## 5 Conclusions  
In this paper, we propose a novel TV+MSG composite regularization approach for 3D ground-penetrating radar full-waveform inversion, offering an effective solution for the simultaneous reconstruction of high-contrast subsurface parameters. This methodology employs TV regularization for permittivity reconstruction and MSG regularization for conductivity estimation, for which derivation and comparative analyses were conducted in detail.  
The numerical experiments demonstrate that our composite model-constrained FWI method significantly enhances both the accuracy and stability of simultaneous permittivity and conductivity reconstruction in challenging high-contrast subsurface scenarios. The results show that it can effectively suppress artifacts while preserving an appropriate feature resolution in permittivity imaging via TV regularization, as well as improving boundary sharpness and reducing volumetric distortion in conductivity reconstruction via MSG regularization, thereby achieving robust convergence behavior throughout the inversion process.  
Although the method described in this paper is limited to a simple synthetic case and both the computational performance and reconstruction accuracy require further improvement, it shows potential for practical GPR applications in geophysical exploration, underground utility mapping, and other high-resolution subsurface imaging tasks re  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Limitation** & **Future Work** & **Alternative Method** \\ \hline Manual tuning of parameters & Design adaptive strategy & Combination with automatic functions or \\ No analysis of noise & Discuss noise sensitivity & Multiple data surveys \\ Simple scenario with & & Unstructured mesh subdivision for \\ blocky anomalies & & irregular anomalies \\ Initial models with background & Discuss sensitivity of initial models & Prior information constraint \\ Low accuracy of high & Improve accuracy at depth & Weighting strategy at depth \\ conductivity in deep regions & & Variable projection methods avoiding \\ Reliance on synthetic data & Application in field data & wavelet estimation \\ High computational cost & Parallel acceleration strategy & Iterative solution for large equation systems \\ \hline \hline \end{tabular}
\end{table}
Table 6: Limitations and future alternative methods.  
quiring reliable subsurface media estimation. This study--particularly its discussion of regularization strategies in dual-parameter GPR FWI--serves to motivate the future exploration of more potential regularization combinations for multi-parameter geophysical inverse problems.  
Conceptualization, S.D. and D.F.; methodology, S.D., D.F. and X.W.; software, S.D. and X.W.; validation, S.D.; formal analysis, S.D.; investigation, S.D.; writing--original draft preparation, S.D., T.Y., S.L. and M.Y.; writing--review and editing, D.F. and X.W.; visualization, S.D. and D.F.; supervision, D.F. and X.W.; project administration, D.F.; funding acquisition, D.F. and X.W. All authors have read and agreed to the published version of the manuscript.  
This research was funded in part by the National Natural Science Foundation of China, grant numbers 42474191 and 42474196, and in part by the Natural Science Foundation of Hunan Province, grant number 2025 JJ40033.  
Not applicable.  
The data used in this study are available on request from the authors.  
The authors have reviewed and edited the output and take full responsibility for the content of this publication.  
The authors declare no conflicts of interest.