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- Nordebo, Sven, et al.
(författare)
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Data fusion for electromagnetic and electrical resistive tomography based on maximum likelihood
- 2011
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Ingår i: International Journal of Geophysics. - Hindawi. - 1687-885X. ; :Article ID 617089, s. 1-11
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Tidskriftsartikel (refereegranskat)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 multi-physics 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 productis dened 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 multi-physics 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. Numerical examples are included to illustrate the potential impact of an imbalance between the singular values and the variance of the measurement noise when dierent imaging modalities are incorporated in the inversion. The examples furthermore illustrate the signicance of taking a statistically based weighting of the measurement data into proper account.
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- Nordebo, Sven, et al.
(författare)
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Data fusion for reconstruction algorithms via different sensors in geophysical sensing
- 2011
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Ingår i: Journal of Geophysics and Engineering. - IOP Publishing Ltd. - 1742-2132. ; 8:3, s. S54-S60
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Tidskriftsartikel (refereegranskat)abstract
- Information fusion via multimodal inverse problems and different sensors is addressed using a Fisher information analysis approach. The Fisher information measure is inherently additive, and it facilitates an appropriate weighting of the measurement data that is statistically optimal and can hence be useful with reconstruction algorithms in geophysical sensing. Given that there exists proper knowledge about the sensor noise statistics, correlations and spectral contents, as well as a correct forward model, the Fisher information is a natural measure of information because it is closely linked to the statistical maximum likelihood principle. To illustrate the concept of data correlation based on statistical Fisher information analysis, two simple and generic examples are employed in electrical resistivity and electromagnetic tomography, which are motivated by geophysical applications, such as tunnel detection. The examples demonstrate that a properly weighted data fusion can be of crucial importance for an ill-posed multimodal inverse problem.
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