Abstract
The estimation of the atrial activity (AA) signal from electrocardiogram (ECG) recordings is an important step in the noninvasive analysis of atrial fibrillation (AF), the most common sustained arrhythmia encountered in clinical practice. This problem admits a blind source separation (BSS) formulation that has been recently posed as a tensor factorization, using the Hankel-based block term decomposition (BTD), which is particularly well-suited to the estimation of exponential models like AA during AF. However, persistent forms of AF are characterized by short R-R intervals and very disorganized (or weak) AA, making it difficult to model AA directly and perform its successful extraction through Hankel-BTD. To overcome this drawback, the present work proposes a tensor approach to estimate QRS complexes and subtract them from the ECG, resulting in a signal that, ideally, only contains the AA component. Such an approach tackles the problem of blind separation of rational functions, which models QRS complexes explicitly. The data tensor admitting a BTD is built from Löwner matrices generated from each lead of the observed ECG. To this end, this paper formulates a variant of the recently proposed constrained alternating group lasso (CAGL) algorithm that imposes Löwner structure on the decomposition blocks. This is done by performing an orthogonal projection, which we explicitly derive, at each iteration of CAGL. Results from experiments with synthetic data show the consistency of the proposed Löwner-constrained AGL (LCAGL) in extracting the desired sources. Experimental results obtained on a population of 20 patients suffering from persistent AF show that the proposed variant outperforms other tensor-based methods in terms of atrial signal estimation quality from ECG records as short as a single heartbeat.
Highlights
A RRHYTHMIAS are heart diseases characterized by an irregular rate and/or rhythm of the heartbeats
Lowner-constrained alternating group lasso (AGL) (LCAGL), for each patient whose segments are characterized by short R-R intervals
Persistent atrial fibrillation (AF) is an advanced stage of this arrhythmia where the ECG typically presents a fast heart rate, resulting in short R-R intervals and an atrial activity (AA) signal that is difficult to identify, making the AA extraction a challenging task
Summary
A RRHYTHMIAS are heart diseases characterized by an irregular rate and/or rhythm of the heartbeats. Selecting the AA signal among the estimated sources after performing BSS is an unsolved issue, since no systematic method is reported in the literature for this purpose Aiming to avoid such limitations in these common and challenging persistent AF scenarios, the present work proposes the BTD built from Lowner matrices as a solution for BSS of rational functions [17] to model the VA and separate it from the AA. This strategy suits the characteristics of VA in ECG recordings, since the QRS complex can be well approximated by rational functions [18], [20], and when mapped onto Lowner matrices, the degree of the rational function matches the rank of the Lowner matrix [17].
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