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Statistical and Computational Inverse Problems
The book develops the statistical approach to inverse problems with an emphasis on modeling and computations. The framework is the Bayesian paradigm, where all variables are modeled as random variables, the randomness reflecting the degree of belief of their values, and the solution of the inverse p...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , |
| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New York, NY :
Springer New York : Imprint: Springer,
2005.
|
| Edición: | 1st ed. 2005. |
| Colección: | Applied Mathematical Sciences,
160 |
| Temas: | |
| Acceso en línea: | Texto Completo |
MARC
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| 100 | 1 | |a Kaipio, Jari. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Statistical and Computational Inverse Problems |h [electronic resource] / |c by Jari Kaipio, E. Somersalo. |
| 250 | |a 1st ed. 2005. | ||
| 264 | 1 | |a New York, NY : |b Springer New York : |b Imprint: Springer, |c 2005. | |
| 300 | |a XVI, 340 p. |b online resource. | ||
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| 490 | 1 | |a Applied Mathematical Sciences, |x 2196-968X ; |v 160 | |
| 505 | 0 | |a Inverse Problems and Interpretation of Measurements -- Classical Regularization Methods -- Statistical Inversion Theory -- Nonstationary Inverse Problems -- Classical Methods Revisited -- Model Problems -- Case Studies. | |
| 520 | |a The book develops the statistical approach to inverse problems with an emphasis on modeling and computations. The framework is the Bayesian paradigm, where all variables are modeled as random variables, the randomness reflecting the degree of belief of their values, and the solution of the inverse problem is expressed in terms of probability densities. The book discusses in detail the construction of prior models, the measurement noise modeling and Bayesian estimation. Markov Chain Monte Carlo-methods as well as optimization methods are employed to explore the probability distributions. The results and techniques are clarified with classroom examples that are often non-trivial but easy to follow. Besides the simple examples, the book contains previously unpublished research material, where the statistical approach is developed further to treat such problems as discretization errors, and statistical model reduction. Furthermore, the techniques are then applied to a number of real world applications such as limited angle tomography, image deblurring, electrical impedance tomography and biomagnetic inverse problems. The book is intended to researchers and advanced students in applied mathematics, computational physics and engineering. The first part of the book can be used as a text book on advanced inverse problems courses. The authors Jari Kaipio and Erkki Somersalo are Professors in the Applied Physics Department of the University of Kuopio, Finland and the Mathematics Department at the Helsinki University of Technology, Finland, respectively. | ||
| 650 | 0 | |a Probabilities. | |
| 650 | 0 | |a Mathematical analysis. | |
| 650 | 0 | |a Mathematics-Data processing. | |
| 650 | 0 | |a Mathematical physics. | |
| 650 | 0 | |a Dynamics. | |
| 650 | 0 | |a Nonlinear theories. | |
| 650 | 0 | |a Biomedical engineering. | |
| 650 | 1 | 4 | |a Probability Theory. |
| 650 | 2 | 4 | |a Analysis. |
| 650 | 2 | 4 | |a Computational Mathematics and Numerical Analysis. |
| 650 | 2 | 4 | |a Theoretical, Mathematical and Computational Physics. |
| 650 | 2 | 4 | |a Applied Dynamical Systems. |
| 650 | 2 | 4 | |a Biomedical Engineering and Bioengineering. |
| 700 | 1 | |a Somersalo, E. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
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| 830 | 0 | |a Applied Mathematical Sciences, |x 2196-968X ; |v 160 | |
| 856 | 4 | 0 | |u https://doi.uam.elogim.com/10.1007/b138659 |z Texto Completo |
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| 950 | |a Mathematics and Statistics (SpringerNature-11649) | ||
| 950 | |a Mathematics and Statistics (R0) (SpringerNature-43713) | ||