A time-correlated single photon counting signal denoising method based on elastic variational mode extraction

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.