, University of California, San Diego, 2014. With modern optimization techniques it is generally possible to form some kind of image estimate using an arbitrary collection of views or sensor measurements of an unknown object. The question is what is the best result that one can get with that data and will it be acceptable? We use optimization theory to analyze inverse problems such as this and formulate strategies for understanding how much high resolution information is contained in the data and how to intelligently reconstruct the best image possible.

Statistical and Computational Inverse Problems

Author : Jari Kaipio
Publisher : Springer Science & Business Media
ISBN 13 : 0387271325
Total Pages : 346 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Statistical and Computational Inverse Problems by : Jari Kaipio

Download or read book Statistical and Computational Inverse Problems written by Jari Kaipio and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Fourier Optics and Computational Imaging

Author : Kedar Khare
Publisher : John Wiley & Sons
ISBN 13 : 1118900340
Total Pages : 312 pages
Book Rating : 4.1/5 (189 download)

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Book Synopsis Fourier Optics and Computational Imaging by : Kedar Khare

Download or read book Fourier Optics and Computational Imaging written by Kedar Khare and published by John Wiley & Sons. This book was released on 2015-09-21 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers both the mathematics of inverse problems and optical systems design, and includes a review of the mathematical methods and Fourier optics. The first part of the book deals with the mathematical tools in detail with minimal assumption about prior knowledge on the part of the reader. The second part of the book discusses concepts in optics, particularly propagation of optical waves and coherence properties of optical fields that form the basis of the computational models used for image recovery. The third part provides a discussion of specific imaging systems that illustrate the power of the hybrid computational imaging model in enhancing imaging performance. A number of exercises are provided for readers to develop further understanding of computational imaging. While the focus of the book is largely on optical imaging systems, the key concepts are discussed in a fairly general manner so as to provide useful background for understanding the mechanisms of a diverse range of imaging modalities.

Computational Imaging

Author : Ayush Bhandari
Publisher : MIT Press
ISBN 13 : 0262046474
Total Pages : 482 pages
Book Rating : 4.2/5 (62 download)

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Book Synopsis Computational Imaging by : Ayush Bhandari

Download or read book Computational Imaging written by Ayush Bhandari and published by MIT Press. This book was released on 2022-10-25 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive and up-to-date textbook and reference for computational imaging, which combines vision, graphics, signal processing, and optics. Computational imaging involves the joint design of imaging hardware and computer algorithms to create novel imaging systems with unprecedented capabilities. In recent years such capabilities include cameras that operate at a trillion frames per second, microscopes that can see small viruses long thought to be optically irresolvable, and telescopes that capture images of black holes. This text offers a comprehensive and up-to-date introduction to this rapidly growing field, a convergence of vision, graphics, signal processing, and optics. It can be used as an instructional resource for computer imaging courses and as a reference for professionals. It covers the fundamentals of the field, current research and applications, and light transport techniques. The text first presents an imaging toolkit, including optics, image sensors, and illumination, and a computational toolkit, introducing modeling, mathematical tools, model-based inversion, data-driven inversion techniques, and hybrid inversion techniques. It then examines different modalities of light, focusing on the plenoptic function, which describes degrees of freedom of a light ray. Finally, the text outlines light transport techniques, describing imaging systems that obtain micron-scale 3D shape or optimize for noise-free imaging, optical computing, and non-line-of-sight imaging. Throughout, it discusses the use of computational imaging methods in a range of application areas, including smart phone photography, autonomous driving, and medical imaging. End-of-chapter exercises help put the material in context.

Computational Methods for Applied Inverse Problems

Author : Yanfei Wang
Publisher : Walter de Gruyter
ISBN 13 : 3110259052
Total Pages : 552 pages
Book Rating : 4.1/5 (12 download)

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Book Synopsis Computational Methods for Applied Inverse Problems by : Yanfei Wang

Download or read book Computational Methods for Applied Inverse Problems written by Yanfei Wang and published by Walter de Gruyter. This book was released on 2012-10-30 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nowadays inverse problems and applications in science and engineering represent an extremely active research field. The subjects are related to mathematics, physics, geophysics, geochemistry, oceanography, geography and remote sensing, astronomy, biomedicine, and other areas of applications. This monograph reports recent advances of inversion theory and recent developments with practical applications in frontiers of sciences, especially inverse design and novel computational methods for inverse problems. The practical applications include inverse scattering, chemistry, molecular spectra data processing, quantitative remote sensing inversion, seismic imaging, oceanography, and astronomical imaging. The book serves as a reference book and readers who do research in applied mathematics, engineering, geophysics, biomedicine, image processing, remote sensing, and environmental science will benefit from the contents since the book incorporates a background of using statistical and non-statistical methods, e.g., regularization and optimization techniques for solving practical inverse problems.

