Data Fusion for Electromagnetic and Electrical Resistive Tomography Based on Maximum Likelihood

Sven Nordebo,Therese Sjöden,Mats Gustafsson,Francesco Soldovieri

doi:10.1155/2011/617089

Abstract

This paper presents a maximum likelihood based approach to data fusion for electromagnetic (EM) and electrical resistive (ER) tomography. The statistical maximum likelihood criterion is closely linked to the additive Fisher information measure, and it facilitates an appropriate weighting of the measurement data which can be useful with multiphysics inverse problems. The Fisher information is particularly useful for inverse problems which can be linearized similar to the Born approximation. In this paper, a proper scalar product is defined for the measurements and a truncated Singular Value Decomposition (SVD) based algorithm is devised which combines the measurement data of the two imaging modalities in a way that is optimal in the sense of maximum likelihood. As a multiphysics problem formulation with applications in geophysics, the problem of tunnel detection based on EM and ER tomography is studied in this paper. To illustrate the connection between the Green's functions, the gradients and the Fisher information, two simple and generic forward models are described in detail regarding two-dimensional EM and ER tomography, respectively.

Highlights

Nondestructive monitoring systems based on information, communication, and sensor technologies will be used to provide future emergency and disasters stakeholders with high situation awareness by means of realtime and detailed information and images of the infrastructure status [1]
The Fisher information is useful for inverse problems which can be linearized similar to the Born approximation
As a generic example concerning a multiphysics inverse problem based on geophysical sensing, this paper addresses the problem of tunnel detection [4] based on data fusion with electromagnetic (ER) and electrical resistive (ER) tomography

Summary

Introduction

Nondestructive monitoring systems based on information, communication, and sensor technologies will be used to provide future emergency and disasters stakeholders with high situation awareness by means of realtime and detailed information and images of the infrastructure status [1]. The Fisher information is a local measure of information with respect to the state space of parameter values, and it is useful for inverse problems which can be linearized, such as with the Born approximation [3], and so forth. In this paper, it is shown how the principle of maximum likelihood (under the assumption of Gaussian noise) can be used to derive a proper scalar product for the measurement data. The examples illustrate the significance of taking a statistically based weighting of the measurement data into proper account

Multiphysics Data Fusion Based on Maximum Likelihood

Green’s Functions and Gradients

Numerical Example

Summary

EM Green’s Function for a Homogeneous Cylinder

ER Green’s Function for a Homogeneous Cylinder