基于弹性变分模态提取的时间相关单光子计数信号去噪

汪书潮; 苏秀琴; 朱文华; 陈松懋; 张振扬; 徐伟豪; 王定杰

doi:10.7498/aps.70.20210149

摘要

单光子激光雷达的回波信号具有极低的信噪比, 有效地消除噪声和提取出回波信号特征是提升单光子激光雷达测距精度的关键, 变分模态分解算法需要使用者依据经验确定分解本征模态函数数量, 不具有适用性和通用性. 为此, 本文基于时间相关单光子计数信号特点, 提出了在变分模态分解中让信号按照指定频率进行聚类分解的变分约束条件, 并采用弹性网回归重构不适定问题的求解模型, 提出了弹性变分模态提取算法. 实验结果表明, 在波段850 nm、平均发射功率为25 nW、背景噪声平均功率为19.51 μW的条件下, 利用该方法, 得到了时间相关单光子计数信号重建精度的均方根误差为1.414 ns. 同时在不同的累积时间下, 能够稳定且快速地提取出回波信号特征, 有效地提高了算法的去噪能力和特征提取的性能.

关键词:

Abstract

The performance of the method of measuring the time-correlated single photon counting signal is the key to improving the ranging accuracy of single photon light detection and ranging (LiDAR) technique, where noise elimination is a critically essential step to obtain the characteristics of signal. In this paper, a new method called elastic variational mode extraction (EVME) is proposed to extract the feature of the reflected photons from noisy environment. The method takes into account the characteristic of photon counting signal, and improves variational mode decomposition (VMD) method by adopting a new assumption that the extractive mode signal should be compact around desired center frequency. The proposed method also uses the elastic net regularization to solve ill-posed problem instead of Tikhonov regularization mentioned in VMD. Elastic net regularization takes into account both L2-norm regularization and L1-norm regularization, which can add an extra analysis dimension compared with the Tikhonov regularization. The method is validated with real data which are acquired on condition that average transmitting power is 25 nW while the average background noise power is 19.51 μW. The root mean square error of the reconstruction accuracy reaches 1.414 ns. Furthermore, compared with VMD, Haar wavelet, Hibert envelope, empirical mode decomposition (EMD) and complete ensemble empirical mode decomposition method based on adaptive noise (CEEMDAN) under different conditions, the proposed method show fast and stable performance under an extreme case.

Keywords:

elastic variational mode extraction /
time-correlated single photon counting /
denoise /
feature extraction

作者及机构信息

1.
中国科学院西安光学精密机械研究所, 中国科学院空间精密测量技术重点实验室, 西安　710119

2.
中国科学院大学, 北京　100049

3.
青岛海洋科学与技术试点国家实验室, 青岛　266237

通信作者: 苏秀琴, suxiuqin@opt.ac.cn

基金项目: 中国博士后科学基金(批准号: 2020M683600)和中国科学院战略高技术创新项目(批准号: GQRC-19-19)资助的课题

Authors and contacts

1.
Key Laboratory of Space Precision Measurement Technology, Xi’an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences, Xi’an 710119, China

2.
University of Chinese Academy of Sciences, Beijing 100049, China

3.
Pilot National Laboratory for Marine Science and Technology, Qingdao 266237, China

Corresponding author: Su Xiu-Qin, suxiuqin@opt.ac.cn

Funds: Project supported by the China Postdoctoral Science Foundation (Grant No. 2020M683600) and the Strategic High Technology Innovation Project of the Chinese Academy of Sciences (Grant No. GQRC-19-19)

