Combination Method of Wavelet and Empirical Mode Decomposition with Trend Modulation used for Atmospheric Coherent Length Profile Denoising

Zhi Cheng; Feng He; Silong Zhang; Xu Jing; Zaihong Hou

doi:10.3788/AOS201737.1201002

Journals >Acta Optica Sinica >Volume 37 >Issue 12 >Page 1201002 > Article

Acta Optica Sinica
Vol. 37, Issue 12, 1201002 (2017)

Combination Method of Wavelet and Empirical Mode Decomposition with Trend Modulation used for Atmospheric Coherent Length Profile Denoising

Zhi Cheng^1、2, Feng He^1、*, Silong Zhang¹, Xu Jing¹, and Zaihong Hou¹

Author Affiliations

¹ Key Laboratory of Atmospheric Composition and Optical Radiation, Chinese Academy of Sciences, Anhui Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Hefei, Anhui 230031, China

² University of Science and Technology of China, Hefei, Anhui 230026, China

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DOI: 10.3788/AOS201737.1201002 Cite this Article Set citation alerts

Zhi Cheng, Feng He, Silong Zhang, Xu Jing, Zaihong Hou. Combination Method of Wavelet and Empirical Mode Decomposition with Trend Modulation used for Atmospheric Coherent Length Profile Denoising[J]. Acta Optica Sinica, 2017, 37(12): 1201002 Copy Citation Text

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Fig. 1. Schematic of measurement principle of differential light column image motion lidar

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Fig. 2. Average SNR of r0 profile denoising with three wavelet bases versus number of decomposition layers under 5% Gauss noise level

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Fig. 3. Decomposition results of noisy r0 profile with SNR of 12 dB

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Fig. 4. DFA exponent of each layer of IMF

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Fig. 5. Denoised atmospheric coherent length profiles obtained by different methods under different Gauss noise levels. (a) 5% Gauss noise; (b) 10% Gauss noise; (c) 15% Gauss noise; (d) 20% Gauss noise

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Fig. 6. Retrieved Cn2 profiles before and after denoising under different Gauss noise levels with different methods. (a) 5% Gauss noise; (b) 10% Gauss noise; (c) 15% Gauss noise; (d) 20% Gauss noise

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Fig. 7. Undenoised and denoised atmospheric coherent length profiles of DCIM lidar at different time. (a) 19:59:29 on November 9, 2015; (b) 14:40:26 on November 11, 2015; (c) 20:34:50 on November 11, 2015

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Fig. 8. Comparison between undenoised and denoised atmospheric coherent length profiles of DCIM lidar and balloon profile at different time. (a) 19:59:29 on November 9, 2015; (b) 14:40:26 on November 11, 2015; (c) 20:34:50 on November 12, 2015

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Method	5% Gauss noise		10% Gauss noise
Method	SNR /dB	RMSE /dB	SNR /dB		RMSE /dB		SNR /dB	RMSE /dB	SNR /dB	RMSE /dB
Wavelet	35.0403			0.1122	30.3897	0.1812	27.3677	0.2771	25.4355	0.3653
EMD	30.5011			0.1881	25.3290	0.3536	21.3346	0.5406	19.5972	0.6803
EEMD	32.3656			0.1523	28.1977	0.2242	25.2832	0.3582	23.3892	0.4563
Wavelet-EMD	36.2172			0.1091	32.1452	0.1968	29.3074	0.2220	27.3642	0.2905
Wavelet-trend-EMD	37.5507			0.0972	33.2741	0.1563	31.1308	0.1874	28.9157	0.2492

Table 1. Statistical results of SNR and root-mean-square error (RMSE) of denoised atmospheric coherent length profiles obtained by different methods under different Gauss noise levels

Method	5% Gauss noise		10% Gauss noise
Method	SNR /dB	RMSE /dB	SNR /dB		RMSE /dB		SNR /dB	RMSE /dB	SNR /dB	RMSE /dB
Without denoising	34.6662			0.3260	33.9578	0.3724	33.0201	0.4103	31.6566	0.4979
Wavelet	36.6117			0.2585	35.8395	0.3025	34.9985	0.3179	33.3922	0.3921
EMD	35.3218			0.3089	34.2728	0.3582	33.5335	0.3792	31.9287	0.4671
EEMD	5.7906			0.2834	34.3851	0.3533	34.1409	0.3556	32.1464	0.4489
Wavelet-EMD	37.0984			0.2373	36.4147	0.2395	35.3477	0.3075	34.4655	0.3501
Wavelet-trend-EMD	37.7616			0.2044	36.9076	0.2141	35.9832	0.2893	34.8723	0.3286

Table 2. Statistical results of SNR and RMSE of Cn2 profile retrieved from undenoised and denoised r0 profile under different gauss noise levels

Method	November 9, 2015
Method	SNR /dB	RMSE /dB		SNR /dB		RMSE /dB	SNR /dB	RMSE /dB
Without denoising	29.7723		0.5603		30.6313	0.4531	29.5740	0.5570
Wavelet	30.1182		0.5477		31.2813	0.4205	34.9985	0.3179
EMD	29.9249		0.5505		30.9940	0.4346	30.1918	0.5187
EEMD	29.9632		0.5432		30.8663	0.4410	31.1919	0.4623
Wavelet-EMD	30.2245		0.5380		31.4912	0.4104	31.7527	0.4334
Wavelet-trend-EMD	30.8970		0.4922		31.8762	0.3918	32.0745	0.4176

Table 3. Undenoised and denoised SNR and RMSE of retrieved Cn2 profiles measured by DCIM lidar

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