Biomedical Engineering Reference
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in Figs.
3.5
cand
3.6
c. The method does a good job, but some residual ventricular
interference still remains around the R-peak locations.
Results by BSS-based methods are shown in plots (d)-(h) of Figs.
3.5
and
3.6
.
PCA (Sect.
3.3.2
) is able to condense into just four principal components over
99.5 % of the variance of the 12-lead ECG recording, which illustrates the data
compression capabilities of this decomposition technique (Sect.
3.2.2.3
). Although
not shown here due to space limitations, the first two components are linked to
ventricular activity, while the third and fourth components mainly contain atrial
activity. These produce the reconstructed atrial signal shown in Figs.
3.5
dand
3.6
d.
Again, ventricular residuals are still visible, but seems a little less noticeable than
for STC in this example. The spectral concentration increases accordingly.
The kurtosis-based RobustICA of [
26
] (see also Sect.
3.3.3
) yields the atrial
signal estimate shown in Figs.
3.5
eand
3.6
e, labeled 'ICA'. The ICA approach is
able to concentrate the atrial activity into a single independent source, while PCA
required two components to describe this activity in this particular dataset. The
spectral concentration slightly decreases as compared to PCA, but the time course
shows reduced ventricular interference. With a kurtosis of
0
.
6
, the estimated atrial
source is relatively close to Gaussian, as may be expected in persistent forms of
AF. ICA is thus expected to benefit from a processing refinement based on the time
coherence of the atrial signal, as explained in the previous section.
To carry out this refinement, we note that the last six sources obtained by
RobustICA have a kurtosis value below 1.5. These quasi-Gaussian sources are
passed on to the SOBI algorithm aiming to diagonalize 17 correlation matrices
equally spaced at 20 ms time lags, as proposed in [
6
]. These lags could have been
optimized by taking into account a preliminary estimation of the AF dominant
frequency. Nevertheless, the atrial signal obtained with this simple lag selection
improves on the spectral concentration of PCA and ICA, as shown in the 'ICA-
SOBI'plotofFigs.
3.5
fand
3.6
f.
Section
3.3.4
recalled that the RobustICA-f [
26
] and MaxViT [
18
] methods both
operate in the frequency domain. The former is based on higher-order statistics
whereas the latter only exploits second-order statistics. Despite this key difference,
both methods produce very similar atrial signal estimates and yield the highest
spectral concentration values, as can be observed in the last two plots of Figs.
3.5
and
3.6
.
The surface atrial signal estimated by all tested methods presents a harmonic
structure reminiscent of that of the endocardial recording, with just a 0.2 Hz offset in
the fundamental frequency value. This yields a noninvasive AF cycle length estimate
of 182 ms, quite close to the 175 ms measured invasively on the atrial endocardium.
−
3.3.5.2
Measuring Atrial Fibrillation Organization with PCA
Although PCA yields satisfactory results in the illustrative example of the previous
section, we have seen in Sect.
3.3.2
that it generally fails to perform the separation
under the general form of model (
3.17
). Yet this classical technique proves useful
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