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© 2015

Anomaly Detection in Random Heterogeneous Media

Feynman-Kac Formulae, Stochastic Homogenization and Statistical Inversion

Book

Table of contents

  1. Front Matter
    Pages 1-18
  2. Probabilistic interpretation of EIT

    1. Front Matter
      Pages 9-9
    2. Martin Simon
      Pages 11-22
    3. Martin Simon
      Pages 23-51
  3. Anomaly detection in heterogeneous media

    1. Front Matter
      Pages 53-53
    2. Martin Simon
      Pages 91-110
  4. Back Matter
    Pages 111-150

About this book

Introduction

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.

Keywords

Calderón’s inverse conductivity problem EIT applied probability theory electrical impedance tomography random media statistical inverse problems stochastic analysis

Authors and affiliations

  1. 1.Institut für MathematikJohannes Gutenberg-Universität MainzMainzGermany

About the authors

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. 

Bibliographic information