Improved UNet++ Based on Kolmogorov-Arnold Convolutions

Deep learning models, particularly U-Net, have achieved remarkable success in medical image segmentation. However, U-Net faces limitations due to the semantic gap between its encoder and decoder, which can reduce segmentation accuracy. To overcome this, U-Net++ introduced dense skip connections to bridge this gap. Recently, Kolmogorov-Arnold Networks (KANs), inspired by the Kolmogorov-Arnold theorem, have garnered attention for replacing linear weight matrices with learnable splines, thereby reducing model parameters and improving generalizability. In this paper, we propose an enhanced U-Net++ architecture that replaces traditional Convolutional Neural Networks (CNNs) with convolutional KANs. To further optimize performance, we conducted an ablation study evaluating various nonlinear convolutional layer functions, including B-splines, Radial Basis Functions (RBFs), Chebyshev polynomials, and Rectified Linear Unit (ReLU) KANs. Our results demonstrate the critical impact of the chosen basis function on segmentation accuracy, with the Jacobi-Kolmogorov Arnold Network achieving the best performance. The proposed architecture demonstrated superior accuracy across two datasets from different imaging modalities.