Information Technology Reference
In-Depth Information
p
i
(
a
)
−
p
i
(
c
)
t
i
=
)
.
(8.44)
n
i
(
a
)+
n
i
(
c
Such maps usually have more focal activities since they contrast the differences
between two states. Other scalar beamformers can be implemented. For example, an
anatomically constrained beamformer (ACB) can be obtained by simply constrain-
ing the dipole orientations to be orthogonal to the cortical surfaces [34].
8.7.5 Dynamic Imaging of Coherent Sources (DICS)
Beamforming can be performed in the frequency domain using the dynamic imaging
of coherent sources (DICS) algorithm, whose spatial filter matrix for frequency
f
is
given by
L
:
i
˜
)
−
1
L
:
i
−
1
L
:
i
˜
(
)
dics
)
−
1
Ω
(
f
)=
Σ
(
f
Σ
(
f
,
(8.45)
B
B
i
:
where
˜
is the cross-spectral density matrix for frequency
f
[29]. Note that the
covariance matrix has simply been replaced in (8.42) by the cross-spectral density
matrices. DICS can also be used to reveal which brain regions are coherent with
external reference signals (e.g., electromyogram), and to estimate cortico-cortical
coherence maps.
Σ
B
(
f
)
8.7.6 Other Spatial Filtering Methods
All the spatial filtering methods explained so far depend on the gain vectors asso-
ciated only with the region of interest (i.e., they do not depend on the gain vectors
associated with the rest of the source space). There are other more direct approaches
to spatial filtering that incorporate the gain vectors associated with both the region
of interest and the rest of the source space, and that do not necessarily use the mea-
sured covariance matrix. In the Backus-Gilbert method, a different spread matrix
is computed for each candidate source location [28, 27]. The goal is to penalize the
side lobes of the resolution kernels (i.e., the row vectors of the resolution matrix,
defined as
R
=
Ω
L
, where
L
is the lead field matrix for the entire source space and
Ω
is the optimized linear operator that gives the source estimates when multiplied
with the data). This usually results in a wider main lobe.
In the spatially optimal fast initial analysis (SOFIA) algorithm, virtual leadfields
are constructed that are well concentrated within a region of interest compared to
the rest of the source space [10]. The region of interest can be moved to every source
point. A similar approach is adopted in the local basis expansion (LBEX) algorithm,
which solves a generalized eigenvalue problem to maximize the concentration of
linear combinations of leadfields [51].
As a final remark, it should be emphasized that all of the spatial filtering algo-
rithms presented scan one source point or local region at a time, but can be expanded
