Abstract: To address the challenges of high computational complexity in traditional full waveform inversion, limited nonlinear modeling capability, and insufficient utilization of physical features in existing deep learning methods for Ground Penetrating Radar (GPR) inversion, this paper proposes HUKAN, a GPR permittivity inversion method integrating Hilbert feature enhancement and attention gating. Three key improvements are implemented based on the UKAN architecture: a Hilbert Feature Extraction and Spatial Adaptive Fusion module (HFE-SA) is introduced to extract instantaneous envelope, phase, and frequency attributes, which are dynamically fused via spatial adaptive attention to enhance physical feature representation; a Spatial-Channel Attention Gating mechanism (SCAG) is designed at skip connections to enable adaptive feature selection between encoder and decoder, effectively suppressing noise propagation; a Logarithmic Dynamic Range Compression (LDRC) strategy is adopted to compress the dynamic range of permittivity values and improve reconstruction accuracy for low-value anomalies. Experimental results on simulated datasets containing various typical geological structures demonstrate that HUKAN reduces mean squared error by 45.5%, improves structural similarity index by 1.91%, and increases peak signal-to-noise ratio by 2.72 dB compared with the baseline UKAN model. Ablation studies validate the independent contributions and synergistic effects of each component, and attention map visualization reveals the hierarchical feature selection mechanism and physical interpretability of SCAG across different resolution levels, while noise experiments confirm the robustness of the proposed method. Furthermore, validation experiments on real GPR data collected from concrete test blocks with drilled cavities demonstrate that, through domain-adaptive fine-tuning, HUKAN achieves a mean target localization error of only 0.75 mm, representing a 73.4% reduction compared with UKAN, and exhibits reliable target detection, localization, and permittivity reconstruction capabilities.