GPR Diffraction Separation by Incorporating Multilevel Wavelet Transform and Multiple Singular Spectrum Analysis

By leveraging amplitude differences between reflected and diffracted signals in Ground Penetrating Radar (GPR) data, multiple singular spectrum analysis (MSSA) is considered an attractive approach to separate diffraction, which has identified great potential in their detectability of small-scale geological structures. However, conventional MSSA encounters difficulties in pinpointing the singular value threshold that corresponds to reflection, diffraction, and noise within the singular spectrum, leading to a resolution loss of the extracted diffraction profile. To address this issue, this paper develops a new technique that incorporates multilevel wavelet transform (MWT) and MSSA to separate GPR diffraction. By first implementing the MWT on GPR data decompose, the strategy can obtain various approximate detailed coefficients of multiple transformation levels for the subsequent inverse MWT to construct the corresponding coefficient profile. The issue of coefficient profiles that depict reflections often contains residual diffractions is also addressed by performing multiple singular spectrum SVDs based on the Hankel matrix within the dominant frequency domain. Building upon this, the k-means clustering algorithm is introduced to perform MSSA for classifying singular values into k categories. The diffraction wavefield is rebuilt by combining these outcomes with the coefficient profiles that depict diffractions at various transformation levels. Numerical tests showcase that the biorthogonal wavelet basis function bior4.4 provides remarkably efficient GPR diffraction separation performance, and the number of clusters in the k-means clustering algorithm typically ranges from 9 to 15, accounting for the complexity of the wave components. Compared to plane wave deconstruction (PWD), the proposed MWT-MSSA approach reduces energy loss at the diffraction vertex, decreases residual diffraction energy within the reflection profile, and enhances computational efficiency by approximately 70–80% to facilitate the subsequent subtle imaging.