A distributed spatio-temporal EEG/MEG inverse solver

Abstract

We propose a novel l(1)l(2)-norm inverse solver for estimating the sources of EEG/MEG signals. Based on the standard l(1)-norm inverse solvers, this sparse distributed inverse solver integrates the l(1)-norm spatial model with a temporal model of the source signals in order to avoid unstable activation patterns and "spiky" reconstructed signals often produced by the currently used sparse solvers. The joint spatio-temporal model leads to a cost function with an l(1)l(2)-norm regularizer whose minimization can be reduced to a convex second-order cone programming (SOCP) problem and efficiently solved using the interior-point method. The efficient computation of the SOCP problem allows us to implement permutation tests for estimating statistical significance of the inverse solution. Validation with simulated and human MEG data shows that the proposed solver yields source time course estimates qualitatively similar to those obtained through dipole fitting, but without the need to specify the number of dipole sources in advance. Furthermore, the l(1)l(2)-norm solver achieves fewer false positives and a better representation of the source locations than the conventional l(2) minimum-norm estimates.

Hierarchical Bayesian inference for the EEG inverse problem using realistic FE head models: Depth localization and source separation for focal primary currents

“…For a fair and meaningful comparison one would need to consider only dynamic or static inverse methods. While dynamic formulations of equivalent current dipole and beamforming methods are established in practice, the situation for CDR is, so far, less elaborated (for a recent overview, see Gramfort et al, 2011;Ou et al, 2009). In addition, conducting simulation studies with dynamic inverse methods also incorporates the risk of committing an inverse crime by assuming time courses that are well reflected by some temporal models while inconsistent with other models.…”

Large-scale EEG/MEG source localization with spatial flexibility

“…It has recently been pointed out, that rotational invariance of vectorial quantities can be maintained by choosing a so-called ℓ 1, 2 -norm penalty, which minimizes the (sparsity inducing) ℓ 1 -norm of vector amplitudes (Ding and He, 2008;Haufe et al, 2008;Ou et al, 2008;Bolstad et al, 2009). The difference between "standard" ℓ 1 -norm and the ℓ 1, 2 -norm is that the former leads to entry-wise sparsity, while the latter sets whole rows of C jointly to zero.…”

“…Constraints are here imposed by a dedicated penalty functional reflecting assumptions on the sources. Perhaps the two most common assumptions are smoothness (Hämäläinen and Ilmoniemi, 1994;Pascual-Marqui et al, 1994;Pascual-Marqui, 2002) and focality (Matsuura and Okabe, 1995;Gorodnitsky et al, 1995;Uutela et al, 1999;Huang et al, 2006;Ou et al, 2008;Ding and He, 2008;Bolstad et al, 2009), both of which can be motivated by neurophysiological arguments. Nevertheless both approaches may deliver implausible results in practice.…”

Particle Filters for Magnetoencephalography

“…Another innovative research direction appears to be that of space-time regularization: while most methods described so far and, in general, most methods solving the imaging problem, consider the sequence of MEG data as a collection of independent time points and solve each time point separately, in [34] and in [51] new methods are proposed which account for the temporal characteristics of the neural response. In [34] a traditional L 1 -norm approach is combined with a projection into a subspace of temporal basis functions; in [51] a unified approach is presented, where the L 1 -norm regularization in space is combined with an L 2 -norm regularization in the time direction, so as to provide focal source estimates with smooth amplitude waveform.…”

“…In [34] a traditional L 1 -norm approach is combined with a projection into a subspace of temporal basis functions; in [51] a unified approach is presented, where the L 1 -norm regularization in space is combined with an L 2 -norm regularization in the time direction, so as to provide focal source estimates with smooth amplitude waveform.…”