Statistical and Computational Inverse Problems

Jari Kaipio, Erkki Somersalo - Collection Applied Mathematical Sciences

339 pages, parution le 11/02/2005

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Résumé

This 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 examples that are often non-trivial, but easy to follow. Besides the simple examples, the book contains 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 for researchers and advanced students in applied mathematics, computational physics, and engineering. The first part of the book can be used as a textbook on advanced inverse problems courses.

L'auteur - Jari Kaipio

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.

L'auteur - Erkki Somersalo

Sommaire

Inverse Problems and Interpretation of Measurements
Classical Regularization Methods
Statistical Inversion Theory
Nonstationary Inverse Problems
Classical Methods Revisited
ModelProblems
Case Studies
Appendix A: Linear Algebra and Functional Analysis
Appendix B: Basics on Probability

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	PAPIER
Éditeur(s)	Springer
Auteur(s)	Jari Kaipio, Erkki Somersalo
Collection	Applied Mathematical Sciences
Parution	11/02/2005
Nb. de pages	339
Format	16 x 24
Couverture	Relié
Poids	630g
Intérieur	Noir et Blanc
EAN13	9780387220734
ISBN13	978-0-387-22073-4