Estimating vector fields using sparse basis field expansions
Stefan Haufe, Vadim Nikulin, Klaus-Robert Müller, Andreas Ziehe and Guido Nolte
Advances in Neural Information Processing Sytems
, Cambridge, US
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.