用于近红外宽带腔增强吸收光谱的小波去噪 
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Wavelet Denoising in Near-Infrared Broadband Cavity-Enhanced Absorption Spectroscopy
1 吉林大学集成光电子学国家重点联合实验室,电子科学与工程学院, 吉林 长春 130012
2 吉林省红外气体传感技术工程研究中心, 吉林 长春 130012
图 & 表
图 1. 基于小波去噪的宽带腔增强甲烷气体传感系统
Fig. 1. System diagram of the WD based methane sensor system using broadband cavity-enhanced technique
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图 2. 不同小波函数的去噪效果(含噪信号:虚线;去噪信号:实线)。(a)不同小波函数在无吸收背景区间的去噪效果;(b)不同小波函数在有吸收处的去噪效果;(c)使用db2小波函数的去噪效果
Fig. 2. Denoising effect using different wavelet functions (polluted signal: dash line; denoised signal: solid line). (a) Denoising effect using different wavelet functions in the absorption free background interval; (b) denoising effect using different wavelet functions in the absorption interval; (c) denoising effect using db2 wavelet function
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图 3. 不同分解层数的去噪效果(含噪信号:虚线;去噪信号:实线)。(a)不同分解层数在无吸收背景区间的去噪效果;(b)不同分解层数在有吸收处的去噪效果;(c)使用6级分解的去噪效果
Fig. 3. Denoising effect using different decomposition layers (polluted signal: dash line; denoised signal: solid line). (a) Denoising effect using different decomposition layers in the absorption free background interval; (b) denoising effect using different decomposition layers in the absorption interval; (c) denoising effect using 6 decomposition layers
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图 4. 不同阈值估计准则的去噪效果(含噪信号:虚线;去噪信号:实线)。(a)不同阈值估计准则在无吸收背景区间的去噪效果;(b)不同阈值估计准则在有吸收处的去噪效果;(c)使用heursure阈值估计准则的去噪效果
Fig. 4. Denoising effect using different threshold estimation criteria (polluted signal: dash line; denoised signal: solid line). (a) Denoising effect using different threshold estimation criteria in the absorption free background interval; (b) denoising effect using different threshold estimation criteria in the absorption interval; (c) denoising effect using heursure threshold estimation criterion
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图 5. 小波去噪前后甲烷的吸收系数、拟合吸收截面以及拟合残差。(a)未采用小波去噪的甲烷吸收系数以及拟合吸收截面;(b)未采用小波去噪的拟合残差;(c)采用小波去噪后的甲烷吸收系数以及拟合吸收截面;(d)采用小波去噪后的拟合残差
Fig. 5. Measured absorption coefficient of methane, fitted absorption coefficient, and fitted residual before and after WD. (a) Measured and fitted absorption coefficients of methane without WD; (b) fitted residual without WD; (c) measured and fitted absorption coefficients of methane with WD; (d) fitted residual with WD
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图 6. 小波去噪前后甲烷传感器的Allan标准差曲线
Fig. 6. Allan deviation curves of the methane sensor system before and after WD
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表 1采用不同小波函数得到的ERMS值
Table1. Obtained ERMS values for different wavelet functions
| Wavelet function | ERMS(6050-6055 cm-1) | ERMS(6055-6060 cm-1) |
|---|
| haar | 1.37×10-6 | 7.92×10-6 | | coif1 | 1.10×10-6 | 8.09×10-6 | | sym6 | 1.39×10-6 | 7.92×10-6 | | bior2.2 | 1.02×10-6 | 8.13×10-6 | | db2 | 9.82×10-7 | 7.81×10-6 |
|
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表 2不同分解层数得到的ERMS值
Table2. Obtained ERMS values for different decomposition layers
| Number of decomposition layers | ERMS(6050-6055 cm-1) | ERMS(6055-6060 cm-1) |
|---|
| 3 | 2.15×10-6 | 7.95×10-6 | | 4 | 1.98×10-6 | 7.87×10-6 | | 5 | 1.19×10-6 | 7.74×10-6 | | 6 | 9.82×10-7 | 7.81×10-6 | | 7 | 2.46×10-6 | 1.65×10-5 |
|
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表 3不同阈值估计准则得到的ERMS值
Table3. Obtained ERMS values for different threshold estimation criteria
| Threshold estimation criterion | ERMS(6050-6055 cm-1) | ERMS(6055-6060 cm-1) |
|---|
| rigrsure | 9.82×10-7 | 7.81×10-6 | | sqtwolog | 1.20×10-6 | 8.43×10-6 | | minimaxi | 1.40×10-6 | 8.01×10-6 | | heursure | 9.82×10-7 | 7.81×10-6 |
|
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表 4使用小波去噪前后传感器的性能对比
Table4. Comparison of the sensor performance without and with WD
| Scenario | Residual /cm-1 | Retrieved concentration | SNR | Detection limit (averaging time) |
|---|
| Without WD | 3.3×10-6 | 1.088×10-3 | 17.3 | 5.6×10-5 (20 min) | | With WD | 1.7×10-6 | 1.018 ×10-3 | 33.0 | 3.1×10-5 (20 min) |
|
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姚丹, 郑凯元, 刘梓迪, 李俊豪, 郑传涛, 王一丁. 用于近红外宽带腔增强吸收光谱的小波去噪[J]. 光学学报, 2019, 39(9): 0930006. Dan Yao, Kaiyuan Zheng, Zidi Liu, Junhao Li, Chuantao Zheng, Yiding Wang. Wavelet Denoising in Near-Infrared Broadband Cavity-Enhanced Absorption Spectroscopy[J]. Acta Optica Sinica, 2019, 39(9): 0930006.
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