Johannes Vorwerk

Christian Engwer, Johannes Vorwerk, Jakob Ludewig et al.

In order to perform electroencephalography (EEG) source reconstruction, i.e., to localize the sources underlying a measured EEG, the electric potential distribution at the electrodes generated by a dipolar current source in the brain has to be simulated, which is the so-called EEG forward problem. To solve it accurately, it is necessary to apply numerical methods that are able to take the individual geometry and conductivity distribution of the subject's head into account. In this context, the finite element method (FEM) has shown high numerical accuracy with the possibility to model complex geometries and conductive features, e.g., white matter conductivity anisotropy. In this article, we introduce and analyze the application of a discontinuous Galerkin (DG) method, a finite element method that includes features of the finite volume framework, to the EEG forward problem. The DG-FEM approach fulfills the conservation property of electric charge also in the discrete case, making it attractive for a variety of applications. Furthermore, as we show, this approach can alleviate modeling inaccuracies that might occur in head geometries when using classical FE methods, e.g., so-called "skull leakage effects", which may occur in areas where the thickness of the skull is in the range of the mesh resolution. Therefore, we derive a DG formulation of the FEM subtraction approach for the EEG forward problem and present numerical results that highlight the advantageous features and the potential benefits of the proposed approach.

Jinlong Dong, Milana Komosar, Johannes Vorwerk et al.

The common spatial pattern (CSP) approach is known as one of the most popular spatial filtering techniques for EEG classification in motor imagery (MI) based brain-computer interfaces (BCIs). However, it still suffers some drawbacks such as sensitivity to noise, non-stationarity, and limitation to binary classification.Therefore, we propose a novel spatial filtering framework called scaCSP based on the scatter matrices of spatial covariances of EEG signals, which works generally in both binary and multi-class problems whereas CSP can be cast into our framework as a special case when only the range space of the between-class scatter matrix is used in binary cases.We further propose subspace enhanced scaCSP algorithms which easily permit incorporating more discriminative information contained in other range spaces and null spaces of the between-class and within-class scatter matrices in two scenarios: a nullspace components reduction scenario and an additional spatial filter learning scenario.The proposed algorithms are evaluated on two data sets including 4 MI tasks. The classification performance is compared against state-of-the-art competing algorithms: CSP, Tikhonov regularized CSP (TRCSP), stationary CSP (sCSP) and stationary TRCSP (sTRCSP) in the binary problems whilst multi-class extensions of CSP based on pair-wise and one-versus-rest techniques in the multi-class problems. The results show that the proposed framework outperforms all the competing algorithms in terms of average classification accuracy and computational efficiency in both binary and multi-class problems.The proposed scsCSP works as a unified framework for general multi-class problems and is promising for improving the performance of MI-BCIs.