Statistical and Computational Inverse Problems
Title | Statistical and Computational Inverse Problems PDF eBook |
Author | Jari Kaipio |
Publisher | Springer Science & Business Media |
Total Pages | 346 |
Release | 2006-03-30 |
Genre | Mathematics |
ISBN | 0387271325 |
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.
Computational Methods for Inverse Problems
Title | Computational Methods for Inverse Problems PDF eBook |
Author | Curtis R. Vogel |
Publisher | SIAM |
Total Pages | 195 |
Release | 2002-01-01 |
Genre | Mathematics |
ISBN | 0898717574 |
Provides a basic understanding of both the underlying mathematics and the computational methods used to solve inverse problems.
Statistical and Computational Inverse Problems
Title | Statistical and Computational Inverse Problems PDF eBook |
Author | Jari Kaipio |
Publisher | Springer |
Total Pages | 0 |
Release | 2008-11-01 |
Genre | Mathematics |
ISBN | 9780387501437 |
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.
Computational Methods for Applied Inverse Problems
Title | Computational Methods for Applied Inverse Problems PDF eBook |
Author | Yanfei Wang |
Publisher | Walter de Gruyter |
Total Pages | 552 |
Release | 2012-10-30 |
Genre | Mathematics |
ISBN | 3110259052 |
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.
Parameter Estimation and Inverse Problems
Title | Parameter Estimation and Inverse Problems PDF eBook |
Author | Richard C. Aster |
Publisher | Elsevier |
Total Pages | 404 |
Release | 2018-10-16 |
Genre | Science |
ISBN | 0128134232 |
Parameter Estimation and Inverse Problems, Third Edition, is structured around a course at New Mexico Tech and is designed to be accessible to typical graduate students in the physical sciences who do not have an extensive mathematical background. The book is complemented by a companion website that includes MATLAB codes that correspond to examples that are illustrated with simple, easy to follow problems that illuminate the details of particular numerical methods. Updates to the new edition include more discussions of Laplacian smoothing, an expansion of basis function exercises, the addition of stochastic descent, an improved presentation of Fourier methods and exercises, and more. Features examples that are illustrated with simple, easy to follow problems that illuminate the details of a particular numerical method Includes an online instructor’s guide that helps professors teach and customize exercises and select homework problems Covers updated information on adjoint methods that are presented in an accessible manner
Computational Uncertainty Quantification for Inverse Problems
Title | Computational Uncertainty Quantification for Inverse Problems PDF eBook |
Author | Johnathan M. Bardsley |
Publisher | SIAM |
Total Pages | 141 |
Release | 2018-08-01 |
Genre | Science |
ISBN | 1611975379 |
This book is an introduction to both computational inverse problems and uncertainty quantification (UQ) for inverse problems. The book also presents more advanced material on Bayesian methods and UQ, including Markov chain Monte Carlo sampling methods for UQ in inverse problems. Each chapter contains MATLAB? code that implements the algorithms and generates the figures, as well as a large number of exercises accessible to both graduate students and researchers. Computational Uncertainty Quantification for Inverse Problems is intended for graduate students, researchers, and applied scientists. It is appropriate for courses on computational inverse problems, Bayesian methods for inverse problems, and UQ methods for inverse problems.
An Introduction to Data Analysis and Uncertainty Quantification for Inverse Problems
Title | An Introduction to Data Analysis and Uncertainty Quantification for Inverse Problems PDF eBook |
Author | Luis Tenorio |
Publisher | SIAM |
Total Pages | 275 |
Release | 2017-07-06 |
Genre | Mathematics |
ISBN | 1611974917 |
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.