[1] Gong S H, Chen W P, Yang G T et al. Retrieval of temperature structure and identification of gravity wave events in the middle atmosphere from Rayleigh lidar observations[J]. Acta Optica Sinica, 43, 2428006(2023).

[2] Fang H T, Huang D S, Wu Y H. Antinoise approximation of the lidar signal with wavelet neural networks[J]. Applied Optics, 44, 1077-1083(2005).

[3] Seng H S. A new approach of moving average method in time series analysis[C](2013).

[4] Podder P, Khan T Z, Khan M H et al. Comparative performance analysis of Hamming, Hanning and Blackman window[J]. International Journal of Computer Applications, 96, 1-7(2014).

[5] Sarvani M, Raghunath K, Rao S V B. Lidar signal denoising methods-application to NARL Rayleigh lidar[J]. Journal of Optics, 44, 164-171(2015).

[6] Mao J D. Noise reduction for lidar returns using local threshold wavelet analysis[J]. Optical and Quantum Electronics, 43, 59-68(2012).

[7] Fang H T, Huang D S. Noise reduction in lidar signal based on discrete wavelet transform[J]. Optics Communications, 233, 67-76(2004).

[8] Qin X Z, Mao J D. Noise reduction for lidar returns using self-adaptive wavelet neural network[J]. Optical Review, 24, 416-427(2017).

[9] Zhou Z R, Hua D X, Yang R et al. De-noising method for Mie scattering lidar echo signal based on wavelet theory[J]. Acta Photonica Sinica, 45, 0701002(2016).

[10] Zhang M, Zhang X L, Jin Z et al. Research and application of denoising algorithm for Mie lidar signal[J]. Laser & Optoelectronics Progress, 60, 2028011(2023).

[11] Wu S H, Liu Z S, Liu B Y. Enhancement of lidar backscatters signal-to-noise ratio using empirical mode decomposition method[J]. Optics Communications, 267, 137-144(2006).

[12] Tian P F, Cao X J, Liang J N et al. Improved empirical mode decomposition based denoising method for lidar signals[J]. Optics Communications, 325, 54-59(2014).

[13] Wu Z H, Huang N E. Ensemble empirical mode decomposition: a noise-assisted data analysis method[J]. Advances in Adaptive Data Analysis, 1, 1-41(2009).

[14] Dragomiretskiy K, Zosso D. Variational mode decomposition[J]. IEEE Transactions on Signal Processing, 62, 531-544(2014).

[15] Yi C C, Lü Y, Dang Z. A fault diagnosis scheme for rolling bearing based on particle swarm optimization in variational mode decomposition[J]. Shock and Vibration, 2016, 9372691(2016).

[16] Wang Y S, Jiang H C, Kong Q M et al. Application of a VMD-wavelet packet analysis denoising method to gas detection signals[J]. Laser & Optoelectronics Progress, 61, 2112006(2024).

[17] Li H X, Chang J H, Xu F et al. Efficient lidar signal denoising algorithm using variational mode decomposition combined with a whale optimization algorithm[J]. Remote Sensing, 11, 126(2019).

[18] Liu Z X, Chang J H, Li H X et al. Signal denoising method combined with variational mode decomposition, machine learning online optimization and the interval thresholding technique[J]. IEEE Access, 8, 223482-223494(2020).

[19] Zhang Y J, Wu T, Zhang X Z et al. Rayleigh lidar signal denoising method combined with WT, EEMD and LOWESS to improve retrieval accuracy[J]. Remote Sensing, 14, 3270(2022).

[20] Wu T, Xu D G, Zhong K et al. A novel Rayleigh lidar signal denoising algorithm for far-field noise suppression and high-accuracy retrieval[J]. Proceedings of SPIE, 12772, 1277205(2023).

[21] Ding H B, Wang Z Z, Liu D. Comparison of de-noising methods of LiDAR signal[J]. Acta Optica Sinica, 41, 2401001(2021).

[22] Hauchecorne A, Chanin M L. Density and temperature profiles obtained by lidar between 35 and 70 km[J]. Geophysical Research Letters, 7, 565-568(1980).

[23] Deng P, Zhang T S, Chen W et al. Lidar measurement for atmospheric density and temperature in middle atmosphere over Hefei[J]. Infrared and Laser Engineering, 46, 0730003(2017).