Objectives Accurate reconstruction of ocean surface waves from X-band marine radar imagery remains a challenging task due to the complex nonlinear characteristics of real sea states and the limitations of radar backscattering mechanisms. Traditional radar-based inversion models often suffer from feature blurring, frequency aliasing, and poor generalization when encountering highly nonlinear and multi-scale ocean waves.

Methods To address these challenges, this study proposes an improved wave field reconstruction approach that integrates the fully nonlinear wave theory with deep learning techniques, aiming to enhance the accuracy and robustness of radar-derived sea surface estimation. In the proposed framework, the radar backscattered intensity images are first preprocessed and decomposed in the temporal domain using Bidimensional Empirical Mode Decomposition (BEMD). This technique adaptively extracts a series of Intrinsic Mode Functions (IMFs) and residual components that represent oscillations at different frequency scales. By separating frequency-dependent modes, BEMD effectively mitigates mode mixing and preserves the intrinsic spatial–temporal variability of the radar data. The resulting multi-component dataset is then structured as a multi-channel input to fully capture the physical diversity of the radar echo signals. Subsequently, the multi-channel input is fed into a modified U-Net network architecture augmented with both spatial attention and channel attention mechanisms. The spatial attention module enhances the model’s sensitivity to locally significant spatial features such as wave crests, troughs, and shadow regions, while the channel attention mechanism adaptively reweights feature channels to emphasize physically meaningful representations. Together, these improvements enable the network to selectively focus on the most relevant radar patterns that correspond to nonlinear wave dynamics. The training process is conducted using numerically simulated radar data generated under various sea states derived from the High-Order Spectral (HOS) wave model, which provides realistic nonlinear surface elevations and velocity fields. Several benchmark models, including the original U-Net and other conventional convolutional architectures, are used for comparative analysis.

Results The experimental results demonstrate that the proposed hybrid method significantly outperforms baseline models in terms of reconstruction precision and stability, particularly under complex and nonlinear wave conditions. The integration of BEMD decomposition and dual-attention learning effectively enhances feature separability and mitigates spectral distortion, resulting in more accurate spatial restoration of the sea surface topography. Furthermore, the proposed framework exhibits strong generalization capability, maintaining consistent accuracy across different radar observation geometries and wave spectra..

Conclusions In conclusion, this study presents a comprehensive and effective methodology for high-fidelity radar-based wave field reconstruction. By combining the physical rigor of the fully nonlinear wave model with the representational power of deep learning, the proposed approach achieves a substantial improvement in reconstruction accuracy and robustness. These findings highlight the potential of physics-informed deep learning frameworks for advancing the application of X-band marine radar in ocean surface monitoring, environmental forecasting, and maritime engineering operations.