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Anomaly Detection in Random Heterogeneous Media

Feynman-Kac Formulae, Stochastic Homogenization and Statistical Inversion

Anomaly Detection in Random Heterogeneous Media by Martin Simon
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This monograph is concerned with the analysis and numerical solution of a stochastic inverse anomaly detection problem in electrical impedance tomography (EIT). Martin Simon studies the problem of detecting a parameterized anomaly in an isotropic, stationary and ergodic conductivity random field whose realizations are rapidly oscillating. For this purpose, he derives Feynman-Kac formulae to rigorously justify stochastic homogenization in the case of the underlying stochastic boundary value problem. The author combines techniques from the theory of partial differential equations and functional analysis with probabilistic ideas, paving the way to new mathematical theorems which may be fruitfully used in the treatment of the problem at hand. Moreover, the author proposes an efficient numerical method in the framework of Bayesian inversion for the practical solution of the stochastic inverse anomaly detection problem.
Springer Fachmedien Wiesbaden; July 2015
153 pages; ISBN 9783658109936
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Title: Anomaly Detection in Random Heterogeneous Media
Author: Martin Simon
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