A Distributed Spatio-temporal EEG/MEG Inverse Solver

Abstract

Abstract. We propose a novel 1 2-norm inverse solver for estimating the sources of EEG/MEG signals. Based on the standard 1-norm inverse solver, the proposed sparse distributed inverse solver integrates the 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 original solvers. The joint spatio-temporal model leads to a cost function with an 1 2-norm regularizer whose minimization can be reduced to a convex second-order cone programming problem and efficiently solved using the interior-point method. Validation with simulated and real 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 1 2-norm solver achieves fewer false positives and a better representation of the source locations than the conventional 2 minimum-norm estimates.

Multi-condition M/EEG Inverse Modeling with Sparsity Assumptions: How to Estimate What Is Common and What Is Specific in Multiple Experimental Conditions

“…In [3], the problem solved corresponds to (1) where φ (X) equals to X 21 . This ℓ 21 mixed norm is defined for a matrix…”

“…In order to demonstrate that the portion of the active set that is common between conditions is more consistently recovered with the SMC solver, we have compared our results with the single condition spatiotemporal sparse solver proposed in [3]. We ran this solver on each condition successively and defined the common active sets as the intersection between all the A (X k 21 ).…”

“…With ℓ p norms, a value of p ≤ 1 induces "sparsity", i.e., , a small number of sources with non-zero amplitudes, while with ℓ 2 all sources have non-zero amplitudes. This observation led to the development of FOCUSS [2] and MCE [1] that work instant by instant, and more recently to a promising spatiotemporal inverse method based on a mixed ℓ 2 -ℓ 1 norm [3]. We call such solvers sparse solvers and the set of estimated active dipoles the active set.…”

“…ℓ 1 with MCE [1], ℓ 0 with FOCUSS [2], ℓ 2 -ℓ 1 [3]) offer a way to select a set of active dipoles. Indeed, sparsity inducing norms lead to solutions where most of the sources are set to zero and the remaining non zero sources form the set of estimated active dipoles.…”

Spatio-temporal reconstruction of brain dynamics from EEG with a Markov prior

“…To stabilize the solution it is useful to impose some level of temporal smoothness. A basic scheme is to enforce that the locations of activity are 50 fixed throughout an analysis window (Wipf and Rao, 2007;Friston et al, 2008;Ou et al, 2009;Zhang and Rao, 2011;Hansen et al, 2013c). While useful for short time windows, this may be less appropriate for more extended and non-stationary settings.…”