It is a key issue denoising airborne LiDAR bathymetry (ALB) full waveforms in extracting underwater topography. Empirical mode decomposition (EMD) is suitable for the nonlinear and nonstationary characteristics of ALB full waveforms and obviates the necessity for preset basis functions. Still, the direct discarding of noise-dominated intrinsic mode functions (IMFs) by traditional EMD leads to oversmoothing or undersmoothing of signals. In this letter, an EMD-based multiresolution analysis (EMD-MRA) method is suggested for ALB full-waveform denoising. This method utilizes the zero-padding technique based on the discrete cosine transform (DCT) to achieve the second-layer decomposition of the noise-dominant IMFs obtained in the first layer. Subsequently, Savitzky–Golay (S–G) filtering is employed for the noise-dominant IMFs from the second-layer decomposition. The intricate details embedded in the IMFs are meticulously extracted through a process of scaling the signal from a coarse to a fine resolution, ensuring the preservation of valuable information. The experiments, conducted using measurement data, demonstrate that the EMD-MRA method is effective in adaptively denoising the ALB full-waveform data, showcasing sufficient robustness. Compared with traditional EMD and wavelet threshold denoising (WTD) methods, the signal-to-noise ratio (SNR) of the denoising results using the proposed approach is improved by 6.769 and 0.971 dB in area a and by 19.672 and 5.317 dB in area b. The root mean square error (RMSE) is reduced by 0.455 and 0.971 in area a and by 0.979 and 0.47 in area b, effectively retaining the complex details of the original signal.

中文翻译：

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使用基于 EMD 的多分辨率分析对机载 LiDAR 测深全波形进行自适应去噪

机载激光测深（ALB）全波形去噪是提取水下地形的关键问题。经验模态分解（EMD）适合ALB全波形的非线性和非平稳特性，无需预设基函数。尽管如此，传统 EMD 直接丢弃噪声主导的本征模态函数 (IMF) 会导致信号过度平滑或欠平滑。在这封信中，建议采用基于 EMD 的多分辨率分析 (EMD-MRA) 方法来进行 ALB 全波形去噪。该方法利用基于离散余弦变换（DCT）的补零技术来实现第一层获得的噪声主导IMF的第二层分解。随后，对第二层分解中的噪声主导 IMF 采用 Savitzky-Golay (S-G) 滤波。通过将信号从粗分辨率缩放到精细分辨率的过程，精心提取嵌入 IMF 中的复杂细节，确保保留有价值的信息。使用测量数据进行的实验表明，EMD-MRA方法能够有效地对ALB全波形数据进行自适应去噪，并表现出足够的鲁棒性。与传统EMD和小波阈值去噪（WTD）方法相比，该方法去噪结果的信噪比（SNR）在a区域分别提高了6.769和0.971 dB，在b区域分别提高了19.672和5.317 dB 。 a区域的均方根误差（RMSE）降低了0.455和0.971，b区域的均方根误差（RMSE）降低了0.979和0.47，有效保留了原始信号的复杂细节。