Biomedical Engineering Reference
In-Depth Information
3.7 Narrow-Band Beamformer
3.7.1 Background
Stimulus-induced power modulation of spontaneous brain activity has been the sub-
ject of intense investigations. Such power modulation is sometimes referred to as the
event-related spectral power change. When the power change is negative, it is cus-
tomarily termed as event-related desynchronization (ERD), and when it is positive,
it is termed as event-related synchronization (ERS) [
13
].
The narrow-band dual-state beamformer [
7
] is a powerful tool for localization of
specific brain activities related to these power changes. This is because the power
change is frequency-specific, and the narrow-band beamformer uses a weight tuned
to a specific target frequency. In this section, we describe the time-domain and the
frequency-domain implementations of the narrow-band beamformer.
3.7.2 Time-Domain Implementation
Since the induced brain activity is not time-locked to the stimulus, the sample covari-
ance matrix should be computed from nonaveraged raw trials. We assume that total
N
E
trials denoted as
b
1
(
),...,
b
N
E
are obtained. To compute a frequency-specific
weight, these raw trials are band-pass filtered with a specific frequency band of inter-
est. The band-pass filtered sensor data for the
n
th trial is denoted as
b
n
(
t
t
,
f
)
, where
f
represents the frequency band of interest.
4
The sample covariance matrix is computed using the band-pass filtered data, such
that
N
E
K
1
N
E
)
b
n
(
R
1
b
n
(
(
f
)
=
t
k
,
f
t
k
,
f
).
(3.67)
n
=
1
k
=
Since we use the nonaveraged trial data, the data naturally contains a significant
amount of influence from brain activities that are not related to the activity of interest.
To remove the influence of such unwanted brain activities, we use dual-state
datasets: one from the target time period and the other from the baseline period. We
try to reconstruct source activities that cause the power change in a specific frequency
band. That is, using Eq. (
3.67
), we compute the frequency-specific covariance matrix
for the target period,
R
T
(
, and for the baseline period,
R
C
(
.
We then reconstruct frequency-specific power changes between the target and
baseline periods by using the
F
-ratio method. That is, using
R
T
(
f
)
f
)
and
R
C
(
)
)
f
f
,the
F
-ratio method computes the frequency-specific filter weight such that
4
The notation
f
may indicate the center frequency of the frequency band of interest.
