Presentation of electromagnetic multichannel data: The signal space separation method

TLDR

Measuring external magnetic fields yields information about internal electric current distributions, as exemplified by magnetoencephalography devices that sample brain‑generated fields at hundreds of scalp locations. The study introduces the signal space separation (SSS) method, which establishes a fundamental linear basis for all measurable multichannel magnetic signal vectors. SSS constructs this basis by expressing the magnetic field as two rapidly converging harmonic expansions—one for sources inside the sensor array volume and one for sources outside—leveraging the distinct convergence domains and the sensor array’s placement in a source‑current‑free region. The method yields uncorrelated expansion terms, offers a stable, device‑independent decomposition, effectively suppresses external interference, and enables diverse improved multichannel data analyses.

Abstract

Measurement of external magnetic fields provides information on electric current distribution inside an object. For example, in magnetoencephalography modern measurement devices sample the magnetic field produced by the brain in several hundred distinct locations around the head. The signal space separation (SSS) method creates a fundamental linear basis for all measurable multichannel signal vectors of magnetic origin. The SSS basis is based on the fact that the magnetic field can be expressed as a combination of two separate and rapidly converging expansions of harmonic functions with one expansion for signals arising from inside of the measurement volume of the sensor array and another for signals arising from outside of this volume. The separation is based on the different convergence volumes of the two expansions and on the fact that the sensors are located in a source current-free volume between the interesting and interfering sources. Individual terms of the expansions are shown to contain uncorrelated information of the underlying source distribution. SSS provides a stable decomposition of the measurement into a fundamental device-independent form when used with an accurately calibrated multichannel device. The external interference signals are elegantly suppressed by leaving the interference components out from the reconstruction based on the decomposition. Representation of multichannel data with the SSS basis is shown to provide a large variety of applications for improved analysis of multichannel data.