Adaptive Variational Mode Decomposition and Principal Component Analysis-Based Denoising Scheme for Borehole Radar Data

To address the significant impact of noise on the target detection performance of borehole radar (BHR), a key type of ground-penetrating radar (GPR), a denoising scheme based on the whale optimization algorithm (WOA) for adaptive variational mode decomposition (VMD) and multiscale principal component analysis (MSPCA) is proposed. This study initially conducts the modal decomposition of BHR data using an improved adaptive VMD method based on the WOA; it then automatically selects modes meeting specific frequency band standards. The correlation coefficients between these modes and the original signal are computed, discarding weakly correlated modes before signal reconstruction. Finally, MSPCA further suppresses noise, yielding denoised BHR data. Simulations show that the proposed scheme increases the signal-to-noise ratio by 17.964 dB or higher, surpassing the more established denoising techniques of robust principal component analysis (RPCA), MSPCA, and empirical mode decomposition (EMD), and obtains the most favorable results in terms of the RMSE and MSE metrics. The experimental results demonstrate that the proposed scheme more effectively suppresses vertical and random noise signals in BHR data. Both the numerical simulations and experimental results confirm the effectiveness of this scheme in noise reduction for BHR data.