A Diffraction–Reflection Jointly Constrained Multi-Scale Inversion Framework for Dielectric Permittivity Estimation on Chang’E-4 LPR Data

Summary Retrieving dielectric permittivity from ground-penetrating radar (GPR) data in planetary environments is challenging due to limited ground-truth constraints and complex observational conditions governing radar signal acquisition. Moreover, the band-limited nature of radar signals fundamentally restricts the simultaneous recovery of large-scale structural trends and fine-scale variations. Existing approaches typically rely on a single type of wavefield, resulting in an intrinsic trade-off between stability and resolution. In this study, we propose a unified diffraction–reflection jointly constrained multi-scale inversion framework for dielectric permittivity estimation from Chang’E-4 Lunar Penetrating Radar (LPR) data. Diffraction signals are exploited through migration velocity analysis to constrain the large-scale background velocity field, while reliable reflection coefficients are recovered through sequential mixed-phase wavelet correction and sparse reflectivity recovery, and subsequently integrated to reconstruct band-limited logarithmic-impedance perturbations. The reflection-derived perturbations are first calibrated to the diffraction-derived background through spectral-power matching and subsequently fused in the logarithmic-impedance domain, thereby preserving the original spectral relationship during multi-scale integration. Synthetic experiments and application to Chang’E-4 LPR data demonstrate that the proposed framework preserves large-scale structural trends, enhances layer-to-layer contrasts, and improves the delineation of localized subsurface features, thereby improving the stability and resolution of dielectric permittivity estimation. Application to extensive Chang’E-4 LPR observations spanning 70 lunar days further reveals a stratified subsurface structure with lateral variations along the rover traverse and delineates impact-related features. These results demonstrate that the proposed framework provides a physically consistent and robust strategy for multi-scale dielectric permittivity reconstruction in complex planetary subsurface environments.