Bioelectric source analysis in the human brain from scalp electroencephalography (EEG) signals is sensitive to the conductivities of different head tissues. The conductivity of tissues is subject dependent, so non-invasive methods for conductivity estimation are necessary to fine tune EEG models. To do so, the EEG forward problem solution (so-called lead field matrix) must be computed for a large number of conductivity configurations. Computing a lead field requires a matrix inversion which is computationally intensive for realistic head models. Thus, the required time for computing a large number of lead fields can become impractical. In this work, we propose to approximate the lead field matrix for a set of conductivity configurations, using the exact solution only for a small set of support points in the conductivity space. Our approach accelerates the computation time, while controlling the approximation error. Our method is tested on simulated and measured EEG data for brain and skull conductivity estimation. This test demonstrates that the approximation does not introduce any bias and runs significantly faster than if exact lead field were to be computed.

Functional Electrical Stimulation (FES) stimulates the affected region of the human body thus providing a neuroprosthetic interface to non-recovered muscle groups. FES in combination with Brain-computer interfacing (BCI) has a wide scope in rehabilitation because this system can directly link the cerebral motor intention of the users with its corresponding peripheral mucle activations. Such a rehabilitative system would contribute to improve the cortical and peripheral learning and thus, improve the recovery time of the patients. In this paper, we examine the effect of electrical stimulation by FES on the electroencephalography (EEG) during learning of a motor imagery task. The subjects are asked to perform four motor imagery tasks over six sessions and the features from the EEG are extracted using common spatial algorithm and decoded using linear discriminant analysis classifier. Feedback is provided in form of a visual medium and electrical stimulation representing the distance of the features from the hyperplane. Results suggest a significant improvement in the classification accuracy when the subject was induced with electrical stimulation along with visual feedback as compared to the standard visual one.

This work provides a theoretical analysis framework for features that belong to the high dimensional Riemannian manifold of symmetric positive definite matrices. In non-invasive EEG-based Brain Computer Interfaces, such as the P300 speller, these are sample covariance matrices of the epoched EEG signal that are classified into two classes. An analysis of the class shape on the manifold is performed, and the separability level of the two classes is evaluated. The main contribution is the Separability Marker (SM)-confidence method, a method that appends a confidence marker to the prediction of a binary classifier whose decision function is based on the comparison of Riemannian distances.

A brain-computer interface (BCI) allows users to “communicate” with a computer without using their muscles. BCI based on sensori-motor rhythms use imaginary motor tasks, such as moving the right or left hand to send control signals. The performances of a BCI can vary greatly across users but also depend on the tasks used, making the problem of appropriate task selection an important issue. This study presents a new procedure to automatically select as fast as possible a discriminant motor task for a brain-controlled button. We develop for this purpose an adaptive algorithm UCB-classif based on the stochastic bandit theory. This shortens the training stage, thereby allowing the exploration of a greater variety of tasks. By not wasting time on inefficient tasks, and focusing on the most promising ones, this algorithm results in a faster task selection and a more efficient use of the BCI training session. Comparing the proposed method to the standard practice in task selection, for a fixed time budget, UCB-classif leads to an improve classification rate, and for a fix classification rate, to a reduction of the time spent in training by 50%.

The forward electroencephalography (EEG) problem involves finding a potential V from the Poisson equation inverted Delta x (sigma inverted Delta V) f, in which f represents electrical sources in the brain, and sigma the conductivity of the head tissues. In the piecewise constant conductivity head model, this can be accomplished by the boundary element method (BEM) using a suitable integral formulation. Most previous work uses the same integral formulation, corresponding to a double-layer potential. In this paper we present a conceptual framework based on a well-known theorem (Theorem 1) that characterizes harmonic functions defined on the complement of a bounded smooth surface. This theorem says that such harmonic functions are completely defined by their values and those of their normal derivatives on this surface. It allows us to cast the previous BEM approaches in a unified setting and to develop two new approaches corresponding to different ways of exploiting the same theorem. Specifically, we first present a dual approach which involves a single-layer potential. Then, we propose a symmetric formulation, which combines single- and double-layer potentials, and which is new to the field of EEG, although it has been applied to other problems in electromagnetism. The three methods have been evaluated numerically using a spherical geometry with known analytical solution, and the symmetric formulation achieves a significantly higher accuracy than the alternative methods. Additionally, we present results with realistically shaped meshes. Beside providing a better understanding of the foundations of BEM methods, our approach appears to lead also to more efficient algorithms.

Studies the recovery of shape from texture under perspective projection. We regard shape from texture as a statistical estimation problem, the texture being the realization of a stochastic process. We introduce warplets, which generalize wavelets over the 2D affine group. At fine scales, the warpogram of the image obeys a transport equation, called texture gradient equation. In order to recover the 3D shape of the surface, one must estimate the deformation gradient, which measures metric changes in the image. This is made possible by imposing a notion of homogeneity for the original texture, according to which the deformation gradient is equal to the velocity of the texture gradient equation. By measuring the warplet transform of the image at different scales, we obtain a deformation gradient estimator.

This paper is a contribution to the recovery of shape from texture under perspective projection. We regard shape from texture as a statistical estimation problem, the texture being the realization of a stochastic process. There are two minimal conditions in order for the problem to be solvable: the first is a stationarity condition on the texture with respect to the surface; the second is the regularity of the surface. Information about the surface is obtained by estimating a deformation map. We prove that at a fine scale, the wavelet decomposition of the image obeys a transport PDE, the coefficients of which can be estimated, and related to the deformation map. We show how the global surface shape can then be integrated.