DINFNN: Data Inpainting Fourier Neural Network for Cloud-Induced Extensive Missing Area in Sea Surface Temperature

Sea surface temperature (SST) serves as a critical indicator of oceanic environmental changes. However, the uninterrupted observation of vast oceanic areas via remote sensing is frequently impeded by cloud cover, resulting in persistent data gaps. Consequently, the completion of SST data emerges as an essential technique. Recently, the utilization of deep neural networks (DNNs), particularly generative models, has shown promising results by effectively leveraging historical data for training. However, these approaches often concentrate on spatial domain features, neglecting the inherent chaotic nature of the ocean as a complex system, thus failing to accurately reflect the complexity of oceanic processes. Therefore, this study introduces a novel approach to SST completion focusing on frequency domain features, utilizing Fourier neural operators. We propose an innovative Data INpainting Fourier Neural Network (DINFNN), for data completion to facilitate feature learning in complex oceanic systems. Our method employs a triple-stream neural network to capture periodic steady-state features, adjacent temporal features, and current context. By integrating high-pass and low-pass filters and dynamically combining them, we adaptively extract essential frequency domain features for completion. Particularly, a two-cascaded fusion module is utilized dynamically to amalgamate these distinct attributes to form a composite feature set, encompassing both steady and dynamic frequency domain elements, aimed at achieving a comprehensive SST field reconstruction. In our experimental evaluations, our method demonstrates significant improvements under various conditions. Specifically, when the cover ratio is 68% and the Noise-to-Signal (N/S) is set to 0.1, 0.2, and 0.3, we observe enhancements of 11.2%, 10.8%, and 16.2% in R-squared ( $R^{2}$ ), respectively. Furthermore, corresponding reductions of 7.2%, 13.1%, and 7.3% in root mean square error (RMSE) are achieved, respectively. Moreover, comprehensive ablation experiments confirm the effectiveness of each component within our method and emphasize the superiority of DINFNN over conventional operators.