EAN: 9783658109929

ANOMALY DETECTION IN RANDOM HETEROGENEOUS MEDIA...

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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