This paper describes the work being conducted in the domain of brain-computer interaction (BCI) at the Multimodal Interaction Group, Computer Vision and Multimedia Laboratory, University of Geneva, Geneva, Switzerland. The application focus of this work is on multimodal interaction rather than on rehabilitation, that is how to augment classical interaction by means of physiological measurements. Three main research topics are addressed. The first one concerns the more general problem of brain source activity recognition from EEGs. In contrast with classical deterministic approaches, we studied iterative robust stochastic based reconstruction procedures modeling source and noise statistics, to overcome known limitations of current techniques. We also developed procedures for optimal electroencephalogram (EEG) sensor system design in terms of placement and number of electrodes. The second topic is the study of BCI protocols and performance from an information-theoretic point of view. Various information rate measurements have been compared for assessing BCI abilities. The third research topic concerns the use of EEG and other physiological signals for assessing a user's emotional status.

Abstract-This paper introduces the general purpose Gaussian Transform of distributions, which aims at representing a generic symmetric distribution as an infinite mixture of Gaussian distributions. We start by the mathematical formulation of the problem and continue with the investigation of the conditions of existence of such a transform. Our analysis leads to the derivation of analytical and numerical tools for the computation of the Gaussian Transform, mainly based on the Laplace and Fourier transforms, as well as of the afferent properties set (e.g. the transform of sums of independent variables). The Gaussian Transform of distributions is then analytically derived for the Gaussian and Laplacian distributions, and obtained numerically for the Generalized Gaussian and the Generalized Cauchy distribution families. In order to illustrate the usage of the proposed transform we further show how an infinite mixture of Gaussians model can be used to estimate/denoise non-Gaussian data with linear estimators based on the Wiener filter. The decomposition of the data into Gaussian components is straightforwardly computed with the Gaussian Transform, previously derived. The estimation is then based on a two-step procedure, the first step consisting in variance estimation, and the second step in data estimation through Wiener filtering. To this purpose we propose new generic variance estimators based on the Infinite Mixture of Gaussians prior. It is shown that the proposed estimators compare favorably in terms of distortion with the shrinkage denoising technique, and that the distortion lower bound under this framework is lower than the classical MMSE bound.Index Terms-Gaussian mixture, Gaussian Transform of distributions, Generalized Gaussian, denoising, shrinkage I. INTRODUCTIONGaussian distributions are extensively used in the (broad sense) signal processing community, mainly for computational benefits. For instance, in an estimation problem Gaussian priors yield quadratic functionals and linear solutions. In ratedistortion and coding theories, closed form results are mostly available for Gaussian source and channel descriptions [11]. However, real data is most often non-Gaussian distributed, and is best described by other types of distribution (e.g in image processing, the most commonly used model for the wavelet coefficients distribution is the Generalized Gaussian distribution [6]). The goal of the work presented in this paper is to describe non-Gaussian distributions as an infinite mixture of Gaussian distributions, through direct computation of the mixing functions from the non-Gaussian distribution.In a related work [4], it was proven that any distribution can be approximated through a mixture of Gaussian up to an arbitrary level of precision. However, no hint was given by the author on how to obtain the desired mixture in the general case. In the radar community the problem of modeling nonGaussian radar clutters led to the theory of Spherically Invariant Random Processes (SIRP) [13], which aimed at generating n...

The surface Laplacian is known to be a theoretical reliable approximation of the cortical activity. Unfortunately, because of its high pass character and the relative low density of the EEG caps, the estimation of the Laplacian itself tends to be very sensitive to noise.We introduce a method based on vector field regularization through diffusion for denoising the Laplacian data and thus obtain robust estimation. We use a forward-backward diffusion aiming for source energy minimization while preserving contrasts between active and non-active regions. This technique uses headcap geometry specific differential operators to counter the low sensor density. The comparison with classical denoising schemes clearly demonstrates the advantages of our method.We also propose an algorithm based on the GaussOstrogradsky theorem for estimation of the Laplacian on missing (bad) electrodes, which can be combined with the regularization technique in order to provide a joint validation framework.

We present in this paper a novel statistical based focalized reconstruction method for the underdetermined EEG (electroencephalogram) inverse problem. The algorithm is based on the representation of non-Gaussian distributions as an Infinite Mixture of Gaussians (IMG) and relies on an iterative procedure consisting out of alternated variance estimation/ linear inversion operations. By taking into account noise statistics, it performs implicit spurious data rejection and produces robust focalized solutions allowing for straightforward discrimination of active/non-active brain regions. We apply the proposed reconstruction procedure to average evoked potentials EEG data and compare the reconstruction results with the corresponding known physiological responses.

We are aiming at using EEG source localization in the framework of a Brain Computer Interface project. We propose here a new reconstruction procedure, targeting source (or equivalently mental task) differentiation. EEG data can be thought of as a collection of time continuous streams from sparse locations. The measured electric potential on one electrode is the result of the superposition of synchronized synaptic activity from sources in all the brain volume. Consequently, the EEG inverse problem is a highly underdetermined (and ill-posed) problem. Moreover, each source contribution is linear with respect to its amplitude but non-linear with respect to its localization and orientation. In order to overcome these drawbacks we propose a novel two-step inversion procedure. The solution is based on a double scale division of the solution space. The first step uses a coarse discretization and has the sole purpose of globally identifying the active regions, via a sparse approximation algorithm. The second step is applied only on the retained regions and makes use of a fine discretization of the space, aiming at detailing the brain activity. The local configuration of sources is recovered using an iterative stochastic estimator with adaptive joint minimum energy and directional consistency constraints.