文章全文 : translate this paragraph

参考文献

[1]	孟文东, 张海峰, 邓华荣, 汤凯, 吴志波, 王煜蓉, 吴光, 张忠萍, 陈欣扬 2020 物理学报 69 019502 Google Scholar Meng W D, Zhang H F, Deng H R, Tang K, Wu Z B, Wang Y R, Wu G, Zhang Z P, Chen X Y 2020 Acta Phys. Sin. 69 019502 Google Scholar
[2]	Aurora M, Framncesco M D R, Aongus M, Robert H, Gerald S B 2019 Opt. Express 27 28437 Google Scholar
[3]	David B L, Gordon W, Matthew O T 2019 ACM Trans. Graph. 38 116
[4]	Li Z P, Huang X, Cao Y, Wang B, Li Y H, Jin W J, Yu C, Zhang J, Zhang Q, Peng C Z, Xu F H, Pan J W 2020 Photonics Res. 8 9
[5]	Swamy P C A, Sivaraman G, Priyanka R N, Raja S O 2020 Coord. Chem. Rev. 411 213233 Google Scholar
[6]	Shangguan M J, Xia H Y, Wang C, Qiu J W, Lin S F, Dou X K, Zhang Q, Pan J W 2017 Opt. Lett. 42 3541 Google Scholar
[7]	Rachael T, Abderrahim H, Aongus M, Martin L, Framk C, Gerald S B 2019 Opt. Express 27 4590 Google Scholar
[8]	Ingerman E A, London R A, Heintzmann R, Gustafsson M G L 2019 J. Microsc. 273 3 Google Scholar
[9]	Chen S M, Halimi A, Ren X M, McCarthy A, Su X Q, McLaughlin S, Buller G S 2020 IEEE Trans. Image Process 29 3119 Google Scholar
[10]	Ren X M, Frick S, McMillan A, Chen S M, Halimi A, Connolly P W R, Joshi S K, Mclaughlin S, Rarity J G, Matthews J C F, Buller G B, 2020 Conference on Lasers and Electro-Optics San Jose, CA, USA May 10–15 2020 pAM3K6
[11]	Chervyakov N, Lyakhov P, Kaplun D, Butusov D, Nagornov N 2018 Electronics 8 135
[12]	Buyukcakir B, Elmaz F, Mutlu A Y 2020 Comput. Biol. Med. 119 103665 Google Scholar
[13]	Flandrin P, Rilling G, Goncalves P 2004 IEEE Signal Process Lett. 11 112 Google Scholar
[14]	Zhang Z C, Hong W C 2019 Nonlinear Dyn. 98 1107 Google Scholar
[15]	Li N, Huang W G, Guo W J, Gao G Q, Z hu, Z K 2020 IEEE Trans. Instrum. Meas. 69 770 Google Scholar
[16]	Asbjornsson G, Erdem I, Evertsson M 2020 Miner. Eng. 147 106086 Google Scholar
[17]	Rakshit M, Das S 2018 Biomed Signal Process Control 40 140 Google Scholar
[18]	Abdelkader R, Kaddour A, Bendiabdellah A, Derouiche Z 2018 IEEE Sens. J. 18 7166 Google Scholar
[19]	Dragomiretskiy K, Zosso D 2014 IEEE Trans. Signal Process. 62 531 Google Scholar
[20]	Li Z X, Jiang Y, Guo Q, Hu C, Peng Z X 2018 Renewable Energy 116 55 Google Scholar
[21]	Nazari M, Sakhaei S M 2018 IEEE J. Biomed. Health Inform. 22 1059 Google Scholar
[22]	Zhang Y G, Pan G F, Chen B, Han J Y, Zhao Y, Zhang C H 2020 Renewable Energy 156 1373 Google Scholar
[23]	许子非岳敏楠李春 2019 物理学报 68 238401 Google Scholar Xu Z F, Yue M N, Li C 2019 Acta Phys. Sin. 68 238401 Google Scholar
[24]	Diao X, Jiang J C, Shen G D, Chi Z Z, Wang Z R, Ni L, Mebarki A, Bian H T, Hao Y M 2020 Mech. Syst. Signal Process. 143 106787 Google Scholar
[25]	Fu W L, Wang K, Li C S, Tan J W 2019 Energy Convers. Manage. 187 356 Google Scholar

施引文献

图 1 系统工作原理图

Fig. 1. The principal components of the system.

下载: 全尺寸图片幻灯片

图 2 实验系统实物图

Fig. 2. Experimental system.

下载: 全尺寸图片幻灯片

图 3 时间相关单光子探测原始信号与6种方法对其重建的信号效果图　(a)激光器理论发射光信号; (b)实际接收信号; (c) Hilbert包络; (d) EMD; (e) CEEMDAN; (f) Haar小波软阈值法; (g) VMD; (h)本文方法

Fig. 3. The curves of time-correlated single photon single-photon signal and its six reconstruction algorithms: (a) Original signal; (b) theoretical output signal; (c) Hilbert envelope; (d) EMD; (e) CEEMDAN; (f) Haar wavelet; (g) VMD; (h) proposed method.

下载: 全尺寸图片幻灯片

图 4 6种方法在不同累积时间下去噪性能对比

Fig. 4. The line chart of the results comparison among proposed method and previously published methods.

下载: 全尺寸图片幻灯片

表 1 6种方法重建信号性能分析

Table 1. Performance comparison among proposed method and previously published methods.

信号特征	重建方法	RMSE/ns	MAE/ns	SMAPE/%
峰值	本文方法	1.779	1.167	1.156
	VMD	2.415	2.167	2.100
	Haar WT	3.829	3.000	2.959
	EMD	4.242	3.667	3.599
	CEEMDAN	5.147	4.167	3.599
	Hilbert包络	4.143	3.167	3.104
半高全宽	本文方法	1.528	1.333	1.056
	VMD	1.969	1.417	1.115
	Haar WT	2.369	2.250	1.096
	EMD	8.539	6.333	5.060
	CEEMDAN	8.150	6.000	4.740
	Hilbert包络	10.00	5.333	4.469
短时能量	本文方法	1.414	1.000	0.855
	VMD	1.826	1.667	1.402
	Haar WT	2.3811	2.000	1.694
	EMD	4.143	3.500	2.962
	CEEMDAN	4.163	3.667	3.107
	Hilbert包络	4.282	3.667	3.140

下载: 导出CSV

表 2 本文方法耗时与其他方法的对比

Table 2. Time consumption comparison among proposed method and previously published methods.

