Biomedical Engineering Reference
In-Depth Information
Chapter 5
Bayesian Factor Analysis: A Versatile
Framework for Denoising, Interference
Suppression, and Source Localization
5.1 Introduction
This chapter describes Bayesian factor analysis (BFA), which is a technique that
can decompose multiple sensor time courses into time courses of independent factor
activities, where the number of factors is much smaller than the number of sensors.
The factors are artificially-introduced “abstract” causes that explain the temporal
behavior of the sensor data, and do not necessarily correspond to physical sources.
Since the factor activities cannot directly be observed, they are considered latent
variables.
The Bayesian factor analysis is a versatile framework. It can be used for selectively
extracting signal components from noise-contaminated sensor data. It can provide
an estimate of the data covariance matrix better than a sample covariance matrix,
and such covariance estimate can be used in source reconstruction algorithms such
as adaptive beamformers. It is extended to suppress interference components in
interference-overlapped sensor data [
1
]. It is also extended to a virtual-sensor type
source localization method, which is called the Saketini algorithm [
2
].
We start this chapter by explaining the basic form of the Bayesian factor analysis
and then extend it to the variational Bayesian factor analysis (VBFA) [
3
] in which the
model order (the number of factors) is determined by the algorithm itself. Following
VBFA arguments, we describe the extensions for interference suppression and source
localization.
5.2 Bayesian Factor Analysis
5.2.1 Factor Analysis Model
As in the previous chapters, let us define the output of the
m
th sensor at time
t
as
y
m
(
t
)
, and the data vector as
y
(
t
)
, such that
