A Hyperbola-Prior-Guided Initialization Strategy for Ground-Penetrating Radar Waveform Inversion

Ground-penetrating radar (GPR) waveform inversion is sensitive to the initial model. This study proposes a hyperbola-prior-guided initialization strategy for two-dimensional GPR permittivity inversion. B-scan preprocessing, robust hyperbola fitting, and bootstrap resampling are used to estimate target geometry and positional uncertainty. The fitted prior, an engineering radius constraint, and uncertainty estimates define an adaptive region; envelope- and amplitude-based coarse scanning selects an initial anomaly permittivity without using the true target value. Four initial models—a homogeneous background (M1), a perturbed model (M2), a hard-boundary prior model (M3), and a sigmoid soft-boundary model (M4)—are compared under identical inversion settings. Simulations of a single PVC pipe in homogeneous soil show that the prior-informed models offer complementary benefits relative to conventional initializations. The main trends remain stable across tested noise levels: M3 provides better regional and boundary reconstruction when the geometric prior is accurate, whereas M4 generally yields smaller target-center errors and lower ROI-RMSE degradation under the tested geometric perturbations.