基于能量阈值的双参数阈值函数在生理信号降噪中的应用

doi:10.12382/bgxb.2022.1058

摘要/Abstract

摘要：

针对弱生理信号在采集过程中易被噪声淹没,传统小波去噪算法存在去噪效果差和信号提取失真的问题,根据小波系数的能量分布特点,提出一种改进的小波阈值去噪算法。通过计算各层小波系数的能量来确定阈值,避免阈值计算的不平衡性,同时提高自适应性和弱信号的保真度;采用一种改进的可调节的双参数阈值函数对小波系数进行处理,在小波系数压缩程度可控的同时可以自由调节阈值函数的变化趋势。实验结果表明:改进的小波阈值去噪算法相较于两种传统去噪算法(经验模态分解算法和滤波器算法)以及12种传统小波阈值和阈值函数组合算法,在信噪比、均方根百分比和均方根误差上都具有明显的优势,并且在实测生理信号中取得了最小的平均相对误差和最小的波动性。

关键词: 小波变换, 能量梯度阈值, 改进阈值函数, 生理信号, 去噪

Abstract:

To deal with the problems that the weak physiological signals are easily drowned by noise and the poor denoising effect and signal extraction distortion exist in traditional wavelet denoising method, an improved wavelet threshold denoising method based on the energy distribution characteristics of wavelet coefficients is proposed. The threshold is determined by calculating the energy of wavelet coefficient in each layer, which avoids the imbalance of threshold calculation while improving the adaptivity and the fidelity of weak signals. An improved adjustable two-parameter threshold function is used to process the wavelet coefficients, which allows the changing trend of threshold function to be freely adjusted while the degree of compression of the wavelet coefficients is controlled. The experimental results show that the improved wavelet threshold denoising method has more obvious advantages in signal-to-noise ratio, root-mean-square percentage and root-mean-square error compared with two traditional denoising algorithms (the empirical modal decomposition algorithm and the filter algorithm) and 12 traditional algorithms for combining wavelet thresholding and thresholding functions, and achieves the smallest average relative error and the smallest volatility in the measured physiological signal.

Key words: wavelet transform, energy gradient threshold, improved threshold function, physiological signal, denoising

中图分类号:

TN957.51

赵薇, 卓智海, 张月霞. 基于能量阈值的双参数阈值函数在生理信号降噪中的应用[J]. 兵工学报, 2024, 45(4): 1264-1272.

ZHAO Wei, ZHUO Zhihai, ZHANG Yuexia. Application of Two-parameter Threshold Function Based on Energy Thresholds in Denoising of Physiological Signal[J]. Acta Armamentarii, 2024, 45(4): 1264-1272.

图/表 14

图1 小波阈值去噪基本框图

Fig.1 Basic block diagram of wavelet threshold denoising

图2 不同阈值公式得到的各层小波阈值

Fig.2 Wavelet thresholds for each layer obtained from different threshold formulas

图3 软、硬和新阈值函数(不同p、q取值)

Fig.3 Soft, hard, and new threshold functions (different values of p and q)

图4 小波阈值法提取生理信号流程图

Fig.4 Flow chart of wavelet thresholding method to extract physiological signals

图5 ECG时域信号

Fig.5 ECG time domain signals

图6 不同小波基处理不同信噪比信号能力对比

Fig.6 Comparison of the abilities of different wavelet bases to process signals with different signal-to-noise ratios

表1 各种小波基去噪衡量指标表

Table 1 List of denoising measures for various wavelet bases

小波基	SNR	SNR'	η	σ_c	σ_r
sym3	7.9342	18.8275	2.3730	0.9934	0.1170
db4	7.9342	18.6875	2.3553	0.9932	0.1189
haar	7.9342	16.7295	2.1085	0.9893	0.1496
bior3.1	7.9342	6.3611	0.8017	0.8768	0.5572

图7 14种去噪算法去噪后的ECG时域信号

Fig.7 ECG time domain signal of the signal after denoising with 14 denoising algorithms

图8 经验分解算法以及相应的IMF和残差

Fig.8 Empirical decomposition algorithm, corresponding IMFs and residual

表2 不同噪声强度下的随机10组ECG信号去噪性能指标对比

Table 2 Comparison of the denoising performance indexes of ten random ECG signals with different noise intensities

去噪算法	SNR	σ_r	σ_p
λ_b+ω_b	14.5885	0.0963	0.1488
λ_b+ω_h	12.7328	0.0718	0.2090
λ_b+ω_s	11.2421	0.0883	0.2493
λ_Z+ω_b	10.9285	0.1065	0.2682
λ_Z+ω_h	9.2749	0.1333	0.3518
λ_Z+ω_s	7.0072	0.1780	0.5111
λ_D+ω_b	13.2187	0.0796	0.2233
λ_D+ω_h	12.8372	0.0834	0.2653
λ_D+ω_s	9.7004	0.1118	0.2755
λ_f+ω_b	8.5310	0.1330	0.3658
λ_f+ω_h	8.4779	0.1330	0.3823
λ_f+ω_s	7.6883	0.1400	0.3872
EMD	1.5329	0.3655	1.0127
带通滤波器	1.5462	0.3354	0.9293

表3 毫米波雷达的参数配置

Table 3 Millimeter-wave radar parameter configuration

实验参数	数值
起始频率/GHz	77
调频斜率/(MHz·μs^-1)	70
有效带宽/MHz	3500
ADC采样点数	200
采样率/(kS·s^-1)	4000
每帧时间/s	0.05
采集帧数	1024

表4 5种算法去噪后的生理信号波峰波谷平均检测结果

Table 4 Results of peak-to-trough average detection of physiological signals after denoising by 5 algorithms

算法	呼吸频率			心跳频率
算法	参考值	波峰波谷检测结果	误差	参考值	波峰波谷检测结果	误差
λ_Z+ω_h	23	15.2344	7.7656	86	75.0000	9.0000
λ_D+ω_s	23	15.2344	7.7656	86	75.0000	9.0000
λ_b+ω_b	23	25.0938	2.0938	86	87.9922	1.9922
EMD	23	27.5391	4.5319	86	69.7266	16.2734
带通滤波器	23	18.7500	4.3500	86	88.4766	2.4766

表5 5种算法的平均相对误差

Table 5 Average relative errors of five algorithms

算法	呼吸频率平均相对误差	心跳频率平均相对误差
λ_Z+ω_h	0.1680	0.2343
λ_D+ω_s	0.1680	0.2343
λ_b+ω_b	0.0547	0.0781
EMD	0.3125	0.1874
带通滤波器	0.0859	0.0938

表6 5种算法的最小二乘损失函数对比

Table 6 Comparison of least squares loss functions of five algorithms

算法	呼吸频率最小二乘损失函数	心跳频率最小二乘损失函数
λ_Z+ω_h	12.47	45.56
λ_D+ω_s	12.47	45.56
λ_b+ω_b	5.87	5.09
EMD	43.24	16.17
带通滤波器	6.58	15.59

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