Spatial weighted averaging for ERP denoising in EEG data

In the present paper we intend to improve the practical accuracy of ERP denoising methods proposed in earlier research by allowing them to take into account possible violations of the underlying assumptions, which often take place in practice. Here we consider ERP denoising approaches operating within the framework of the linear instantaneous mixing model that consist three steps: (1) forward linear transformation, (2) identification of the components related to signal and noise subspaces, (3) inverse transformation during which the components that belong to the noise subspace are disregarded, i.e. dimension reduction in the component space. The separation matrix is found based on problem-specific assumptions formalized in terms of the second-order statistics. The subspace separation problem is concerned rather than the source separation. For the purpose of increasing the accuracy of spatial separation of ERP and noise sources we propose a spatial weighted averaging method analogous to weighted averaging technique developed for single channel use, which takes into account variable variances of the sources over trials.