Noninvasive Cardiac Signal Analysis Using Data Decomposition Techniques - Modeling in Computational Biology and Biomedicine - page 105

to as maximum variance in tails (MaxViT) , can be cast in a more general source
separation framework based on a conditional maximum likelihood principle [ 18 , 19 ].
The narrowband character of the atrial signal during AF can also be exploited by
using higher-order statistics, even if the amplitude of the atrial time course is near
Gaussian [ 26 ]. The trick consists of working in the frequency domain, where the
marked sparsity of the atrial signal due to its reduced spectral support is linked with
strong non-Gaussianity. As a result, the atrial source can typically be found among
the most kurtic frequency-domain sources extracted by a BSS technique based on
kurtosis maximization such as RobustICA [ 26 ], which is able to handle complex-
valued sources with noncircular distributions. We refer to this frequency-domain
ICA method as RobustICA-f . A common feature of the RobustICA-f and MaxViT
methods is that, by incorporating some prior information about the frequency
content of the desired source, they mitigate the permutation ambiguity of the BSS
model (Sect. 3.3.1 ), thus sparing the need to separate all sources to recover the
atrial signal. Further details on these refined BSS-based techniques for atrial activity
extraction can be found in [ 25 ].

3.3.5 Success Stories

3.3.5.1 Atrial Activity Extraction in Persistent Atrial Fibrillation

Recall that the first two plots of Figs. 3.5 and 3.6 show the endocardial and surface
ECG recordings of a persistent AF patient, as introduced in Sect. 3.1.2.2 . The whole
12-lead ECG over 10 s is available for processing, yet only lead V1 is plotted over
the last 5 s to ease visualization. In plots (c)-(h), the results of different atrial signal
estimation methods are compared with the lead V1 signal plotted in the background.
In Fig. 3.6 , the endocardial signal spectrum is also plotted on a magnified amplitude
scale ( 10 ) using light-grey dashed lines. The spectral concentration (SC in the

plots) is computed as the relative power around the dominant or fundamental
frequency ( f p ) and the second harmonic. The vertical dashed and dash-dotted lines
mark the location of f p and the frequency bounds used in the computation of spectral
concentration.
Automatic beat detection in the surface ECG reveals an average R-R period
of 418 ms, linked to the fundamental frequency of 2.4 Hz, i.e., 144 beats per
minute, displayed in Fig. 3.6 b. The fundamental frequency of 5.7 Hz in Fig. 3.6 a
corresponds to an average atrial cycle length of 175 ms. These values illustrate the
lack of synchronization between the atrial and ventricular activities, supporting the
appropriateness of the independence assumption exploited by the BSS approach
to atrial activity extraction (Sect. 3.3.1 ). Remark that the endocardial signal is not
known to the atrial signal estimation methods evaluated next.
The STC approach of [ 17 ](seealso[ 27 ]) is employed as a benchmark. As briefly
summarized at the beginning of Sect. 3.3 , this approach mainly differs from BSS in
that it does not aim at the atrial sources, but directly at the atrial contribution to
the leads under study. In lead V1, STC produces the estimated atrial signal shown

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