Objective  Single-pixel imaging (SPI) has emerged as an innovative technology with significant potential for applications in challenging environments, particularly in underwater imaging. Unlike traditional imaging systems, SPI utilizes a single photodetector to capture information from the scene, reducing the complexity of the system while maintaining high performance in terms of anti-interference and long-range capabilities. These advantages make SPI a promising solution for underwater imaging, where conventional methods often fail due to issues such as turbidity, scattering, and poor lighting conditions. Despite its benefits, however, SPI faces significant challenges when applied to underwater environments, such as the checkerboard effect caused by Krawtchouk moments (KMSI), a key technique used in SPI. Additionally, the backscattering of light in the water complicates the process of obtaining high-quality images. To address these challenges and further enhance the imaging quality of SPI systems in underwater conditions, this work introduces a novel approach based on Krawtchouk moments, known as KMSI. The aim of this research is to eliminate the checkerboard effect and reduce the impact of backscattering in underwater environments, ultimately advancing the potential of SPI for high-quality underwater imaging and lidar applications.

Methods  The proposed method involves the integration of KMSI into a single-pixel imaging system, specifically designed to tackle the unique challenges posed by underwater environments. To overcome the checkerboard effect typically observed with original KMSI methods, the research introduces a distance-selected slice imaging system. This system consists of a pulsed light source and a time-resolved gated detector, both of which are crucial in addressing the challenges posed by turbidity and backscattering in underwater environments. The pulsed light source provides a controlled illumination of the scene, while the time-resolved gated detector ensures that only light reflected from a specific distance is captured (Fig.5). This configuration allows for effective rejection of light scattered from the surrounding water, ensuring that only relevant data is used to form the image. Experimental setups, both in real underwater environments and simulated conditions, were employed to validate the effectiveness of the proposed system (Fig.10). The system was tested under various turbidity and turbulent conditions at sub-Nyquist sampling ratios, specifically at a ratio of 0.05, which is known to be a challenging condition for most SPI systems.

Results and Discussions  The experimental and simulation results demonstrate that the KMSI system significantly outperforms other existing SPI models, especially in challenging underwater environments (Tab.1). Under sub-Nyquist sampling conditions, where traditional SPI systems often struggle with maintaining image quality due to insufficient sampling, the KMSI-based SPI system was able to produce clearer, more accurate images (Fig.2 and Fig.4). One of the key innovations of this system is its ability to eliminate the checkerboard effect, a common problem encountered with Krawtchouk moments when applied to imaging systems. The distance-selected slice imaging system proved to be highly effective in filtering out unwanted backscattered light, which is a major issue in underwater imaging. By using time-resolved gating, the system selectively captures light reflected from objects at specific distances, thereby enhancing the clarity and precision of the reconstructed images. Additionally, the system demonstrated robustness in environments with varying levels of turbidity and turbulence, further highlighting its potential for real-world underwater applications (Fig.12-Fig.14). The results suggest that the KMSI system offers a substantial improvement over traditional SPI systems, making it highly suitable for high-quality underwater imaging, especially in situations where clarity and resolution are critical.

Conclusions  In conclusion, this research successfully introduces a novel KMSI-based single-pixel imaging system that addresses the key challenges of underwater imaging, including the elimination of the checkerboard effect and the reduction of backscattering from water. The proposed system, through the use of a distance-selected slice imaging system, combines a pulsed light source and a time-resolved gated detector to enhance imaging quality in turbidity and turbulent conditions. Experimental and simulation results confirm that the KMSI system outperforms traditional SPI models under sub-Nyquist sampling conditions, offering clearer, more accurate images. The demonstrated advantages of the KMSI-based SPI system open new possibilities for high-quality underwater imaging, with potential applications in both underwater lidar and other imaging technologies. This research not only improves the state-of-the-art in underwater SPI but also paves the way for future advancements in imaging systems for difficult-to-reach environments. The proposed approach holds great promise for a variety of applications, including marine biology, environmental monitoring, and underwater robotics.