U-KAN: Hybrid Spatial-Functional Deep Learning for Tumor Depth Estimation in Fluorescence-Guided Cancer Surgery

Accurately estimating subsurface tumor depth during fluorescence-guided surgery remains an open challenge, as current intraoperative methods provide only surface-level fluorescence contrast without quantitative depth information. Spatial Frequency Domain Imaging offers a pathway toward quantitative fluorescence imaging by capturing both reflectance and optical property maps; however, its application to tumor depth estimation is limited by the scarcity of patient-derived datasets and significant domain gaps between simulated and experimental measurements. To address these challenges, we propose U-KAN, a hybrid deep learning framework that combines a siamese attention U-Net for spatial feature extraction with a Kolmogorov-Arnold Network (KAN) regression head for functional depth mapping. The U-Net captures morphological and structural cues from fluorescence and optical property inputs, while the KAN performs nonlinear pixelwise regression to improve generalization under limited data. Experiments on diffusion-theory, Monte Carlo, and patient-derived phantom datasets demonstrate that the hybrid model achieves more accurate and robust tumor depth estimation than either model alone, establishing a promising foundation for quantitative, depthaware fluorescence imaging in surgical oncology. U-KAN reduced tumor-region MAE by more than 30 % and cut minimum-depth errors nearly in half on phantom data, demonstrating markedly improved cross-domain robustness.