Statistical and Computational Inverse Problems

Name: Statistical and Computational Inverse Problems
Brand: Springer-Verlag New York Inc.
SKU: 9781441919649
Price: 2417 CZK
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Autor: Jari Kaipio, E. Somersalo

Jazyk:

Vazba: Brožovaná

Vydavatel: Springer-Verlag New York Inc.

Dostupnost: Skladem u dodavatele

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This book covers the statistical mechanics approach to computational solution of inverse problems, a...

Informace o knize

Autor

Jari Kaipio, E. Somersalo

Jazyk

Angličtina

Vazba

Kniha - Brožovaná

Vydáno

2010

Stránek

340

EAN

9781441919649

ISBN

1441919643

Enbook ID

01420854

Vydavatel

Springer-Verlag New York Inc.

Hmotnost

545

Rozměry

155 x 235 x 20

Kompletní popis

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.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 Besides the simple examples, the book contains previously unpublished research material, where the statistical approach is developed further to treat such problems as discretization errors, and statistical model reduction.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.

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