Biomedical Engineering Reference
In-Depth Information
Chapter 3
Adaptive Beamformers
3.1 Introduction and Basic Formulation
The beamformer is a location-dependent spatial filter applied to the sensor data. It
is used for estimating the strength of brain activity at a particular spatial location,
which is referred to as the beamformer pointing location. Thus, the beamformer may
be interpreted as a technique that forms a virtual sensor whose sensitivity pattern
is localized at its pointing location. By postprocessing, the pointing location can be
scanned over the source space to obtain the source three-dimensional reconstruction.
Let us assume momentarily that the source orientation is predetermined and avoid
the orientation estimation. In this case, using the data vector,
y
(
t
)
, the beamformer
reconstructs the source magnitude,
s
(
r
,
t
)
,using
T
(
,
)
=
w
(
)
(
),
s
r
t
r
y
t
(3.1)
where
is the estimated source magnitude at location
r
and time
t
.InEq.(
3.1
),
a column vector
s
(
r
,
t
)
expresses the beamformer's weight, which characterizes the
properties of the beamformer. There are two types of beamformers. One is the non-
adaptive beamformer in which the weight vector depends solely on the lead field
of the sensor array, and the other is the adaptive beamformer in which the weight
depends on the measured data as well as the lead field of the sensor array.
Adaptive beamformers were originally developed in the field of seismic explo-
ration [
1
] and introduced later into the field of electromagnetic brain imaging [
2
-
5
].
In recent years, brain imaging with adaptive beamformers has increasingly been used
for clinical and basic human neuroscience studies, and it is a very popular method
for analyzing rhythmic brain activity. You may find detailed arguments on various
aspects of adaptive beamformers in [
6
].
This chapter presents a concise review on the adaptive beamformers. It presents
Bayesian-flavored formulations of scalar and vector adaptive beamformers, as well
as the conventional derivations. It also describes the narrow-band beamformer and
its application to five-dimensional (space-time-frequency) brain imaging [
7
], which
can be used for the source-space connectivity analysis.
w
(
r
)
