5 EEG Source Imaging and Multimodal Neuroimaging
97
framework (for a detailed derivation and description, see [35]). The MNE solution
is generally suitable for the estimation of superficially distributed sources; however,
MNE is also known to underestimate deeper sources.
To alleviate the depth-bias of MNE, a weighted minimum-norm estimates (wMNE)
algorithm was introduced, in which:
L
ˆ
J
W ˆ
J
2
2
(5.30)
where W is the weighting matrix used to compensate for deeper sources, constructed
from the norm of each column of the lead field matrix G. This is expressed as:
W ⊗ I 3
(5.31)
where is a diagonal matrix of size P × P, , ii equals to the norm of the ith column
of the lead field matrix, and the inverse operator is expressed as:
M wM N E
W
T W
−1 G
T
G
W
T W
−1 G
T + λI
−1
(5.32)
5.2.2.2 Low Resolution Electromagnetic Tomography
The low resolution electromagnetic tomography (LORETA) method [64] aims to
incorporate physiological principles into the EEG inverse solution; specifically, the
idea that neighboring neural sources are activated simultaneously and synchronously.
To this end, LORETA implements a smoothing operation on the source space in
the form of a Laplacian operator. The inverse solution obtained from the LORETA
method is then presented as:
M L O R ET A
W
T W
−1 G
T
G
W
T W
−1 G
T + λI
−1
W ( ⊗ I 3 )B
T B( ⊗ I 3 )
(5.33)
where B is a discrete spatial Laplacian operator. When given the task of localizing two
simultaneous point sources (one deep and one superficial) within the same simulation
study, LORETA achieved superior source localization accuracy when compared to
MNE and wMNE. The minimum-norm approaches were unable to reproduce the
deep source, while LORETA yielded a highly blurred reconstruction [65].
5.2.2.3 Standardized Solutions of Minimum-Norm Estimates
Another method applied to aid in the reconstruction of deep sources was the standardization of the MNE solution. The most popular accepted standardizations are the
dynamic statistical parametric mapping (dSPM) method and standardized low res-
97
framework (for a detailed derivation and description, see [35]). The MNE solution
is generally suitable for the estimation of superficially distributed sources; however,
MNE is also known to underestimate deeper sources.
To alleviate the depth-bias of MNE, a weighted minimum-norm estimates (wMNE)
algorithm was introduced, in which:
L
ˆ
J
W ˆ
J
2
2
(5.30)
where W is the weighting matrix used to compensate for deeper sources, constructed
from the norm of each column of the lead field matrix G. This is expressed as:
W ⊗ I 3
(5.31)
where is a diagonal matrix of size P × P, , ii equals to the norm of the ith column
of the lead field matrix, and the inverse operator is expressed as:
M wM N E
W
T W
−1 G
T
G
W
T W
−1 G
T + λI
−1
(5.32)
5.2.2.2 Low Resolution Electromagnetic Tomography
The low resolution electromagnetic tomography (LORETA) method [64] aims to
incorporate physiological principles into the EEG inverse solution; specifically, the
idea that neighboring neural sources are activated simultaneously and synchronously.
To this end, LORETA implements a smoothing operation on the source space in
the form of a Laplacian operator. The inverse solution obtained from the LORETA
method is then presented as:
M L O R ET A
W
T W
−1 G
T
G
W
T W
−1 G
T + λI
−1
W ( ⊗ I 3 )B
T B( ⊗ I 3 )
(5.33)
where B is a discrete spatial Laplacian operator. When given the task of localizing two
simultaneous point sources (one deep and one superficial) within the same simulation
study, LORETA achieved superior source localization accuracy when compared to
MNE and wMNE. The minimum-norm approaches were unable to reproduce the
deep source, while LORETA yielded a highly blurred reconstruction [65].
5.2.2.3 Standardized Solutions of Minimum-Norm Estimates
Another method applied to aid in the reconstruction of deep sources was the standardization of the MNE solution. The most popular accepted standardizations are the
dynamic statistical parametric mapping (dSPM) method and standardized low res-