Cédric Gouy-Pailler

On the blind source separation of human electroencephalogram by approximate joint diagonalization of second order statistics

Over the last ten years blind source separation (BSS) has become a prominent processing tool in the study of human electroencephalography (EEG). Without relying on head modeling BSS aims at estimating both the waveform and the scalp spatial pattern of the intracranial dipolar current responsible of the observed EEG. In this review we begin by placing the BSS linear instantaneous model of EEG within the framework of brain volume conduction theory. We then review the concept and current practice of BSS based on second-order statistics (SOS) and on higher-order statistics (HOS), the latter better known as independent component analysis (ICA). Using neurophysiological knowledge we consider the fitness of SOS-based and HOS-based methods for the extraction of spontaneous and induced EEG and their separation from extra-cranial artifacts. We then illustrate a general BSS scheme operating in the time-frequency domain using SOS only. The scheme readily extends to further data expansions in order to capture experimental source of variations as well. A simple and efficient implementation based on the approximate joint diagonalization of Fourier cospectral matrices is described (AJDC). We conclude discussing useful aspects of BSS analysis of EEG, including its assumptions and limitations.

Nonstationary Brain Source Separation for Multiclass Motor Imagery

This paper describes a method to recover task-related brain sources in the context of multiclass brain--computer interfaces (BCIs) based on noninvasive EEG. We extend the method joint approximate diagonalization (JAD) for spatial filtering using a maximum likelihood framework. This generic formulation: 1) bridges the gap between the common spatial patterns (CSPs) and blind source separation of nonstationary sources; and 2) leads to a neurophysiologically adapted version of JAD, accounting for the successive activations/deactivations of brain sources during motor imagery (MI) trials. Using dataset 2a of BCI Competition IV (2008) in which nine subjects were involved in a four-class two-session MI-based BCI experiment, a quantitative evaluation of our extension is provided by comparing its performance against JAD and CSP in the case of cross-validation, as well as session-to-session transfer. While JAD, as already proposed in other works, does not prove to be significantly better than classical one-versus-rest CSP, our extension is shown to perform significantly better than CSP for cross-validated and session-to-session performance. The extension of JAD introduced in this paper yields among the best session-to-session transfer results presented so far for this particular dataset; thus, it appears to be of great interest for real-life BCIs.

An iterative subspace denoising algorithm for removing electroencephalogram ocular artifacts

BACKGROUND Electroencephalogram (EEG) measurements are always contaminated by non-cerebral signals, which disturb EEG interpretability. Among the different artifacts, ocular artifacts are the most disturbing ones. In previous studies, limited improvement has been obtained using frequency-based methods. Spatial decomposition methods have shown to be more effective for removing ocular artifacts from EEG recordings. Nevertheless, these methods are not able to completely separate cerebral and ocular signals and commonly eliminate important features of the EEG. NEW METHOD In a previous study we have shown the applicability of a deflation algorithm based on generalized eigenvalue decomposition for separating desired and undesired signal subspaces. In this work, we extend this idea for the automatic detection and removal of electrooculogram (EOG) artifacts from multichannel EEG recordings. The notion of effective number of identifiable dimensions, is also used to estimate the number of dominant dimensions of the ocular subspace, which enables the precise and fast convergence of the algorithm. RESULTS The method is applied on real and synthetic data. It is shown that the method enables the separation of cerebral and ocular signals with minimal interference with cerebral signals. COMPARISON WITH EXISTING METHOD(S) The proposed approach is compared with two widely used denoising techniques based on independent component analysis (ICA). CONCLUSIONS It is shown that the algorithm outperformed ICA-based approaches. Moreover, the method is computationally efficient and is implemented in real-time. Due to its semi-automatic structure and low computational cost, it has broad applications in real-time EEG monitoring systems and brain-computer interface experiments.

Multivariate temporal dictionary learning for EEG.

This article addresses the issue of representing electroencephalographic (EEG) signals in an efficient way. While classical approaches use a fixed Gabor dictionary to analyze EEG signals, this article proposes a data-driven method to obtain an adapted dictionary. To reach an efficient dictionary learning, appropriate spatial and temporal modeling is required. Inter-channels links are taken into account in the spatial multivariate model, and shift-invariance is used for the temporal model. Multivariate learned kernels are informative (a few atoms code plentiful energy) and interpretable (the atoms can have a physiological meaning). Using real EEG data, the proposed method is shown to outperform the classical multichannel matching pursuit used with a Gabor dictionary, as measured by the representative power of the learned dictionary and its spatial flexibility. Moreover, dictionary learning can capture interpretable patterns: this ability is illustrated on real data, learning a P300 evoked potential.

