Estimating vector fields using sparse basis field expansions

Stefan Haufe; Vadim V. Nikulin; Andreas Ziehe; Klaus Robert Müller; Guido Nolte

Estimating vector fields using sparse basis field expansions

Stefan Haufe, Vadim V. Nikulin, Andreas Ziehe, Klaus Robert Müller, Guido Nolte

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

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.

Original language	English
Title of host publication	Advances in Neural Information Processing Systems 21 - Proceedings of the 2008 Conference
Pages	617-624
Number of pages	8
Publication status	Published - 2009
Event	22nd Annual Conference on Neural Information Processing Systems, NIPS 2008 - Vancouver, BC, Canada Duration: 2008 Dec 8 → 2008 Dec 11

Publication series

Name	Advances in Neural Information Processing Systems 21 - Proceedings of the 2008 Conference

Other

Other	22nd Annual Conference on Neural Information Processing Systems, NIPS 2008
Country	Canada
City	Vancouver, BC
Period	08/12/8 → 08/12/11

ASJC Scopus subject areas

Information Systems

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Haufe, S., Nikulin, V. V., Ziehe, A., Müller, K. R., & Nolte, G. (2009). Estimating vector fields using sparse basis field expansions. In Advances in Neural Information Processing Systems 21 - Proceedings of the 2008 Conference (pp. 617-624). (Advances in Neural Information Processing Systems 21 - Proceedings of the 2008 Conference).

Estimating vector fields using sparse basis field expansions. / Haufe, Stefan; Nikulin, Vadim V.; Ziehe, Andreas; Müller, Klaus Robert; Nolte, Guido.

Advances in Neural Information Processing Systems 21 - Proceedings of the 2008 Conference. 2009. p. 617-624 (Advances in Neural Information Processing Systems 21 - Proceedings of the 2008 Conference).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Haufe, S, Nikulin, VV, Ziehe, A, Müller, KR & Nolte, G 2009, Estimating vector fields using sparse basis field expansions. in Advances in Neural Information Processing Systems 21 - Proceedings of the 2008 Conference. Advances in Neural Information Processing Systems 21 - Proceedings of the 2008 Conference, pp. 617-624, 22nd Annual Conference on Neural Information Processing Systems, NIPS 2008, Vancouver, BC, Canada, 08/12/8.

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abstract = "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.",

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AB - 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.

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