Multi-way space–time–wave-vector analysis for EEG source separation

Abstract

Deterministic approaches for source localization and extraction are desirable for short or nonstationary data, as opposed to techniques based on second or higher order statistics. Techniques based on tensor decompositions are recognized to be efficient in this framework, provided some diversity is available, in addition to time and space. With this goal, some authors have proposed to decompose a SpaceTime-Frequency data tensor. In this paper, we propose a new multiway approach based on Space-Time-Wave-Vector (STWV) data which is obtained by a 3D local Fourier transform over space accomplished on the measured data. This method does not only permit to accurately localize sources even in a noisy environment, but simultaneously extracts the temporal behaviour associated with each source. The performance of this STWV analysis is investigated by means of computer simulations in the context of ElectroEncephaloGraphic (EEG) data analysis. 1

EEG extended source localization: Tensor-based vs. conventional methods

“…Contrary to previous studies of tensor-based approaches (Miwakeichi et al, 2004;Morup et al, 2006;De Vos et al, 2007a,b;Deburchgraeve et al, 2009;Becker et al, 2012), which have mainly focused on source separation and equivalent dipole localization, we have conducted our analysis using a realistic head model and have aimed at identifying the spatial extent of the sources. The localization of extended sources has also been addressed in several other publications (Limpiti et al, 2006;Friston et al, 2008;Ding, 2009;Bolstad et al, 2009;Birot et al, 2011;Chowdhury et al, 2013), based on different algorithms including scanning methods, MEM, Bayesian and sparse approaches.…”

“…In (Becker et al, 2010(Becker et al, , 2012, we have introduced an alternative method, which is based on a local spatial Fourier transform of the EEG measurements. This leads to a Space-Time-Wave-Vector (STWV) tensor, that can also be decomposed using the CP model.…”

“…This is of particular interest when patches with identical, but shortly delayed, source activities have to be identified, i.e., in the context of interictal spikes when spreading of epileptic spikes is suspected between two regions. Furthermore, we have addressed the topic of extended source localization after the tensor-based preprocessing by proposing the Binary Coefficient Matching Pursuit (BCMP) algorithm (Becker et al, 2012). This technique iteratively selects dipoles from a predefined grid to model a larger source region.…”

Semi-nonnegative joint diagonalization by congruence and semi-nonnegative ICA

“…The second method is based on an ALS procedure, in order to minimize (2) due to its advantages brought to light in the context of the CP decomposition.…”

“…This decomposition is very useful in many applications, such as in phonetics [1], in biomedical engineering [2] and in chemometrics [3]. More particularly, for a third-order array, X ∈ | I×J×K , this model can also be expressed as a congruent diagonalization of a set of its K frontal slices, called {X (1) , · · · , X (K) } as follows:…”