Topographical Dynamics of Brain Connections for the Design of Asynchronous Brain-Computer Interfaces

This article presents a new processing method to design brain-computer interfaces (BCIs). It shows how to use the perturbations of the communication between different cortical areas due to a cognitive task. For this, the network of the cerebral connections is built from correlations between cortical areas at specific frequencies and is analyzed using graph theory. This allows us to describe the topological organisation of the networks using quantitative measures. This method is applied to an auditive steady-state evoked potentials experiment (dichotic binaural listening) and compared to a more classical method based on spectral filtering.

Bayesian Model for Multiple Change-Points Detection in Multivariate Time Series

This paper addresses the issue of detecting change-points in time series. The proposed model, called the Bernoulli Detector, is presented first in a univariate context. This approach differs from existing counterparts by making only assumptions on the nature of the change-points, and does not depend on hypothesis on the distribution of the data, contrary to the parametric methods. It relies on the combination of a local robust statistical test, based on the computation of ranks and acting on individual time segments, with a global Bayesian framework able to optimize the change-points configurations from multiple local statistics, provided as

Single trial variability in brain–computer interfaces based on motor imagery: Learning in the presence of labeling noise

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Backward hidden Markov chain for outlier-robust filtering and fixed-interval smoothing

-values. The control of the detection of a single change-point is proved even for small samples. The interest of such a generalizable nonparametric approach is shown on simulated data by the good performances attained for Gaussian noise as well as in presence of outliers, without adapting the model. The model is extended to the multivariate case by introducing the probabilities that the change-points affect simultaneously several time series. The method presents then the advantage to detect both unique and shared change-points for each signal. We finally illustrate our algorithm with real datasets from energy monitoring and genomic. Segmentations are compared to state-of-the-art approaches like the group lasso and the BARD algorithm.

Multi-dimensional sparse structured signal approximation using split bregman iterations

This article addresses the issue of learning efficient linear spatial filters and a classification function to match noninvasive electroencephalographic (EEG) signals to motor imagery tasks voluntarily performed by the subjects. The new perspective used in this article consists in releasing the widely accepted hypothesis stating that motor tasks‐related brain activities should have similar time course across trials. This work proposes a learning model that takes into account two previously unconsidered sources of variability. First, the time course of the subjects brain activity, while performing a motor imagery task, will be considered as a trial‐dependent variable. This means that the optimal time, defined as an amount of time after the trial cue, chosen to determine the task performed by the subject might be different between distinct trials. The second released hypothesis deals with the spectral discriminative brain response. Although usual learning methods do not allow any dependency between the optimal discriminative time and frequency bands, our model takes into account this possible source of variability. Therefore, the brain response in distinct frequency bands, e.g., in the mu band or beta band, could be used by the decision function at distinct instants. Based on this underlying enhanced model, we propose a two‐step procedure. In the first step, the algorithm carefully analyzes, using cross‐validation techniques, the training data to identify previously mentioned sources of variability. In the second step, the enhanced frequency‐dependent linear spatial filters and the classification function are determined. As by‐products of this analysis, substantial piece of knowledge about motor imagery is provided. First, the method allows the identification and quantification of labeling noise in brain–computer interfaces (BCIs) based on motor imagery. Second, the algorithm gives a comparative estimation of the spectral time courses during motor imagery. This article makes an extensive use of the dataset I of BCI Competition IV, which took place in 2008. It consists of a training set and a test set of 59 EEG signals recording on four subjects while performing an asynchronous BCI experiment. The two‐step procedure presented in this article is shown to significantly outperform a comparative naive approach.

Multi-dimensional signal approximation with sparse structured priors using split Bregman iterations

This paper addresses the problem of recursive estimation of a process in presence of outliers among the observations. It focuses on deriving robust approximate Kalman-like backward filtering and backward-forward fixed-interval smoothing algorithms in the context of linear hidden Markov chain with heavy-tailed measurement noise. The proposed algorithms are derived based on the backward Markovianity of the model as well as the variational Bayesian approach. In a simulation design, our algorithms are shown to outperform the classical Kalman filter in the presence of outliers.