Electrocardiogram signal reconstruction based on mode component identification by heartbeat physical feature in improved empirical mode decomposition domain
1.Shanxi Key Laboratory of Signal Capturing and Processing, North University of China, Taiyuan 030051, China 2.Department of Physics, Changzhi Medical College, Changzhi 046000, China 3.Department of Biomedical Engineering, Changzhi Medical College, Changzhi 046000, China
Fund Project:Project supported by the National Natural Science Foundation of China (Grant Nos. 61842103, 61871351, 61801437), the Key Laboratory of National Defense Science and Technology for Electronic Testing Technology Foundation, China (Grant No. 6142001180410), and the Science and Technology Innovation Foundation of the Higher Education Institutions of Shanxi Province, China (Grant Nos. 2020L0301, 2020L0389).
Received Date:14 July 2020
Accepted Date:02 September 2020
Available Online:22 January 2021
Published Online:05 February 2021
Abstract:Electrocardiogram (ECG) diagnosis is based on the waveform, duration and amplitude of characteristic wave, which are required to have a high accuracy for ECG signal reconstruction. As an effective nonlinear signal processing method, empirical mode decomposition (EMD) has been widely used for diagnosing and reconstructing the ECG signal, but there are two problems arising here. One is the mode mixing, and the other is that the mode components used in reconstruction are identified by experience. Therefore, the method of reconstruction is not adaptive and universal, and reconstructed ECG signal loses accuracy. Firstly, we propose an improved EMD method, which is called integral mean mode decomposition (IMMD). The analysis of 5000 samples of Gaussian white noise shows that IMMD has better multi-resolution analysis ability than EMD, and it can effectively alleviate mode mixing consequently. Secondly, based on the inherent physical characteristics of ECG signal, cardiac cycle or heart rate (HR), it has practical physical significance to identify the mode components used in ECG signal reconstruction. The cardiac cycle feature acts as the intrinsic mode function (IMF) component through two modes. 1) For the low-order IMF that belongs to the ECG signal, the cardiac cycle feature acts as the amplitude modulation. The envelope of the IMF component has the characteristics of the cardiac cycle, and the frequency corresponding to the maximum amplitude in the spectrum of the envelope is equal to HR. 2) For the high-order IMF that belongs to the ECG signal, the cardiac cycle feature acts as frequency modulation. Those IMF components have the harmonic characteristics of periodic heartbeats, and the maximum amplitude in the spectrum corresponds to an integral multiple of HR (usually 1-3 times). The noise attributed to IMF component cannot show the above two cardiac cycle characteristics. Thus the proposed method is adaptive and universal. The 47 ECG signals with baseline drift and muscle artifact noise are tested. The results show that the proposed method is more effective than the variational mode decomposition (VMD), Haar wavelet with soft threshold, ensemble empirical mode decomposition (EEMD) and EMD. Among the 47 correlation coefficients between reconstructed and original ECG signals, the proposed method has 31 better than VMD, 33 better than Haar wavelet, 42 better than EEMD and 45 better than EMD. The mean of 47 correlation coefficients from the proposed method is 0.8904, and the variance is 0.0071, which shows that the proposed method has good performance and stability. Keywords:electrocardiogram/ reconstruction/ heart rate/ integral mean mode decomposition
文献[23]研究了EMD分解5000个长度N = 512, 均值为0, 方差为1的高斯白噪声数据样本, 得到如下结论: EMD类似于小波变换Mallat算法, 等效于一个恒定品质因子Q的二分(或二进)滤波器组, 具有多分辨率分解信号能力. 本节将采用同样方法, 分析IMMD分解高斯白噪声特性, 以此说明方法分解信号的性能. IMMD分解每个高斯白噪声样本, 得到至少10个IMF. 对所有样本相应阶数IMF求平均傅里叶功率谱, 结果见图1(a). IMF1相当于一个高通滤波器, 其余IMF等效于一组重叠带通滤波器, 且后一IMF等效带通滤波器中心频率约是前一 IMF等效带通滤波器中心频率的2/3. IMMD方法分解高斯白噪声等效于滤波器组, 且具有三分特性. 图 1 IMMD和EMD方法分解高斯白噪声的等效滤波器组特性 (a) IMMD (实线)和EMD (虚线)的IMF分量的平均功率谱; (b) 基于(5)式, IMMD (实线)和EMD (虚线)的IMF分量的平均功率谱坍缩重合 Figure1. Equivalent filter banks of IMMD and EMD decomposing Gauss white noises: (a) Averaged power spectra of IMFs from IMMD (solid curves) and EMD (dotted curves); (b) collapse and coincidence of the average power spectrum of IMFs from IMMD (solid curves) and EMD (dotted curves) based on Eq. (5).
图 4 含噪105 ECG信号IMFs的功率谱(蓝色曲线), 及IMFs包络的功率谱(红色曲线) Figure4. Power spectra of envelopes of IMFs (red curves) and of IMFs (blue curves) of noisy No. 105 ECG signal.
为了显示所提出方法的能力, 将本文方法同近年来常用VMD、小波软阈值法、EEMD以及EMD重建105 ECG信号进行对比, 利用这五种方法重建的105 ECG信号如图5所示. 由图5可见, 五种方法都很好地消除了BW噪声. 由于MA噪声宽频特性, 五种方法重建ECG信号中仍然存在少量MA噪声分量, 特别是Harr小波软阈值方法. EMD方法重建ECG信号畸变最为严重, 其次是EEMD. 实际中, EEMD对含噪105 ECG信号的多次重建结果之间都有轻微不同, 这是由辅助白噪声的随机性引起的[28]. 另外, VMD方法中特征R波的峰值失真比本文提出方法严重, 例如, 图5(b)中第10个R波波峰峰值损失14.5%, 本文方法为3.2%. 图 5 原105 ECG信号(蓝色点虚线)与由五种方法重建的105 ECG信号(红色实线) (a) 本文方法; (b) VMD; (c) Haar小波软阈值; (d) EMMD; (e) EMD Figure5. Original No. 105 ECG signal (blue dotted curves) and the No. 105 ECG signals (red solid curves) reconstructed by 5 methods: (a) The proposed method; (b) VMD; (c) Haar wavelet with soft threshold; (d) EEMD; (e) EMD.