Biomedical Engineering Reference
In-Depth Information
non-Gaussian probability distributions. This is usually the case in early, often
more organized, stages of AF or in related conditions such as atrial flutter. As the
disease evolves, however, the atrial activity becomes more disorganized and tends
to present quasi-Gaussian distributions, making it difficult for ICA techniques to
perform its extraction from other sources of Gaussian noise and interference. Hence,
refinements of the classical ICA approach are necessary for a successful atrial signal
estimation in the general case.
The most successful refinements capitalize on the time coherence or narrowband
spectrum of the atrial signal in the surface ECG. Indeed, the atrial frequency spec-
trum is typically concentrated around a dominant peak located in the 3-9 Hz band
and its harmonics. To benefit from this property, a two-stage approach is adopted
in [ 6 ]. In the first stage, classical ICA estimates the ventricular activity sources,
which are strongly non-Gaussian signals. The remaining ICA sources contain a
mixture of atrial components and noise, and are further processed by another
separation technique known as second-order blind identification (SOBI) [ 1 ]. Like
PCA (Sect. 3.3.2 ), SOBI is based on the diagonalization of correlation matrices, but
also considers time lags different from zero:
{ x ( t ) x ( t − τ ) T
R x ( τ )=E
},
(cf. Eq. ( 3.2 )). Hence, this second stage is particularly suited to the separation
of sources with long correlation functions or, equivalently, narrowband frequency
spectra. The improvement brought about by the second processing stage is more
beneficial in cases where the atrial source distribution is close to Gaussian.
The spectral concentration, or relative power contained in a narrow band around
the fundamental frequency, is a quantitative measure of the time coherence of
the atrial signal [ 6 ]. The spectral concentration is explicitly exploited in [ 18 ]by
assuming that the atrial source dominates, in terms of power, the other sources in
the narrow frequency band, denoted [ f 1 ,f 2 ] Hz, where it appears; we call this band
(contained within the 3-9 Hz AF band) the significant spectral support of the atrial
activity signal. According to this assumption, the optimal separating filter can be
found by maximizing the filter output relative power in the atrial spectral support.
After whitening the observations, e.g., by means of PCA as in Sect. 3.3.2 , the atrial
activity extracting filter can be computed algebraically as the dominant eigenvector
of the frequency-constrained spectral covariance matrix
= f 2
f 1
e x ( f ) x ( f ) H d f,
( f 1 ,f 2 )
x
˜
R
R
) H
where x ( f ) represents the Fourier transform of x ( t ) , symbol (
·
denotes the
Hermitian (conjugate-transpose) operator and
yields the real part of its
complex argument. As opposed to classical ICA, this second stage is not based
on higher-order statistics but on conditional second-order statistics computed on the
significant spectral support of the desired signal and, as a result, it can also deal
with near-Gaussian atrial signals. This atrial signal extraction technique, referred
R
e
{·}
Search WWH ::




Custom Search