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Estimating vector fields using sparse basis field expansions

: Haufe, S.; Nikulin, V.V.; Ziehe, A.; Müller, K.-R.; Nolte, G.

Advances in Neural Information Processing Systems 21 - Proceedings of the 2008 Conference
Red Hook, NY: Curran, 2009
ISBN: 978-1-605-60949-2
Annual Conference on Neural Information Processing Systems (NIPS) <22, 2008, Vancouver>
Conference Paper
Fraunhofer FIRST ()

We introduce a novel framework for estimating vector fields using sparse basis field expansions (S-FLEX). The notion of basis fields, which are an extension of scalar basis functions, arises naturally in our framework from a rotational invariance requirement. We consider a regression setting as well as inverse problems. All variants discussed lead to second-order cone programming formulations. While our framework is generally applicable to any type of vector field, we focus in this paper on applying it to solving the EEG/MEG inverse problem. It is shown that significantly more precise and neurophysiologically more plausible location and shape estimates of cerebral current sources from EEG/MEG measurements become possible with our method when comparing to the state-of-the-art.