Enhanced Block Term Decomposition for Atrial Activity Extraction in Atrial Fibrillation ECG Lucas N. Ribeiro 1 , Andr´ e L. F. de Almeida 1 and Vicente Zarzoso 2 Abstract—Atrial fibrillation (AF) is the most prevalent sus- tained cardiac arrhythmia but is still considered a challenging research subject since its electrophysiological mechanisms are not yet fully understood. Analyzing the atrial activity (AA) signal observed in surface electrocardiograms (ECG) is useful for clinical management and better understanding the propagation mechanisms inside the atria, but ventricular activity (VA) masks the AA in time and frequency domains. Signal processing techniques have been used to extract the AA signal. Blind Source Separation (BSS) methods can accomplish this task from multi- lead ECG. Recently, a deterministic tensor-based BSS method based on the Block Term Decomposition (BTD) was proposed and offered promising results in AA estimation. This method assumes that AF ECG leads can be expressed as linear combinations of damped exponential sources. However, QRST complexes of VA do not match this model, causing numerical issues. The present contribution proposes a Principal Component Analysis (PCA) preprocessing stage to attenuate the ventricular components. Experimental results show that this stage alleviates the ECG model mismatch, resulting in better AA estimation compared to competing methods and improved numerical properties com- pared to BTD without preprocessing. I. I NTRODUCTION Signal processing is a fundamental tool in the study of cardiac electrophysiology. Electrocardiogram (ECG) signal processing methods aim at extracting features that provide insights into the heart’s conditions. Besides being useful for clinical management, these features aid researchers to better understand the electrophysiological mechanisms of heart dis- eases. Atrial fibrillation (AF) is the most prevalent sustained cardiac arrhythmia, and has been attracting increasing research attention, because its genesis and propagation mechanisms are not yet completely understood. AF consists of disorganized electrical activation of the atria caused by ectopic sources around the pulmonary veins and the propagation of multiple self-sustaining wavelets. In AF ECG, these wavelets are re- flected as the fibrillatory waves (f-waves) that replace the P- wave of normal atrial activation. Spectral features of f-waves, such as the dominant frequency (DF), are thought to correlate with the atrial tissue refractoriness, thus providing knowledge on AF physiological properties. However, AA is masked by the QRST complex of ventricular activity (VA) at each heartbeat, as illustrated in Figs. 1(a) and 4(a). Since masking also occurs 1 Lucas N. Ribeiro and Andr´ e L. F. de Almeida are with the Federal Univer- sity of Cear´ a, Fortaleza, Brazil {nogueira,andre}@gtel.ufc.br 2 Vicente Zarzoso is with the I3S Laboratory, University of Nice Sophia Antipolis, France zarzoso@i3s.unice.fr. He is a member of the Institut Universitaire de France. This work was partially supported by CNPq/CAPES/FUNCAP (Brazil). in the frequency domain, signal processing techniques are necessary to properly estimate the AA before further analysis. Average Beat Subtraction (ABS) and Blind Source Separa- tion (BSS) methods are among the most popular approaches to noninvasive AA extraction [1]–[3]. In [4], [5], we have introduced a deterministic tensor-based BSS method based on the Block Term Decomposition (BTD) [6]. As opposed to ABS and classical BSS techniques, this tensor approach offers the possibility of processing short data records. The method assumes that AF ECG leads can be expressed as linear combinations of damped exponential sources, which is a plausible assumption due to the quasi-harmonic structure of the fibrillatory waves. Source separation is then performed by computing the BTD of the ECG data tensor, obtained by map- ping the ECG leads onto Hankel matrices and arranging them in a third-order tensor. Computer experiments showed that AA could be extracted provided that the decomposition parameters were correctly selected. The experiments also showed that block terms with large multilinear rank were necessary to separate the AA from VA, resulting in numerical issues such as slow convergence and large decomposition residual error. This phenomenon could mainly be explained by the sharp peaks of VA, as shown in Figs. 1(a) and 4(a), which do not match the assumed model, producing high-rank block terms. The present contribution employs signal subspace methods to attenuate the VA on multilead AF ECG as a preprocessing stage prior to BTD computation. This preprocessing mitigates the effects of model mismatch on the BTD step. We investigate the performance of Principal Component Analysis (PCA) in this preprocessing task. Next, the applicability of this improved BTD is evaluated on real AF ECG by comparing its perfor- mance to those of two benchmark methods: Adaptive Singular Value Cancellation (ASVC) [7] and RobustICA-f [8]. II. METHODS A. Database and Signal Acquisition Standard 12-lead ECG signals were recorded on two pa- tients diagnosed with persistent AF at the Cardiology Depart- ment of Princess Grace Hospital, Monaco. These recordings were acquired at a sampling rate of 977 Hz and lasted about 60 s each. ECG were processed by a forward-backward type-II Chebyshev bandpass filter with cut-off frequencies of 0.5 Hz and 30 Hz to remove baseline wander and powerline interfer- ence. The resulting signals were stored in matrix Y 2 R 12⇥N , where N denotes the sample size. Simultaneous invasive elec- trogram (EGM) recordings were acquired by placing bipolar catheters inside the left atrial appendage (LAA).