Due to the susceptibility of LiDAR echo signals to various noise interferences, which severely affect their detection quality and accuracy, this paper proposes a joint denoising method combining Variational Mode Decomposition (VMD), Crested Porcupine Optimizer (CPO), and Improved Wavelet Thresholding (IWT), named VMD-CPO-IWT. The parameter-adaptive CPO optimization algorithm is employed to optimize the key parameters of VMD (decomposition level k, quadratic penalty factor α), effectively solving the challenge of determining the optimal parameter combination in the VMD algorithm. Based on the probability density function (PDF), the Wasserstein distance is used as a similarity metric to screen intrinsic mode functions. Subsequently, the IWT is applied to obtain the optimal wavelet threshold, which compensates for the shortcomings of traditional threshold methods while further suppressing both low-frequency and high-frequency noise in the signal, ultimately yielding the denoising result. Experimental results demonstrate that for both simulated signals and actual LiDAR echo signals, the VMD-CPO-IWT method outperforms Neighcoeff-db4 wavelet denoising (WT-db4), EMD combined with detrended fluctuation analysis denoising (EMD-DFA), and VMD combined with Whale Optimization Algorithm (VMD-WOA) in terms of improving the Signal-to-Noise Ratio (SNR) and reducing the Root Mean Square Error (RMSE). For the actual LiDAR echo signal at a detection range of 25 m, the SNR is improved by 13.64 dB, and the RMSE is reduced by 62.6%. This method provides an efficient and practical solution for denoising LiDAR echo signals.
Zha et al. (Tue,) studied this question.