Handbook of Mathematical Methods in Imaging

Author : Otmar Scherzer
Publisher : Springer Science & Business Media
ISBN 13 : 0387929193
Total Pages : 1626 pages
Book Rating : 4.3/5 (879 download)

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Book Synopsis Handbook of Mathematical Methods in Imaging by : Otmar Scherzer

Download or read book Handbook of Mathematical Methods in Imaging written by Otmar Scherzer and published by Springer Science & Business Media. This book was released on 2010-11-23 with total page 1626 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Computational Imaging

Author : Ayush Bhandari
Publisher : MIT Press
ISBN 13 : 0262368374
Total Pages : 482 pages
Book Rating : 4.2/5 (623 download)

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Book Synopsis Computational Imaging by : Ayush Bhandari

Computational Imaging

Author :
Publisher :
ISBN 13 :
Total Pages : 464 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Computational Imaging by :

Download or read book Computational Imaging written by and published by . This book was released on 2006 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Fixed-Point Algorithms for Inverse Problems in Science and Engineering

Author : Heinz H. Bauschke
Publisher : Springer Science & Business Media
ISBN 13 : 1441995692
Total Pages : 409 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis Fixed-Point Algorithms for Inverse Problems in Science and Engineering by : Heinz H. Bauschke

Download or read book Fixed-Point Algorithms for Inverse Problems in Science and Engineering written by Heinz H. Bauschke and published by Springer Science & Business Media. This book was released on 2011-05-27 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Fixed-Point Algorithms for Inverse Problems in Science and Engineering" presents some of the most recent work from top-notch researchers studying projection and other first-order fixed-point algorithms in several areas of mathematics and the applied sciences. The material presented provides a survey of the state-of-the-art theory and practice in fixed-point algorithms, identifying emerging problems driven by applications, and discussing new approaches for solving these problems. This book incorporates diverse perspectives from broad-ranging areas of research including, variational analysis, numerical linear algebra, biotechnology, materials science, computational solid-state physics, and chemistry. Topics presented include: Theory of Fixed-point algorithms: convex analysis, convex optimization, subdifferential calculus, nonsmooth analysis, proximal point methods, projection methods, resolvent and related fixed-point theoretic methods, and monotone operator theory. Numerical analysis of fixed-point algorithms: choice of step lengths, of weights, of blocks for block-iterative and parallel methods, and of relaxation parameters; regularization of ill-posed problems; numerical comparison of various methods. Areas of Applications: engineering (image and signal reconstruction and decompression problems), computer tomography and radiation treatment planning (convex feasibility problems), astronomy (adaptive optics), crystallography (molecular structure reconstruction), computational chemistry (molecular structure simulation) and other areas. Because of the variety of applications presented, this book can easily serve as a basis for new and innovated research and collaboration.

Fourier Optics and Computational Imaging

Author : Kedar Khare
Publisher : John Wiley & Sons
ISBN 13 : 1118900375
Total Pages : 314 pages
Book Rating : 4.1/5 (189 download)

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Book Synopsis Fourier Optics and Computational Imaging by : Kedar Khare

Download or read book Fourier Optics and Computational Imaging written by Kedar Khare and published by John Wiley & Sons. This book was released on 2015-08-04 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers both the mathematics of inverse problems and optical systems design, and includes a review of the mathematical methods and Fourier optics. The first part of the book deals with the mathematical tools in detail with minimal assumption about prior knowledge on the part of the reader. The second part of the book discusses concepts in optics, particularly propagation of optical waves and coherence properties of optical fields that form the basis of the computational models used for image recovery. The third part provides a discussion of specific imaging systems that illustrate the power of the hybrid computational imaging model in enhancing imaging performance. A number of exercises are provided for readers to develop further understanding of computational imaging. While the focus of the book is largely on optical imaging systems, the key concepts are discussed in a fairly general manner so as to provide useful background for understanding the mechanisms of a diverse range of imaging modalities.

