Soft/hard focalization in the EEG inverse problem

Alecu, Teodor; Missonnier, Pascal; Voloshynovskiy, Slava; Giannakopoulos, Pantéleimon; Pun, Thierry

doi:10.1109/ssp.2005.1628737

Cited by 4 publications

(2 citation statements)

References 12 publications

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“…Similarly to (15), it is possible to compute the Gaussian Transforms of other usual symmetric distributions using the Laplace transform tables [1]. We exemplify with the Laplacian and Cauchy distributions.…”

Section: A Analytic Gaussian Transformsmentioning

confidence: 99%

“…While the IMG MAP estimator does not outperform the cumulative estimator, nor the shrinkage estimator for 1 γ ≥ , and while the IMG CE estimator does not outperform the classical MMSE estimate, the linear nature of the estimator (23), coupled with the simple analytical forms (38) and (30) for 1 γ = , allowed the successful use of the IMG MAP and IMG CE estimators in the highly underdetermined EEG (electroencephalogram) inverse problem [15] with Laplacian prior, where a direct application of the MAP principle would lead to an underdetermined quadratic programming problem, and where a direct application of the MMSE principle would lead to highly expensive computations.…”

Section: Figure 8 Empirical Distortion Curvesmentioning

confidence: 99%

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The Gaussian Transform of Distributions: Definition, Computation and Application

Alecu

Voloshynovskiy²,

Pun³

2006

IEEE Trans. Signal Process.

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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...

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Section: A Analytic Gaussian Transformsmentioning

confidence: 99%

Section: Figure 8 Empirical Distortion Curvesmentioning

confidence: 99%

The Gaussian Transform of Distributions: Definition, Computation and Application

Alecu

Voloshynovskiy²,

Pun³

2006

IEEE Trans. Signal Process.

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Brain-computer interaction research at the computer vision and multimedia laboratory, University of Geneva

Pun

Alecu

Chanel

et al. 2006

IEEE Trans. Neural Syst. Rehabil. Eng.

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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.

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Robust focalized brain activity reconstruction using electroencephalograms

Alecu¹

2005

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Soft/hard focalization in the EEG inverse problem

Cited by 4 publications

References 12 publications

The Gaussian Transform of Distributions: Definition, Computation and Application

The Gaussian Transform of Distributions: Definition, Computation and Application

Brain-computer interaction research at the computer vision and multimedia laboratory, University of Geneva

Robust focalized brain activity reconstruction using electroencephalograms

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