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. 2019 Apr 10;19(7):1718.
doi: 10.3390/s19071718.

Sparse ECG Denoising With Generalized Minimax Concave Penalty

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Free PMC article

Sparse ECG Denoising With Generalized Minimax Concave Penalty

Zhongyi Jin et al. Sensors (Basel). .
Free PMC article

Abstract

The electrocardiogram (ECG) is an important diagnostic tool for cardiovascular diseases. However, ECG signals are susceptible to noise, which may degenerate waveform and cause misdiagnosis. In this paper, the ECG noise reduction techniques based on sparse recovery are investigated. A novel sparse ECG denoising framework combining low-pass filtering and sparsity recovery is proposed. Two sparsity recovery algorithms are developed based on the traditional ℓ 1 -norm penalty and the novel generalized minimax concave (GMC) penalty, respectively. Compared with the ℓ 1 -norm penalty, the non-differentiable non-convex GMC penalty has the potential to strongly promote sparsity while maintaining the convexity of the cost function. Moreover, the GMC punishes large values less severely than ℓ 1 -norm, which is utilized to overcome the drawback of underestimating the high-amplitude components for the ℓ 1 -norm penalty. The proposed methods are evaluated on ECG signals from the MIT-BIH Arrhythmia database. The results show that underestimating problem is overcome by the proposed GMC-based method. The GMC-based method shows significant improvement with respect to the average of output signal-to-noise ratio improvement ( S N R i m p ), the average of root mean square error (RMSE) and the percent root mean square difference (PRD) over almost any given SNR compared with the classical methods, thus providing promising approaches for ECG denoising.

Keywords: ECG denoising; Generalized Minimax Concave Penalty (GMC); sparse recovery; ℓ1-norm.

Conflict of interest statement

The authors declare no conflict of interest.

Figures

Figure 1
Figure 1
Block diagram of the sparsity electrocardiogram (ECG) denoising process.
Figure 2
Figure 2
Illustration of the generalized minimax concave (GMC) penalty function.
Figure 3
Figure 3
The detail flowchart of sparse ECG denoising with GMC-penalty.
Figure 4
Figure 4
Denoising effect of original signal of MIT-BIH database.
Figure 5
Figure 5
Comparison of the original ECG signal y, the noisy ECG signal s, the low-pass filtered signal l˜ and the residual sparse component dw in the proposed sparse denoising framework. (a) No.100 MIT-BIH ECG; (b) Noisy ECG with 10 dB SNR; (c) Output of the LPF; (d) Residual noisy sparse component.
Figure 6
Figure 6
The updating rate of the recovered signal versus iterating numbers.
Figure 7
Figure 7
Output of the sparsity recovery block.
Figure 8
Figure 8
Comparison of the recovered signals in time domain.
Figure 9
Figure 9
Comparison time-frequency properties of the GMC and 1-norm methods.
Figure 10
Figure 10
RMSE versus λ with γ=0.8.
Figure 11
Figure 11
Performance evaluation over RMSE, PRD and SNRimp criteria.
Figure 12
Figure 12
Performance evaluation over RMSE, PRD and SNRimp criteria for different data sources.
Figure 13
Figure 13
Comparison of waveform outputs of different algorithms for a normal ECG signal (No.100 in the MIT-BIH database).
Figure 13
Figure 13
Comparison of waveform outputs of different algorithms for a normal ECG signal (No.100 in the MIT-BIH database).
Figure 14
Figure 14
Comparison of waveform outputs of different algorithms for an arrhythmia ECG signal (No.230 in the MIT-BIH database).

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