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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.
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Keywords:
- elastic variational mode extraction /
- time-correlated single photon counting /
- denoise /
- feature extraction
[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
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[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
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[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
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[22] Zhang Y G, Pan G F, Chen B, Han J Y, Zhao Y, Zhang C H 2020 Renewable Energy 156 1373
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[23] 许子非岳敏楠李春 2019 物理学报 68 238401
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Xu Z F, Yue M N, Li C 2019 Acta Phys. Sin. 68 238401
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图 1 系统工作原理图
Figure 1. The principal components of the system.
图 2 实验系统实物图
Figure 2. Experimental system.
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
Figure 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.
图 4 6种方法在不同累积时间下去噪性能对比
Figure 4. The line chart of the results comparison among proposed method and previously published methods.
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 
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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
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[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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