A quality evaluation method for wavelet denoising based on combinatorial weighting method
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摘要:
针对传统质量评价指标在小波阈值去噪中理论依据不足的问题，提出了一种基于组合赋权法的小波去噪质量评价方法，能够为小波去噪参数的选择提供有效评价。通过分析在真值未知情况下均方根误差（RMSE）、信噪比（SNR）、平滑度等单项指标的特点，选取RMSE与平滑度作为小波去噪指标，对其进行归一化处理，采用信息熵权与变异系数的方法进行组合赋权，将归一化指标与对应权值线性组合，得到一种新的指标即为复合评价指标，其值越小，说明去噪效果越好，所选参数越优。仿真实验表明，在真值已知情况下，该评价指标具有更高的准确性，能够适用于不同的分解层数与小波基函数，具有比传统方法更好的适用性;实测数据表明，所提方法得出的小波去噪峰值域更加光滑，波形更加平稳，去噪效果更佳。
Abstract:Addressing such a problem with the traditional indicator system for quality evaluation as an insufficient theoretical basis for wavelet threshold denoising, a combination weighting approach-based method for evaluation of wavelet denoising quality is proposed with the expectation of effectively evaluating the selection of wavelet denoising parameters. Through analysis of characteristics of individual indicators such as root-mean-square error (RMSE), signal-noise ratio (SNR) and smoothness with the truth-value unknown, RMSE and smoothness are selected as wavelet denoising indicators. They are first normalized, then processed with information entropy and coefficient of variation for combination weighting, and, in the end, linearly combined with the corresponding weights to produce a new indicator, i.e., the composite index. A smaller composite index indicates better denoising effect and better parameters selected. According to a simulated experiment, the index outperforms the conventional approach in terms of accuracy given the truth-value and is applicable to various decomposition levels and wavelet base functions. According to experimental data, this method achieves smoother wavelet denoising peak regions, steadier waveforms, and a better denoising effect.
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图 1 真值已知的多普勒信号的单一评价指标趋势
Figure 1. Trends of single evaluation index of Doppler signal with known truth value
图 2 真值未知的陀螺输出数据的单一评价指标趋势
Figure 2. Trends of single evaluation index of gyro output data with unknown truth value
图 3 原始信号与降噪信号时域曲线
Figure 3. Time-domain curves of original signal and denoising signal
图 5 原始信号与降噪信号功率谱密度图
Figure 5. Power spectral density diagram of original signal and denoising signal
表 1 真值未知时评价指标特点
Table 1. Characteristics of evaluation indexes when truth value is unknown
评价指标 关注信息 与分解层数相关性 RMSE 细节信息 正相关 SNR 细节信息 负相关 平滑度 近似信息 负相关 
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表 2 不同分解层数利用sym4小波基处理的评价指标
Table 2. Evaluation indexes of sym4 wavelet basis processing for different decomposition layers
分解层数 真值已知 真值未知 T S H RMSE SNR RMSE r 2 0.581 1 13.861 7 0.778 1 0.103 0 0.866 5 0.890 3 0.899 5 3 0.465 0 15.796 9 0.844 7 0.069 7 0.212 3 0.256 6 0.193 3 4 0.416 2 16.761 3 0.856 8 0.065 4 0.132 8 0.233 3 0.105 9 5 0.406 2 16.970 8 0.866 2 0.064 6 0.128 8 0.122 3 0.097 9 6 0.400 6 17.093 4 0.867 2 0.064 5 0.127 5 0.146 2 0.096 2 7 0.405 6 16.985 4 0.869 9 0.064 4 0.130 6 0.109 7 0.098 3 8 0.405 5 16.986 0 0.869 9 0.064 4 0.130 6 0.116 4 0.098 3 9 0.418 7 16.876 8 0.870 4 0.064 4 0.131 2 0.132 0 0.098 7 10 0.410 1 16.888 8 0.872 1 0.064 3 0.133 5 0.100 5
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表 3 不同分解层数利用db5小波基处理的评价指标
Table 3. Evaluation indexes of db5 wavelet basis processing for different decomposition layers
分解层数 真值已知 真值未知 T S H RMSE SNR RMSE r 2 0.5411 14.4805 0.8219 0.0808 0.8593 0.8925 0.8933 3 0.456 1 15.965 5 0.883 3 0.050 0 0.236 9 0.267 8 0.219 0 4 0.414 9 16.788 0 0.895 5 0.045 7 0.156 1 0.248 9 0.129 6 5 0.382 5 17.492 8 0.905 7 0.044 4 0.140 3 0.157 4 0.108 7 6 0.375 8 17.648 3 0.909 4 0.044 1 0.139 7 0.119 5 0.106 5 7 0.375 2 17.662 2 0.910 3 0.044 0 0.140 0 0.109 5 0.10627 8 0.379 5 17.562 9 0.910 7 0.044 0 0.140 1 0.108 7 0.106 3 9 0.379 7 17.558 6 0.910 9 0.044 0 0.140 7 0.107 5 0.106 5 10 0.380 2 17.546 3 0.911 0 0.044 0 0.144 5 0.106 7
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表 4 不同小波基对应的最优分解层数
Table 4. Number of optimal decomposition layers corresponding to different wavelet bases
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表 5 SPAN-ISA-100C陀螺仪Allan方差分析结果
Table 5. Allan variance analysis results of SPAN-ISA-100C gyroscope
坐标轴 角度随机游走/
$({(^\circ )}\cdot{ {\text{h} }^{-\frac{ {1} }{ {2} } } })$零偏不稳定性/
$((^\circ) \cdot{\text{h} }^{-1})$角速率随机游走/
$((^\circ )\cdot{ {\text{h} }^{-\frac{ {3} }{ {2} } } })$x轴 0.030 4 0.045 5 0.054 2 y轴 0.026 9 0.120 8 0.185 7 z轴 0.025 4 0.043 0 0.057 9
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表 6 MP-M39陀螺仪Allan方差分析结果
Table 6. Allan variance analysis results of MP-M39 gyroscope
坐标轴 角度随机游走/
$({(^\circ )}\cdot{ {\text{h} }^{-\frac{ {1} }{ {2} } } })$零偏不稳定性/
$((^\circ) \cdot{\text{h} }^{-1})$角速率随机游走/
$((^\circ )\cdot{ {\text{h} }^{-\frac{ {3} }{ {2} } } })$x轴 0.199 3 9.504 1 28.599 4 y轴 0.136 3 4.198 7 14.920 2 z轴 0.186 8 7.591 2 29.389 7
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表 7 陀螺数据对应的最优分解层数
Table 7. Number of optimal decomposition layers corresponding to gyro data
方法 陀螺数据 x1 y1 z1 x2 y2 z2 本文 4 5 5 5 5 5 文献[9] 4 4 4 4 4 4
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表 8 陀螺数据对应的最佳小波基函数
Table 8. Optimal wavelet basis functions corresponding to gyro data
陀螺数据 x1 y1 z1 x2 y2 z2 小波基 sym6 sym4 db8 db7 db7 db7
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