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| Titel |
Data fusion for reconstruction algorithms via different sensors in geophysical sensing |
| VerfasserIn |
Sven Nordebo, Mats Gustafsson, Francesco Soldovieri |
| Konferenz |
EGU General Assembly 2010
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 12 (2010) |
| Datensatznummer |
250036630
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| Zusammenfassung |
| 1 Abstract
A unified approach to sensitivity analysis and data fusion for multi-physics inverse scattering
problems will be presented which is based on Fisher information analysis for distributed
parameter systems, cf., [4]. This approach is particularly useful when there is a diversity of
measurement sensors having varying noise spectral content and signal to noise ratios, such as
with information fusion with multi-physics data. Here, the Fisher information analysis
yields a systematic procedure to incorporate a statistically based weighting of the
measurements.
The forward operator is the mapping that takes the unknown material parameters of
interest to the measurement data. It will be shown that the Fisher information analysis
is equivalent to performing a Singular Value Decomposition (SVD) analysis of
the linearized forward operator [1,2,5], provided that the measurement noise is
Gaussian distributed and that the appropriate scalar product is chosen for the space of
measurement data. Hence, the Fisher information concept provides a systematic means of
choosing the scalar product for the related Hilbert space in a way that is statistically
optimum.
In particular, if J denotes the Jacobian, or the Fréchet derivative of the forward operator,
then the Fisher information integral operator is given by I = 2J*J where J* is the Hilbert
adjoint operator, see e.g., [3] for the finite-dimensional case. Hence, the truncated SVD
algorithm [1,2,5] corresponds here to a regularized pseudo-inverse based on the Fisher
information operator.
Application examples using the truncated SVD algorithm [5] for multi-physics inverse
problems in geophysical sensing will be considered.
References
[1]   M. Bertero. Linear inverse and ill–posed problems. Advances in electronics
and electron physics, 75, 1–120, 1989.
[2]   Q. Fang, P. M. Meaney, and K. D. Paulsen. Singular value analysis of
the Jacobian matrix in microwave image reconstruction. IEEE Trans. Antennas
Propagat., 54(8), 2371–2380, aug 2006.
[3]   S. M. Kay. Fundamentals of Statistical Signal Processing, Estimation Theory.
Prentice-Hall, Inc., NJ, 1993.
[4]   S. Nordebo, A. Fhager, M. Gustafsson, and B. Nilsson. Fisher information
integral operator and spectral decomposition for inverse scattering
problems. Technical Report LUTEDX/(TEAT-7180)/1–21/(2009), Lund Institute
of Technology, Department of Electrical and Information Technology, P.O. Box
118, S-211 00 Lund, Sweden, 2009. Submitted to Inverse Problems in Science and
Engineering.
[5]   R. Pierri, A. Liseno, and F. Soldovieri. Shape reconstruction from PO
multifrequency scattered fields via the singular value decomposition approach.
IEEE Trans. Antennas Propagat., 49(9), 1333–1343, September 2001. |
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