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Anomaly Detection in Random Heterogeneous Media - Feynman-Kac Formulae, Stochastic Homogenization and Statistical Inversion (Paperback, 1st ed. 2015)
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Anomaly Detection in Random Heterogeneous Media - Feynman-Kac Formulae, Stochastic Homogenization and Statistical Inversion (Paperback, 1st ed. 2015)
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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.
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