Graph-enhanced global dependency modeling for complex wavefront retrieval

Convolutional neural networks (CNNs) have become the dominant backbone in complex wavefront retrieval (CWR). However, their reliance on local receptive fields constrains their ability to capture global dependencies in wavefront data, leading to performance bottlenecks. To address this challenge, we propose a graph-enhanced neural network (GENet), which integrates graph convolution into a convolutional backbone to jointly exploit local feature extraction and global dependency modeling. This topology-aware design conforms to the physical characteristics of wavefront data, enabling message passing across non-local yet semantically relevant regions and substantially enhancing the network's representational capacity. Both simulations and experiments indicate that GENet significantly outperforms GS- and CNN-based methods in amplitude and phase reconstruction-for a representative test case, it achieves an amplitude SSIM of 0.78 and a phase RMSE of 0.52 radians, compared to 0.22/1.15 for GS and 0.42/1.08 for IPMnet-highlighting its potential for robust and high-precision CWR in practical applications.