# Search Results for "discrete-inverse-problems-insight-and-algorithms-fundamentals-of-algorithms"

## Discrete Inverse Problems

*Insight and Algorithms*

**Author**: Per Christian Hansen**Publisher:**SIAM**ISBN:**089871883X**Category:**Inverse problems (Differential equations)**Page:**213**View:**3844

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

**Author**: Jennifer L. Mueller,Samuli Siltanen**Publisher:**SIAM**ISBN:**9781611972344**Category:**Mathematics**Page:**351**View:**615

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.

## Deblurring Images

*Matrices, Spectra, and Filtering*

**Author**: Per Christian Hansen,James G. Nagy,Dianne P. O'Leary**Publisher:**SIAM**ISBN:**9780898718874**Category:**Image processing**Page:**130**View:**5893

Describes the deblurring algorithms and techniques collectively known as spectral filtering methods, in which the singular value decomposition, or a similar decomposition with spectral properties, is used to introduce the necessary regularization or filtering in the reconstructed image. The concise MATLAB® implementations described in the book provide a template of techniques that can be used to restore blurred images from many applications.

## Inverse Problem Theory and Methods for Model Parameter Estimation

**Author**: Albert Tarantola**Publisher:**SIAM**ISBN:**9780898717921**Category:**Engineering**Page:**342**View:**4554

While the prediction of observations is a forward problem, the use of actual observations to infer the properties of a model is an inverse problem. Inverse problems are difficult because they may not have a unique solution. The description of uncertainties plays a central role in the theory, which is based on probability theory. This book proposes a general approach that is valid for linear as well as for nonlinear problems. The philosophy is essentially probabilistic and allows the reader to understand the basic difficulties appearing in the resolution of inverse problems. The book attempts to explain how a method of acquisition of information can be applied to actual real-world problems, and many of the arguments are heuristic.

## Mathematical Foundations of Imaging, Tomography and Wavefield Inversion

**Author**: Anthony J. Devaney**Publisher:**Cambridge University Press**ISBN:**1139510142**Category:**Science**Page:**N.A**View:**3860

Inverse problems are of interest and importance across many branches of physics, mathematics, engineering and medical imaging. In this text, the foundations of imaging and wavefield inversion are presented in a clear and systematic way. The necessary theory is gradually developed throughout the book, progressing from simple wave equation based models to vector wave models. By combining theory with numerous MATLAB based examples, the author promotes a complete understanding of the material and establishes a basis for real world applications. Key topics of discussion include the derivation of solutions to the inhomogeneous and homogeneous Helmholtz equations using Green function techniques; the propagation and scattering of waves in homogeneous and inhomogeneous backgrounds; and the concept of field time reversal. Bridging the gap between mathematics and physics, this multidisciplinary book will appeal to graduate students and researchers alike. Additional resources including MATLAB codes and solutions are available online at www.cambridge.org/9780521119740.

## Linear and Nonlinear Inverse Problems with Practical Applications

**Author**: Jennifer L. Mueller,Samuli Siltanen**Publisher:**SIAM**ISBN:**9781611972344**Category:**Mathematics**Page:**351**View:**4546

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.

## Numerical Methods for Inverse Problems

**Author**: Michel Kern**Publisher:**John Wiley & Sons**ISBN:**1119136962**Category:**Mathematics**Page:**228**View:**7557

This book studies methods to concretely address inverse problems. An inverse problem arises when the causes that produced a given effect must be determined or when one seeks to indirectly estimate the parameters of a physical system. The author uses practical examples to illustrate inverse problems in physical sciences. He presents the techniques and specific methods chosen to solve inverse problems in a general domain of application, choosing to focus on a small number of methods that can be used in most applications. This book is aimed at readers with a mathematical and scientific computing background. Despite this, it is a book with a practical perspective. The methods described are applicable, have been applied, and are often illustrated by numerical examples.

## Introduction to Algorithms

**Author**: Thomas H. Cormen**Publisher:**MIT Press**ISBN:**0262533057**Category:**Computers**Page:**1292**View:**9574

A new edition of the essential text and professional reference, with substantial new material on such topics as vEB trees, multithreaded algorithms, dynamic programming, and edge-based flow.

## Planning Algorithms

**Author**: Steven M. LaValle**Publisher:**Cambridge University Press**ISBN:**1139455176**Category:**Computers**Page:**N.A**View:**3856

Planning algorithms are impacting technical disciplines and industries around the world, including robotics, computer-aided design, manufacturing, computer graphics, aerospace applications, drug design, and protein folding. This coherent and comprehensive book unifies material from several sources, including robotics, control theory, artificial intelligence, and algorithms. The treatment is centered on robot motion planning, but integrates material on planning in discrete spaces. A major part of the book is devoted to planning under uncertainty, including decision theory, Markov decision processes, and information spaces, which are the 'configuration spaces' of all sensor-based planning problems. The last part of the book delves into planning under differential constraints that arise when automating the motions of virtually any mechanical system. This text and reference is intended for students, engineers, and researchers in robotics, artificial intelligence, and control theory as well as computer graphics, algorithms, and computational biology.

