Wavelet spectral-aware Kolmogorov-Arnold Network for organ and tumor segmentation

High-precision organ and tumor segmentation is a fundamental task in medical image analysis, requiring a balance between global anatomical consistency and local detail delineation to support clinical diagnosis and treatment planning. However, existing deep learning methods are often constrained by the nonlinear representational capacity of fixed activation functions, making it difficult to effectively model complex anatomical structures and lesion. To address this, we propose MedWKAN, a novel 3D organ and tumor segmentation model that embeds wavelet spectral-aware mechanism within Kolmogorov-Arnold Network. Specifically, the proposed Gram Polynomial-inspired Wavelet Kolmogorov-Arnold (GWKA) module reconstructs the KAN operator through polynomial nonlinear mapping of wavelet low-frequency components during encoding, enabling adaptive global modeling while preserving high-frequency details for enhanced nonlinear feature representation. Furthermore, the Multi-Residual Collaborative Module (MRCM) employs hierarchical feature modeling and progressive residual fusion in skip connections to achieve semantic alignment and stable feature propagation between the encoder and decoder. The synergy between GWKA and MRCM enables unified representation of complex anatomical structures and lesion regions. Experiments on six public datasets demonstrate that MedWKAN outperforms ten state-of-the-art methods in terms of Dice and IoU metrics, highlighting its accuracy and generalizability.