Image Processing Reference
In-Depth Information
TABLE 8.1
Notation Used throughout This Chapter
Symbol
Meaning
K
Number of simultaneously active voxels
N
Number of voxels, i.e.,
spatial resolution of high spatial resolution
modality (fMRI)
M
Number of EEG/MEG sensors, i.e.,
spatial resolution of low spatial
resolution modality
T
Number of time points of high temporal resolution modality (EEG, MEG)
U
Number of time points of low temporal resolution modality (fMRI)
L
Number of orthogonal axes for dipole moment components,
L
Å_{1, 2, 3}
I
Identity matrix (
n
×
n
)
n
0
Zero matrix of appropriate dimensionality
X
General E/MEG data matrix; can contain EEG or MEG data or both (
M
×
T
)
B
BOLD fMRI data matrix (
N
×
U
)
Q
Dipole sources matrix
G
General E/MEG lead function, incorporating information for EEG or MEG or both
G
General E/MEG lead matrix
F
i
Spatial filter matrix for the
i
th dipole (
M
×
L
)
ν
Variance
C
Covariance matrix
K
Matrix of correlation coefficients
M
_
Matrix transpose
M
+
Generalized matrix inverse (pseudo-inverse)
x
x
null
M
The
null space
of
M
, the set of vectors {
|
M
=
0}
diag
M
The diagonal matrix with the same diagonal elements as
M
Note:
We chose our notation to match the most popular conventions in the field, and at the same
time minimize confusion. Regrettably, it is likely to differ from the notation used by each particular
paper we reference. Following the usual conventions, we use bold uppercase symbols for matrices,
bold lowercase for vectors, and nonbold symbols for scalars.
8.2.1
A
U
I
SSUMPTIONS
NDERLYING
NTEGRATION
EEG
MEG
OF
AND
The theory of electromagnetism and Maxwell's equations, under the assumption
of quasi stationarity,* theoretically defines the relationship between observed
magnetic and electric fields that are induced by the ionic currents generated inside
the brain (see Malmivuo and Plonsey [
7
], Okada et al. [
8
], Murakami et al. [
9
],
for more information about the biophysics of E/MEG signals).
* A signal is quasistatic if it does not change its parameters in time. The nonstationary term present
in the E/MEG physical model is relatively small and can be considered zero in the range of signal
frequencies that are captured by E/MEG. See [
6
] for a more detailed description.
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