CV-CPKAN: Complex-Valued Convolutional Kolmogorov–Arnold Framework for PolSAR Image Classification

Deep learning has significantly advanced PolSAR image processing, with a growing trend of integrating mathematical theories into deep neural networks to enhance their capabilities with regard to complex data. Kolmogorov–Arnold networks (KANs), which leverage nonlinear mappings derived from the Kolmogorov–Arnold theorem for automatic feature extraction, present a promising yet underexplored direction for PolSAR image classification. However, existing real-valued KAN-based layers fall short in effectively exploiting the complex-valued characteristics of PolSAR data, overlooking the important phase information. In this paper, we propose a complex-valued convolutional Kolmogorov–Arnold framework for PolSAR image classification (CV-CPKAN). The framework introduces complex KAN convolution layers, which are further employed to construct a multi-branch complex KAN convolution (MBComplexKConv) block, effectively extracting multi-scale features from both the amplitude and phase components of PolSAR data. Additionally, a complex-valued variant of PolyLoss (CV-PolyLoss) is proposed as our classification loss function. Through extensive evaluations on three benchmark PolSAR datasets, CV-CPKAN consistently surpasses state-of-the-art models based on CNN, Transformer and Mamba, achieving overall accuracies of 99.86%, 99.80% and 99.74% on Flevoland, San Francisco and Oberpfaffenhofen datasets, respectively. These results underscore the effectiveness of integrating convolutions with KAN-based nonlinear mapping, providing a new avenue for further research in PolSAR image classification.