Anomaly detection in random heterogeneous media [electronic resource] : Feynman-Kac formulae, stochastic homogenization and statistical inversion /
Simon, Martin.author.
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.   Contents Feynman-Kac formulae Stochastic homogenization Statistical inverse problems  Target Groups Students and researchers in the fields of inverse problems, partial differential equations, probability theory and stochastic processes Practitioners in the fields of tomographic imaging and noninvasive testing via EIT  About the Author Martin Simon has worked as a researcher at the Institute of Mathematics at the University of Mainz from 2008 to 2014. During this period he had several research stays at the University of Helsinki. He has recently joined an asset management company as a financial mathematician.
"Research"--Cover.
Includes bibliographical references.
Part I: Probabilistic interpretation of EIT -- Mathematical setting.- Feynman-Kac formulae -- Part II: Anomaly detection in heterogeneous media.- Stochastic homogenization: Theory and numerics.- Statistical inversion.- Appendix A Basic Dirichlet form theory.- Appendix B Random ﬁeld models.- Appendix C FEM discretization of the forward problem.
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.   Contents Feynman-Kac formulae Stochastic homogenization Statistical inverse problems  Target Groups Students and researchers in the fields of inverse problems, partial differential equations, probability theory and stochastic processes Practitioners in the fields of tomographic imaging and noninvasive testing via EIT  About the Author Martin Simon has worked as a researcher at the Institute of Mathematics at the University of Mainz from 2008 to 2014. During this period he had several research stays at the University of Helsinki. He has recently joined an asset management company as a financial mathematician.
Partial differential equations.
Probabilities.
Physics.
Partial Differential Equations.
Probability Theory and Stochastic Processes.
Numerical and Computational Physics, Simulation.