关键词: 探地雷达（GPR）, 变分模态分解（VMD）, 能量损失比, 奇异谱分析（SSA）, 信号去噪

Abstract:  Due to the influence of equipment and environmental factors, the signals collected by ground-penetrating radar (GPR) are vulnerable to varying degrees of noise interference. Traditional variational mode decomposition (VMD) suppresses noise by searching for the optimal solution of variational modes to separate the components with different center frequencies. However, the selection of optimal mode number is challenging and subjective, resulting in the reconstructed signals being affected by different degrees of oscillation. To solve these problems, we proposed a combined denoising method based on the adaptive VMD and singular spectrum analysis (SSA). Firstly, the energy loss ratio is defined to facilitate the adaptive selection of the optimal mode number, and the Pearson correlation coefficient method is employed to extract the valid signal. Secondly, to solve the problem of the low-frequency oscillation phenomenon in VMD, SSA is further used to perform secondary filtering to improve the signal-to-noise ratio (RSN). The effectiveness of the proposed method is verified by the synthetic wavelet experiment, numerical simulation experiment, and field experiment. In the synthetic wavelet experiment, the SNR of VMD-SSA processing is improved maximum by 13.587 8 dB over the ensemble empirical mode decomposition (EEMD) and the traditional VMD methods; in the numerical simulation experiment, the SNR of the processed B-scan using the VMD-SSA method is improved by 3.765 9 dB and 2.655 7 dB respectively compared with the EEMD and traditional VMD methods; in addition, the background noise and the random noise are also properly suppressed in the field data processing. The proposed method not only solves the oscillation problem but also highlights the features of the abnormal signals more effectively.

Key words: ground-penetrating radar (GPR), variational mode decomposition (VMD), energy loss ratio, singular spectrum analysis (SSA), signal denoising