## Computational Methods for Inverse Problems

**Author**: Curtis R. Vogel**Publisher:**SIAM**ISBN:**0898717574**Category:**Mathematics**Page:**183**View:**6362

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

## Discrete Inverse and State Estimation Problems

*With Geophysical Fluid Applications*

**Author**: Carl Wunsch**Publisher:**Cambridge University Press**ISBN:**1139456938**Category:**Science**Page:**N.A**View:**3129

The problems of making inferences about the natural world from noisy observations and imperfect theories occur in almost all scientific disciplines. This 2006 book addresses these problems using examples taken from geophysical fluid dynamics. It focuses on discrete formulations, both static and time-varying, known variously as inverse, state estimation or data assimilation problems. Starting with fundamental algebraic and statistical ideas, the book guides the reader through a range of inference tools including the singular value decomposition, Gauss-Markov and minimum variance estimates, Kalman filters and related smoothers, and adjoint (Lagrange multiplier) methods. The final chapters discuss a variety of practical applications to geophysical flow problems. Discrete Inverse and State Estimation Problems is an ideal introduction to the topic for graduate students and researchers in oceanography, meteorology, climate dynamics, and geophysical fluid dynamics. It is also accessible to a wider scientific audience; the only prerequisite is an understanding of linear algebra.

## Data Assimilation: Methods, Algorithms, and Applications

**Author**: Mark Asch,Marc Bocquet,Maelle Nodet**Publisher:**SIAM**ISBN:**1611974542**Category:**Mathematics**Page:**306**View:**4375

Data assimilation is an approach that combines observations and model output, with the objective of improving the latter. This book places data assimilation into the broader context of inverse problems and the theory, methods, and algorithms that are used for their solution. It provides a framework for, and insight into, the inverse problem nature of data assimilation, emphasizing ?why? and not just ?how.? Methods and diagnostics are emphasized, enabling readers to readily apply them to their own field of study. Readers will find a comprehensive guide that is accessible to nonexperts; numerous examples and diverse applications from a broad range of domains, including geophysics and geophysical flows, environmental acoustics, medical imaging, mechanical and biomedical engineering, economics and finance, and traffic control and urban planning; and the latest methods for advanced data assimilation, combining variational and statistical approaches.

## Computer Vision

*Algorithms and Applications*

**Author**: Richard Szeliski**Publisher:**Springer Science & Business Media**ISBN:**9781848829350**Category:**Computers**Page:**812**View:**6311

Computer Vision: Algorithms and Applications explores the variety of techniques commonly used to analyze and interpret images. It also describes challenging real-world applications where vision is being successfully used, both for specialized applications such as medical imaging, and for fun, consumer-level tasks such as image editing and stitching, which students can apply to their own personal photos and videos. More than just a source of “recipes,” this exceptionally authoritative and comprehensive textbook/reference also takes a scientific approach to basic vision problems, formulating physical models of the imaging process before inverting them to produce descriptions of a scene. These problems are also analyzed using statistical models and solved using rigorous engineering techniques. Topics and features: structured to support active curricula and project-oriented courses, with tips in the Introduction for using the book in a variety of customized courses; presents exercises at the end of each chapter with a heavy emphasis on testing algorithms and containing numerous suggestions for small mid-term projects; provides additional material and more detailed mathematical topics in the Appendices, which cover linear algebra, numerical techniques, and Bayesian estimation theory; suggests additional reading at the end of each chapter, including the latest research in each sub-field, in addition to a full Bibliography at the end of the book; supplies supplementary course material for students at the associated website, http://szeliski.org/Book/. Suitable for an upper-level undergraduate or graduate-level course in computer science or engineering, this textbook focuses on basic techniques that work under real-world conditions and encourages students to push their creative boundaries. Its design and exposition also make it eminently suitable as a unique reference to the fundamental techniques and current research literature in computer vision.

## Discrete Convex Analysis

**Author**: Kazuo Murota**Publisher:**SIAM**ISBN:**9780898718508**Category:**Convex functions**Page:**389**View:**3737

Discrete Convex Analysis is a novel paradigm for discrete optimization that combines the ideas in continuous optimization (convex analysis) and combinatorial optimization (matroid/submodular function theory) to establish a unified theoretical framework for nonlinear discrete optimization. The study of this theory is expanding with the development of efficient algorithms and applications to a number of diverse disciplines like matrix theory, operations research, and economics. This self-contained book is designed to provide a novel insight into optimization on discrete structures and should reveal unexpected links among different disciplines. It is the first and only English-language monograph on the theory and applications of discrete convex analysis.

