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Bayesian Inference Applied to the Electromagnetic
Inverse Problem
David M. Schmidt, John S. George and
C.C. Wood
Abstract
We present a new approach to the electromagnetic inverse problem that
explicitly addresses the ambiguity associated with its ill-posed character.
Rather than calculating a single ``best'' solution according to some criterion,
our approach produces a large number of likely solutions that both fit
the data and any prior information that is used. While the range
of the different likely results is representative of the ambiguity in
the inverse problem even with prior information present, features that
are common across a large number of the different solutions can be identified
and are associated with a high degree of probability. This approach
is implemented and quantified within the formalism of Bayesian inference
which combines prior information with that from measurement in a common
framework using a single measure. To demonstrate this approach,
a general neural activation model is constructed that includes a variable
number of extended regions of activation and can incorporate a great deal
of prior information on neural current such as information on location,
orientation, strength and spatial smoothness. Taken together, this
activation model and the Bayesian inferential approach yield estimates
of the probability distributions for the number, location, and extent
of active regions. Both simulated MEG data and data from a visual
evoked response experiment are used to demonstrate the capabilities of
this approach.
- You may download the preprint version of this paper
in PDF format which has the citation: LA-UR-97-4813.
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- Some of the figures that may be difficult to view in a PDF version
are shown below.
Click on the figure number to enlarge.
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Figure 1
Figure 5
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Figure 10
Figure 16
- For questions, comments, problems with the PDF download, send email
to David Schmidt .
Multi-Modality Integration presentation (PDF)
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