Abstract
In this article, we propose a novel preprocessing method in the spherical harmonics domain to decompose the MEG signal into specific parts, whose sources arise from user-prescribed concentric spherical regions. A particular case of this approach is presented to separate the data into parts corresponding to deep and superficial regions of the brain, without using inverse solutions. Throughout this article, plain italics denote scalars, lower case boldface symbols denote vectors, uppercase boldface symbols denote matrices, superscripts T and H stand for transpose and Hermitian transpose, and ||.||, tr(.), * indicate Euclidean norm, and trace and complex conjugate operations, respectively.
Key Terms in this Chapter
Beamspace: It is a preprocessing method to reduce the dimension of the MEG signal by using a linear transformation matrix that is obtained using leadfields.
Forward Problem: It corresponds to calculating the magnetic field outside the head from a given primary source distribution within the brain.
Gram Matrix: It describes the deterministic second order relations among leadfields for different source locations.
Magnetoencephalography (MEG): It measures extracranial magnetic fields induced by electrical currents in the brain, noninvasively. The very weak magnetic fields of the brain are sensed by superconducting quantum interference devices (SQUIDs).
Signal Space Separation (SSS): A preprocessing method that decomposes the MEG signal into inner source signal and outer noise by using spherical harmonic basis functions.
Spherical Harmonics: They are orthonormal eigenfunctions of the Laplacian operator on the spherical surface, and useful tools to represent EEG/MEG signals on the head for different cases.
Inverse Methods: These methods are utilized to estimate the source locations and strengths from EEG / MEG signals.
Leadfield: It denotes a vector mapping from a unit current source to magnetic measurement on a sensor located in a particular position.