## Rank-Deficient and Discrete Ill-Posed Problems

*Numerical Aspects of Linear Inversion*

**Author**: Per Christian Hansen**Publisher:**SIAM**ISBN:**0898714036**Category:**Equations, Simultaneous**Page:**247**View:**5289

Here is an overview of modern computational stabilization methods for linear inversion, with applications to a variety of problems in audio processing, medical imaging, tomography, seismology, astronomy, and other areas. Rank-deficient problems involve matrices that are either exactly or nearly rank deficient. Such problems often arise in connection with noise suppression and other problems where the goal is to suppress unwanted disturbances of the given measurements. Discrete ill-posed problems arise in connection with the numerical treatment of inverse problems, where one typically wants to compute information about some interior properties using exterior measurements. Examples of inverse problems are image restoration and tomography, where one needs to improve blurred images or reconstruct pictures from raw data. This book describes, in a common framework, new and existing numerical methods for the analysis and solution of rank-deficient and discrete ill-posed problems. The emphasis is on insight into the stabilizing properties of the algorithms and on the efficiency and reliability of the computations. The setting is that of numerical linear algebra rather than abstract functional analysis, and the theoretical development is complemented with numerical examples and figures that illustrate the features of the various algorithms.

## Practical Augmented Lagrangian Methods for Constrained Optimization

**Author**: Ernesto G. Birgin,Josâ Mario Martinez**Publisher:**SIAM**ISBN:**161197335X**Category:**Mathematics**Page:**220**View:**3244

This book focuses on Augmented Lagrangian techniques for solving practical constrained optimization problems. The authors rigorously delineate mathematical convergence theory based on sequential optimality conditions and novel constraint qualifications. They also orient the book to practitioners by giving priority to results that provide insight on the practical behavior of algorithms and by providing geometrical and algorithmic interpretations of every mathematical result, and they fully describe a freely available computational package for constrained optimization and illustrate its usefulness with applications.

## A Taste of Inverse Problems

*Basic Theory and Examples*

**Author**: Martin Hanke**Publisher:**SIAM**ISBN:**1611974941**Category:**Inverse problems (Differential equations)**Page:**162**View:**3552

Inverse problems need to be solved in order to properly interpret indirect measurements. Often, inverse problems are ill-posed and sensitive to data errors. Therefore one has to incorporate some sort of regularization to reconstruct significant information from the given data. This book presents the main achievements that have emerged in regularization theory over the past 50 years, focusing on linear ill-posed problems and the development of methods that can be applied to them. Some of this material has previously appeared only in journal articles. A Taste of Inverse Problems: Basic Theory and Examples rigorously discusses state-of-the-art inverse problems theory, focusing on numerically relevant aspects and omitting subordinate generalizations;presents diverse real-world applications, important test cases, and possible pitfalls; and treats these applications with the same rigor and depth as the theory.

## Mathematical Methods and Algorithms for Signal Processing

**Author**: Todd K. Moon,Wynn C. Stirling**Publisher:**N.A**ISBN:**N.A**Category:**Computers**Page:**937**View:**6357

Mathematical Methods and Algorithms for Signal Processing tackles the challenge of providing readers and practitioners with the broad tools of mathematics employed in modern signal processing. Building from an assumed background in signals and stochastic processes, the book provides a solid foundation in analysis, linear algebra, optimization, and statistical signal processing.Interesting modern topics not available in many other signal processing books; such as the EM algorithm, blind source operation, projection on convex sets, etc., in addition to many more conventional topics such as spectrum estimation, adaptive filtering, etc. For those interested in signal processing.

## Alternating Projection Methods

**Author**: Renâ Escalante,Marcos Raydan**Publisher:**SIAM**ISBN:**1611971934**Category:**Mathematics**Page:**129**View:**1145

A comprehensive textbook for advanced undergraduate or graduate students.

## Randomized Algorithms

**Author**: Rajeev Motwani,Prabhakar Raghavan**Publisher:**Cambridge University Press**ISBN:**1139643134**Category:**Computers**Page:**N.A**View:**378

For many applications a randomized algorithm is either the simplest algorithm available, or the fastest, or both. This tutorial presents the basic concepts in the design and analysis of randomized algorithms. The first part of the book presents tools from probability theory and probabilistic analysis that are recurrent in algorithmic applications. Algorithmic examples are given to illustrate the use of each tool in a concrete setting. In the second part of the book, each of the seven chapters focuses on one important area of application of randomized algorithms: data structures; geometric algorithms; graph algorithms; number theory; enumeration; parallel algorithms; and on-line algorithms. A comprehensive and representative selection of the algorithms in these areas is also given. This book should prove invaluable as a reference for researchers and professional programmers, as well as for students.