Information Technology Reference
In-Depth Information
source points). Here the goal is to estimate the activity at a source point or region
while avoiding the cross talk from other regions so that these affect as little as pos-
sible the estimate at the region of interest.
8.7.1 Matched Filter
The simplest spatial filter, a matched filter, is obtained by normalizing the columns
of the lead field matrix and transposing this normalized dictionary. The spatial filter
for location
r
i
is given by
L
:
i
Ω
(
mf
)
i
:
=
L
:
i
F
.
(8.39)
This approach essentially projects the data onto the column vectors of the lead-
field dictionary. Although this guarantees that the absolute maximum of the map
corresponds to the true maximum when only one source is active and with the cor-
rect fixed dipole orientation, this filter is not recommended since these assumptions
are usually not valid, and since the spatial resolution of the filter is so low given
the high correlation between dictionary columns. This approach can be extended to
fast recursive algorithms, such as matching pursuit and its variants, which sequen-
tially project the data or residual to the nonused dictionary columns to obtain fast
suboptimal sparse estimates.
8.7.2 Multiple Signal Classification (MUSIC)
The MUSIC algorithm was adopted from spectral analysis and modified for spatial
filtering of MEG data [53, 52]. The MUSIC cost function is given by
I
U
s
U
s
L
:
i
P
U
s
L
:
i
2
2
2
2
−
M
i
=
=
,
(8.40)
2
2
2
2
L
:
i
L
:
i
USV
T
is the singular value decomposition of the data,
U
s
is a matrix with
the first
d
s
left singular vectors that form the signal subspace, and
L
:
i
is the gain
vector for the dipole located at
r
i
and with orientation
where
B
=
θ
i
(obtained from anatomy
or using the generalized eigenvalue decomposition).
P
U
s
is an orthogonal projection
operator onto the data noise subspace. The MUSIC map is the reciprocal of the
cost function at all locations scanned. This map can be used to guide a recursive
parametric dipole fitting algorithm. The number
d
s
is usually carefully provided by
an expert user.
