Spatial filters - in search of the virtual electrode

Abstract

A spatial filter is a set of weights which, applied to multichannel data, creates a "virtual channel" with desirable properties. Examples range from simple hard-wired spatial filters (re-referencing, gradient, Laplacian, etc.) to more complex data-driven transforms (beamforming, independent component analysis, etc.). The principle is straightforward, but the properties are obscured by the high dimensionality of the data, and the various "spaces" in which a "spatial" filter operates, inhabited by sources, sensors, fields, or signals. This paper reviews the properties and limits of spatial filters, with particular focus on the popular concept of a "virtual electrode" created by combining channels of a non-invasive recording technique such as EEG or MEG. Whereas a spatial filter can perfectly suppress one or more sources (as many as there are sensors, minus one), it cannot select one source and suppress all others, as might a real electrode. This puts hard limits on what to expect of a virtual electrode, and suggests a slightly different perspective, that of a "virtual scalpel". Spatial filtering, like temporal filtering, plays an important role in brain data analysis. Significance statementSpatial filters are ubiquitous in brain data analysis. This paper reviews their properties and the limits of what can be achieved, with emphasis on aspects that are obscured by the complex geometry of sources and sensors, and the high dimensionality of the data.