MV-PURE Spatial Filters with Application to EEG/MEG Source Reconstruction

TL;DR

This paper introduces novel spatial filters based on the MV-PURE framework for EEG/MEG source reconstruction, improving accuracy by explicitly considering interfering activity and optimizing rank selection to minimize mean-square error.

Contribution

The paper develops and analyzes new MV-PURE based spatial filters for EEG/MEG, incorporating rank-selection criteria and handling interference explicitly, extending existing LCMV and nulling filters.

Findings

Filters effectively reconstruct brain activity from EEG/MEG data.

Proposed methods outperform traditional filters in simulation.

Reproducible simulation framework provided for error estimation.

Abstract

In this paper we propose spatial filters for a linear regression model which are based on the minimum-variance pseudo-unbiased reduced-rank estimation (MV-PURE) framework. As a sample application, we consider the problem of reconstruction of brain activity from electroencephalographic (EEG) or magnetoencephalographic (MEG) measurements. The proposed filters come in two versions depending on whether or not the EEG/MEG forward model explicitly considers interfering activity in the way of brain activity originating in regions different to those of main interest, but measured as correlated with signals of interest by the EEG/MEG sensor array. In both cases, the proposed filters are equipped with a rank-selection criterion minimizing the mean-square error (MSE) of the filter output. Therefore, we consider them as novel nontrivial generalizations of well-known linearly constrained minimum variance (LCMV) and nulling filters. In order to facilitate reproducibility of our research, we provide (jointly with this paper) comprehensive simulation framework that allows for estimation of error of signal reconstruction for a number of spatial filters applied to MEG or EEG signals. Based on this framework, chief properties of proposed filters are verified in a set of detailed simulations.