Single-photon imaging uses single-photon-sensitive picosecond-resolution sensors to capture 3D structure and supports diverse applications, but success remains mostly limited to simple scenes. In complex scenarios, traditional methods degrade and deep learning methods lack flexibility and generalization. Here, we propose a physics-informed deep neural network (PIDNN) framework that effectively addresses both aspects, adapting to complex and variable sensing environments by embedding imaging physics into the deep neural network for unsupervised learning. Within this framework, by tailoring the number of U-Net skip connections, we impose multi-scale spatiotemporal priors that improve photon-utilization efficiency, laying the foundation for addressing the inherent low-signal-to-background ratio (SBR) problem in subsequent complex scenarios. Additionally, we introduce volume rendering into the PIDNN framework and design a dual-branch structure, further extending its applicability to multiple-depth and fog occlusion. We validated the performance of this method in various complex environments through numerical simulations and real-world experiments. The results of photon-efficient imaging with multiple returns show robust performance under low SBR and large fields of view. The method attains lower root mean-squared error than traditional methods and exhibits stronger generalization than supervised approaches. Further multiple depths and fog interference experiments confirm that its reconstruction quality surpasses existing techniques, demonstrating its flexibility and scalability. Both simulation and experimental results validate its exceptional reconstruction performance and flexibility.
Cai et al. (Thu,) studied this question.