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International Journal of Geophysics
Volume 2011 (2011), Article ID 617089, 11 pages
http://dx.doi.org/10.1155/2011/617089
Research Article

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

1School of Computer Science, Physics, and Mathematics, Linnaeus University, 35195 Växjö, Sweden
2Department of Electrical and Information Technology, Lund University, P.O. Box 118, 22100 Lund, Sweden
3Institute for Electromagnetic Sensing of the Environment, National Research Council, Street Diocleziano 328, 80124 Naples, Italy

Received 15 February 2011; Revised 13 April 2011; Accepted 3 May 2011

Academic Editor: Nicola Masini

Copyright © 2011 Sven Nordebo et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.