Biomedical Engineering Reference
In-Depth Information
Although real EEG and MEG datasets are recorded over multiple channels, in
this chapter, we restrict our attention to a single channel, and we focus on extracting
information from multiple trials. It is generally considered that the relevant part
of the signals are the components which repeat across trials, whereas noise is
uncorrelated across trials.
Consider
s
k
(
the time-course of a (single-channel) signal measured at trial
k
,
modeled with an additive noise model
t
)
s
k
(
t
)=
x
(
t
)+
n
k
(
t
)
,
(7.1)
in which the noise
n
k
is decorrelated across trials. Directly averaging the sig-
nals
across trials
K
k
=1
.
Through such cross-trial averaging, one may gain information about the processes
occurring at early stages of sensory processing (visual evoked potentials, auditory
evoked potentials, somatosensory evoked potentials), which are stereotypical, and
do not vary much across trials.
Unfortunately, the simple additive model (
7.1
) is quite far from the truth in
most operational settings: the “relevant” part of the data
x
{
s
1
(
t
)
,...,s
K
(
t
)
}
s
k
(
t
)
provides an estimate of
x
(
t
)
can generally not be
assumed to be constant across trials. There are several sources of variability, that are
represented in Fig.
7.2
:
(
t
)
•When
x
includes oscillatory components, their phase is generally variable
across trials, and cross-trial averaging tends to cancel out the oscillations;
(
t
)
•
The latency, i.e., the time between the stimulus onset and the response, is often
variable, and the resulting averages are blurred estimators of the actual responses.
Rather than the naive additive model (
7.1
), multitrial datasets should be modeled
as the sum of trial-dependent components
x
k
(
t
)
and noise:
s
k
(
t
)=
x
k
(
t
)+
n
k
(
t
)
.
(7.2)
The challenge is then to distinguish between the relevant part of the signals,
x
k
,and
the noise,
n
k
, when both vary across trials. Some constraints must be set on
x
k
and
n
k
in order for their separation to be possible.
7.1.4
Chapter Overview
Public
This chapter is mainly targeted at researchers in cognitive and clinical neuroscience
and in signal and image processing, who are interested in processing brain signals.
Most of the material covered hereafter is presented in sufficient detail for graduate-
level students with a good background in signal processing and linear algebra.
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