## 5 Field Data Test
And more importantly, as listed in Table 1, PWD lasted approximately 39 min, while MWT-MSSA finished the task in 12 min, resulting in a 69.2% improvement in computational efficiency. In this sense, the  
Figure 23: Coefficient profiles of the 5-level wavelet transform of the observed GPR data in Figure 22. (**a,e,i,m,q**) are the profiles reconstructed from the low-frequency approximation coefficients of level 1–5. (**b,f,j,n,r**) are the profiles reconstructed from the high-frequency horizontal detail coefficients of level 1–5. (**c,g,k,o,s**) are the profiles reconstructed from the high-frequency vertical detail coefficients of level 1–5. (**d,h,l,p,t**) are the profiles reconstructed from the high-frequency diagonal detail coefficients of level 1–5. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Reconstructed Profiles** & **Total Clusters** & **Total Singular Values** & **Reconstructed Clusters** & **Reconstructed Singular Values** \\ \hline Figure 23m & 10 & 425 & 4–8 & 7–58 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: _k_-means clustering parameters and singular spectrum truncation for GPR field data. multiple singular spectrum analysis (MSSA). The intrinsic attributes of near-linear reflections and hyperbolic diffractions can be specified by analyzing GPR signals using multiple level detailed coefficients created by singular value decomposition and \(k\)-means clustering. By using clustering analysis, the singular spectrum can be categorically divided based on similarity features, and several multiple clusters of singular values that represent the residual diffraction are identified to contribute to the reconstruction of the GPR diffraction. For the repetition of the proposed method, we focus on the impact of wavelet basis functions on separation performance by investigating three common wavelet basis functions includes haar, db4, and rbio4.4 based on third level wavelet transformation, along with analyzing the determination of clustering parameters and robustness against noise. Numerical experiments and field trials demonstrate that the biorthogonal wavelet basis function bior4.4 provides a remarkable efficiency for separating GPR diffraction. Notably, the \(k\)-means algorithm should take into account the complexity of the GPR wavefield, which typically ranges from 9 to 15 in the proposed MWT-MSSA. The proposed approach has the benefit of reducing energy loss at the diffraction vertex, decreasing residual diffraction energy within the reflection profile, and improving noise immunity when compared to the classical Plane Wave Deconstruction (PWD) method. Additionally, the computation efficiency is raised to 70-80%, which allows for the creation of high-resolution diffraction profiles for efficient data processing and subsequent subtle imaging. Methodology, [PERSON] ([PERSON]) and [PERSON] ([PERSON]); validation, [PERSON] ([PERSON]), [PERSON] ([PERSON]), Z.H. and F.Z. ; formal analysis, Z.H. ; investigation, [PERSON] ([PERSON]), Z.H. and F.Z. ; data curation, [PERSON] ([PERSON]); writing--original draft, [PERSON] ([PERSON]); writing--review and editing, [PERSON] ([PERSON]); supervision, F.Z. ; Funding acquisition, [PERSON] ([PERSON]). All authors have read and agreed to the published version of the manuscript. This research are supported by the National Natural Science Foundation of China (Grant Nos. 42364010) and the Natural Science Foundation of Guangxi Province (Grant Nos. 2022 GXNSFAA035595). Not applicable. The data presented in this study are available upon request from the corresponding author. The authors greatly appreciate the anonymous reviewers and academic editors for their valuable comments. The authors declare no conflicts of interest.