Low-sampling 3D Fourier single-pixel imaging for phase unwrapping in turbid underwater using hNet

In underwater scattering environments, the attenuation effect of light makes it challenging to capture clear images and realize the 3D reconstruction of underwater objects. Single-pixel imaging (SPI) can overcome the limitations of traditional optical imaging, but its imaging efficiency is low due to the cumbersome acquisition process. This paper proposes a new, to our knowledge, Fourier SPI method based on hNet to achieve phase unwrapping and 3D reconstruction of underwater objects at low sampling rates under high-turbidity conditions. First, a 3D-UFSPI-hNet network is designed to accurately recover the absolute phases of objects, and it can reconstruct highly accurate absolute phases from low-sampling-rate deformed fringe patterns in strongly scattering environments, thereby reducing the time required for image acquisition and phase unwrapping. Subsequently, the 3D shape reconstruction of underwater objects is achieved by combining the system calibration parameters using the self-developed SPI system. Numerical simulations and physical experiments show that the proposed method can achieve high-quality absolute phase reconstruction images and 3D imaging at a sampling rate of 5% and a turbidity of 50NTU for the first time. Compared with 3D-SPI methods based on traditional Fourier SPI, such as the UNet and the UNet 3+, our approach offers a new strategy for underwater optical 3D imaging, especially in environments with low sampling rates and strong scattering conditions.