Information Technology Reference
In-Depth Information
T
(
map
−
L
2
)
. Note that dSPM performs noise nor-
malization after the inverse operator
diag
Ω
(
map
−
L
2
)
Σ
ϒ
Ω
where
v
=
Ω
(
map
−
L
2
)
has been computed. Thus, the noise-
normalized source activity estimates are given by
S
(
dspm
)
=
Ω
(
dspm
)
B
)
−
1
/
2
J
(
map
−
L
2
)
.
=
(
diag
v
(8.21)
More generally, to include the case where dipole orientation constraints are not
enforced, the noise-normalized dSPM time series of source power at the
i
th source
point is computed as
diag
J
T
(
map
−
L
2
)
i
:
T
tr
S
2
(
dspm
)
i
:
J
(
map
−
L
2
)
i
:
Ω
(
map
−
L
2
)
i
:
T
(
map
−
L
2
)
=
/
Σ
ϒ
Ω
.
(8.22)
i
:
8.6.3 Standardized Low Resolution Brain Electromagnetic
Tomography (sLORETA)
An alternative approach for depth-bias compensation and source standardization is
the sLORETA technique [65]. In contrast to the dSPM method, the MNE is modi-
fied by the resolution matrix,
R
=
Ω
(
map
−
L
2
)
L
, that is associated with the inverse
Ω
(
map
−
L
2
)
and
L
. For fixed dipole orientations, the pseudo-
statistics of power and absolute activation at the
i
th source point for a time slice are
respectively given by
and forward operators:
j
i
R
ii
and
√
ϕ
i
,
ϕ
i
=
(8.23)
and the standardized sLORETA inverse operator can be written as
Ω
(
sloreta
)
=
)
−
1
/
2
Ω
(
map
−
L
2
)
,
diag
(
r
(8.24)
where
r
=
diag
(
R
)
. Thus, the sLORETA activity time-series is computed by
S
(
sloreta
)
=
Ω
(
sloreta
)
B
)
−
1
/
2
J
(
map
−
L
2
)
.
=
diag
(
r
(8.25)
More generally, for the case of no dipole orientation constraints, the sLORETA
standardized source power time series at the
i
th source point is computed as
diag
J
T
(
map
−
L
2
)
i
:
T
S
2
(
sloreta
)
i
:
R
ii
)
−
1
J
(
map
−
L
2
)
i
:
=
(
.
(8.26)
Interestingly, the sLORETA algorithm is similar to the first step of the sparse
Bayesian learning (SBL) algorithm explained in the next section.