算法	耗时/ms
Hilbert包络	20
本文算法	50
VMD	1470
Haar WT	75
EMD	1100
CEEMDAN	37060

下载: 导出CSV

[1]	孟文东, 张海峰, 邓华荣, 汤凯, 吴志波, 王煜蓉, 吴光, 张忠萍, 陈欣扬 2020 物理学报 69 019502 Google Scholar Meng W D, Zhang H F, Deng H R, Tang K, Wu Z B, Wang Y R, Wu G, Zhang Z P, Chen X Y 2020 Acta Phys. Sin. 69 019502 Google Scholar
[2]	Aurora M, Framncesco M D R, Aongus M, Robert H, Gerald S B 2019 Opt. Express 27 28437 Google Scholar
[3]	David B L, Gordon W, Matthew O T 2019 ACM Trans. Graph. 38 116
[4]	Li Z P, Huang X, Cao Y, Wang B, Li Y H, Jin W J, Yu C, Zhang J, Zhang Q, Peng C Z, Xu F H, Pan J W 2020 Photonics Res. 8 9
[5]	Swamy P C A, Sivaraman G, Priyanka R N, Raja S O 2020 Coord. Chem. Rev. 411 213233 Google Scholar
[6]	Shangguan M J, Xia H Y, Wang C, Qiu J W, Lin S F, Dou X K, Zhang Q, Pan J W 2017 Opt. Lett. 42 3541 Google Scholar
[7]	Rachael T, Abderrahim H, Aongus M, Martin L, Framk C, Gerald S B 2019 Opt. Express 27 4590 Google Scholar
[8]	Ingerman E A, London R A, Heintzmann R, Gustafsson M G L 2019 J. Microsc. 273 3 Google Scholar
[9]	Chen S M, Halimi A, Ren X M, McCarthy A, Su X Q, McLaughlin S, Buller G S 2020 IEEE Trans. Image Process 29 3119 Google Scholar
[10]	Ren X M, Frick S, McMillan A, Chen S M, Halimi A, Connolly P W R, Joshi S K, Mclaughlin S, Rarity J G, Matthews J C F, Buller G B, 2020 Conference on Lasers and Electro-Optics San Jose, CA, USA May 10–15 2020 pAM3K6
[11]	Chervyakov N, Lyakhov P, Kaplun D, Butusov D, Nagornov N 2018 Electronics 8 135
[12]	Buyukcakir B, Elmaz F, Mutlu A Y 2020 Comput. Biol. Med. 119 103665 Google Scholar
[13]	Flandrin P, Rilling G, Goncalves P 2004 IEEE Signal Process Lett. 11 112 Google Scholar
[14]	Zhang Z C, Hong W C 2019 Nonlinear Dyn. 98 1107 Google Scholar
[15]	Li N, Huang W G, Guo W J, Gao G Q, Z hu, Z K 2020 IEEE Trans. Instrum. Meas. 69 770 Google Scholar
[16]	Asbjornsson G, Erdem I, Evertsson M 2020 Miner. Eng. 147 106086 Google Scholar
[17]	Rakshit M, Das S 2018 Biomed Signal Process Control 40 140 Google Scholar
[18]	Abdelkader R, Kaddour A, Bendiabdellah A, Derouiche Z 2018 IEEE Sens. J. 18 7166 Google Scholar
[19]	Dragomiretskiy K, Zosso D 2014 IEEE Trans. Signal Process. 62 531 Google Scholar
[20]	Li Z X, Jiang Y, Guo Q, Hu C, Peng Z X 2018 Renewable Energy 116 55 Google Scholar
[21]	Nazari M, Sakhaei S M 2018 IEEE J. Biomed. Health Inform. 22 1059 Google Scholar
[22]	Zhang Y G, Pan G F, Chen B, Han J Y, Zhao Y, Zhang C H 2020 Renewable Energy 156 1373 Google Scholar
[23]	许子非岳敏楠李春 2019 物理学报 68 238401 Google Scholar Xu Z F, Yue M N, Li C 2019 Acta Phys. Sin. 68 238401 Google Scholar
[24]	Diao X, Jiang J C, Shen G D, Chi Z Z, Wang Z R, Ni L, Mebarki A, Bian H T, Hao Y M 2020 Mech. Syst. Signal Process. 143 106787 Google Scholar
[25]	Fu W L, Wang K, Li C S, Tan J W 2019 Energy Convers. Manage. 187 356 Google Scholar

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