Foundations of Computational Imaging

Author : Charles A. Bouman
Publisher : SIAM
ISBN 13 : 1611977134
Total Pages : 350 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Foundations of Computational Imaging by : Charles A. Bouman

Download or read book Foundations of Computational Imaging written by Charles A. Bouman and published by SIAM. This book was released on 2022-07-06 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: Collecting a set of classical and emerging methods previously unavailable in a single resource, Foundations of Computational Imaging: A Model-Based Approach is the first book to define a common foundation for the mathematical and statistical methods used in computational imaging. The book brings together a blend of research with applications in a variety of disciplines, including applied math, physics, chemistry, optics, and signal processing, to address a collection of problems that can benefit from a common set of methods. Readers will find basic techniques of model-based image processing, a comprehensive treatment of Bayesian and regularized image reconstruction methods, and an integrated treatment of advanced reconstruction techniques, such as majorization, constrained optimization, alternating direction method of multipliers (ADMM), and Plug-and-Play methods for model integration. Foundations of Computational Imaging can be used in courses on model-based or computational imaging, advanced numerical analysis, data science, numerical optimization, and approximation theory. It will also prove useful to researchers or practitioners in medical, scientific, commercial, and industrial imaging.

Data-driven Models in Inverse Problems

Author : Tatiana A. Bubba
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3111251233
Total Pages : 508 pages
Book Rating : 4.1/5 (112 download)

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Book Synopsis Data-driven Models in Inverse Problems by : Tatiana A. Bubba

Download or read book Data-driven Models in Inverse Problems written by Tatiana A. Bubba and published by Walter de Gruyter GmbH & Co KG. This book was released on 2024-11-18 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advances in learning-based methods are revolutionizing several fields in applied mathematics, including inverse problems, resulting in a major paradigm shift towards data-driven approaches. This volume, which is inspired by this cutting-edge area of research, brings together contributors from the inverse problem community and shows how to successfully combine model- and data-driven approaches to gain insight into practical and theoretical issues.

Linear and Nonlinear Inverse Problems with Practical Applications

Author : Jennifer L. Mueller
Publisher : SIAM
ISBN 13 : 1611972345
Total Pages : 349 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Linear and Nonlinear Inverse Problems with Practical Applications by : Jennifer L. Mueller

Download or read book Linear and Nonlinear Inverse Problems with Practical Applications written by Jennifer L. Mueller and published by SIAM. This book was released on 2012-11-30 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Computational Lithography

Author : Xu Ma
Publisher : John Wiley & Sons
ISBN 13 : 111804357X
Total Pages : 225 pages
Book Rating : 4.1/5 (18 download)

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Book Synopsis Computational Lithography by : Xu Ma

Download or read book Computational Lithography written by Xu Ma and published by John Wiley & Sons. This book was released on 2011-01-06 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Unified Summary of the Models and Optimization Methods Used in Computational Lithography Optical lithography is one of the most challenging areas of current integrated circuit manufacturing technology. The semiconductor industry is relying more on resolution enhancement techniques (RETs), since their implementation does not require significant changes in fabrication infrastructure. Computational Lithography is the first book to address the computational optimization of RETs in optical lithography, providing an in-depth discussion of optimal optical proximity correction (OPC), phase shifting mask (PSM), and off-axis illumination (OAI) RET tools that use model-based mathematical optimization approaches. The book starts with an introduction to optical lithography systems, electric magnetic field principles, and the fundamentals of optimization from a mathematical point of view. It goes on to describe in detail different types of optimization algorithms to implement RETs. Most of the algorithms developed are based on the application of the OPC, PSM, and OAI approaches and their combinations. Algorithms for coherent illumination as well as partially coherent illumination systems are described, and numerous simulations are offered to illustrate the effectiveness of the algorithms. In addition, mathematical derivations of all optimization frameworks are presented. The accompanying MATLAB® software files for all the RET methods described in the book make it easy for readers to run and investigate the codes in order to understand and apply the optimization algorithms, as well as to design a set of optimal lithography masks. The codes may also be used by readers for their research and development activities in their academic or industrial organizations. An accompanying MATLAB® software guide is also included. An accompanying MATLAB® software guide is included, and readers can download the software to use with the guide at ftp://ftp.wiley.com/public/sci_tech_med/computational_lithography. Tailored for both entry-level and experienced readers, Computational Lithography is meant for faculty, graduate students, and researchers, as well as scientists and engineers in industrial organizations whose research or career field is semiconductor IC fabrication, optical lithography, and RETs. Computational lithography draws from the rich theory of inverse problems, optics, optimization, and computational imaging; as such, the book is also directed to researchers and practitioners in these fields.