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univariate case, treatments include baseline subtraction (i.e., DC offset) and band-
pass filtering. Signals can also be transformed to the time-frequency/scale domains
with Fourier/wavelet methods, or can be bandpass filtered and Hilbert transformed
to extract instantaneous amplitude and phase information [84, 83, 29]. Filtering or
time-frequency analysis is of great utility for studying wavelike activity and oscil-
lations within specific frequency bands: slow oscillations (
1 Hz), delta (1-4 Hz),
theta (5-8 Hz), alpha (9-12 Hz), mu (9-12 Hz and 18-25 Hz), spindles (
<
14 Hz),
low beta (13-20 Hz), high beta (20-30 Hz), gamma (30-80 Hz), high gamma or
omega (80-200 Hz), ripples of high-frequency oscillations (HFO,
∼
∼
200 Hz), and
sigma bursts (
600 Hz). This great variety is a reflection of the fairly large spectrum
of relevant signals of electrophysiological origin accessible to NSI, using MEG or
ECoG in particular, as the spatial smearing due to the skull barrier in EEG tends to
obliterate its access to higher-frequency oscillations, which are supposed to origi-
nate more locally than the slower oscillations of the neural spectrum.
The continuously and simultaneously acquired time series of all MEG, EEG,
and/or ECoG channels can be concatenated to form a multivariate data array
B
∼
d
t
, where
d
b
is the number of measurement channels and
d
t
is the number
of time points. This data contains correlated noise generated by physiological and
environmental sources. Such perturbations may be reduced using a variety of multi-
variate signal processing tools such as, blind source separation, subspace projection,
and machine learning methods [47,92,48,85,64,104]. The general principle consists
in extracting undesired features from the data using linear transformations that ei-
ther aim to project noise components away from the recordings or to unmix the data
into separate components before recombining those only thought to be originating
from neural sources.
The signal-space projection (SSP) algorithm and principal component analysis
(PCA) are two popular techniques that use the second-order statistics of the data to
estimate the spatiotemporal characteristics of noisy components [92]. SSP may be
applied by default to MEG data based on the statistics of an empty MSR recording
to account for the perturbations that still can get into the MSR from the environ-
ment. The denoised
B
matrix can be cut into epochs time-locked to an event (e.g.,
stimulus onset) for single trial analysis or averaged across epochs to extract the
event-related potential and/or field (ERP/F) [44]. The ERP/F can then be localized
by many different inverse methods as described below.
Alternatively, blind source separation algorithms that use higher order statistics
or temporal information [e.g., infomax/maximum-likelihood independent compo-
nent analysis (ICA) or second-order blind identification (SOBI)] can be applied to
the entire unaveraged multivariate data time series to learn a data representation ba-
sis of sensor mixing vectors (associated with maximally independent time-courses)
that can be localized separately and to reject non-brain components (i.e., denois-
ing) [7, 46, 48, 85].
For MEG, the signal-space separation (SSS) algorithm and its temporal extension
(tSSS) suggest an alternative route to the rejection of external perturbations [86]. In
short, SSS builds a spatial-filter which removes the EM components in the data that
are generated from outside a spherical volume encompassing the brain. This is done
d
b
×
∈
ℜ
