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.

中文翻译：

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使用具有 Lowner 约束的块项张量分解进行持续性心房颤动心电图中的盲源分离


从心电图 (ECG) 记录中估计心房活动 (AA) 信号是房颤 (AF) 无创分析的重要一步，房颤是临床实践中最常见的持续性心律失常。这个问题需要采用盲源分离 (BSS) 公式，该公式最近被提出为张量分解，使用基于 Hankel 的块项分解 (BTD)，特别适合在 AF 期间估计 AA 等指数模型。然而，持续形式的 AF 的特点是 RR 间隔短和 AA 非常混乱（或弱），因此很难直接对 AA 进行建模并通过 Hankel-BTD 成功提取。为了克服这个缺点，目前的工作提出了一种张量方法来估计 QRS 复合波并将其从 ECG 中减去，从而产生理想情况下仅包含 AA 分量的信号。这种方法解决了有理函数的盲目分离问题，对 QRS 复合波进行了明确的建模。接受 BTD 的数据张量是根据观察到的心电图每条导联生成的 Löwner 矩阵构建的。为此，本文制定了最近提出的约束交替群套索（CAGL）算法的变体，该算法在分解块上施加 Löwner 结构。这是通过在 CAGL 的每次迭代中执行正交投影来完成的，我们明确推导了该投影。合成数据实验的结果表明，所提出的 Löwner 约束 AGL (LCAGL) 在提取所需来源方面具有一致性。 在 20 名患有持续性 AF 的患者身上获得的实验结果表明，就短至单次心跳的心电图记录的心房信号估计质量而言，所提出的变体优于其他基于张量的方法。