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<p>With the popularity of wearable devices, real-time electrocardiogram (ECG) monitoring is becoming increasingly important in heart health management. However, ECG signals acquired by these devices are highly susceptible to noises arising in signal acquisition. Diagnostic accuracy may often be lowered by these interfering noises. In this paper, by partitioning an ECG signal into heartbeat segments and establishing an ECG tensor, we propose a two-layer Kalman filter-based variational method (TLKFVM) for ECG signal denoising. In the first layer of the denoising process, we apply the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(l_1\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>l</mi> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation>-norm regularized variational model to remove noises within each heartbeat, which is solved by a Kalman smoother (KS) based on the intra-heartbeat state space model (SSM). In the second layer, by utilizing the similarity of heartbeat segments, we apply the <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(l_2\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>l</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation>-norm regularized variational model to further remove residue noises during the evolution period between consecutive heartbeats, which is solved by a Kalman filter (KF) based on the inter-heartbeat SSM. We call the first layer as the intra-heartbeat denoising and the second layer as the inter-heartbeat denoising. The experiments demonstrate the proposed method’s advantages in denoising quality, computational efficiency, and adaptivity when compared with the state-of-the-art methods for ECG denoising.</p>

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A Kalman filter-based variational method for ECG tensor denoising

  • 期刊论文

  • 发表日期：

    2026年7月24日

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  • Ping Cui,
  • Zi-Han Song,
  • Yu-Mei Huang,
  • Zhuo-Fei Zhang

摘要

With the popularity of wearable devices, real-time electrocardiogram (ECG) monitoring is becoming increasingly important in heart health management. However, ECG signals acquired by these devices are highly susceptible to noises arising in signal acquisition. Diagnostic accuracy may often be lowered by these interfering noises. In this paper, by partitioning an ECG signal into heartbeat segments and establishing an ECG tensor, we propose a two-layer Kalman filter-based variational method (TLKFVM) for ECG signal denoising. In the first layer of the denoising process, we apply the \(l_1\) l 1 -norm regularized variational model to remove noises within each heartbeat, which is solved by a Kalman smoother (KS) based on the intra-heartbeat state space model (SSM). In the second layer, by utilizing the similarity of heartbeat segments, we apply the \(l_2\) l 2 -norm regularized variational model to further remove residue noises during the evolution period between consecutive heartbeats, which is solved by a Kalman filter (KF) based on the inter-heartbeat SSM. We call the first layer as the intra-heartbeat denoising and the second layer as the inter-heartbeat denoising. The experiments demonstrate the proposed method’s advantages in denoising quality, computational efficiency, and adaptivity when compared with the state-of-the-art methods for ECG denoising.