LiDAR imaging in foggy conditions is essential for applications such as autonomous driving, aviation navigation, and surveillance. However, traditional LiDAR systems face significant limitations in such environments due to the scattering and absorption of laser beams by fog, resulting in reduced detection range and degraded image quality. Single photon avalanche diode (SPAD) technology, with its exceptional sensitivity and high resolution, has emerged as a promising solution. SPAD systems can operate under extremely low light conditions. When combined with time-correlated single photon counting (TCSPC), they can effectively detect and process individual photon signals. This capability enables reliable detection and imaging even in low-visibility environments like fog and haze. Therefore, investigating the performance of SPAD-based LiDAR systems in foggy conditions is crucial for advancing these applications.

In this paper, we utilize high-sensitivity SPAD combined with the TCSPC method to extract the depth and intensity information of targets in foggy environments. Monte Carlo simulations are conducted to analyze the transmission characteristics of laser beams in fog, providing a robust scientific foundation for this study. A Gamma distribution is used to model the scattering peaks caused by fog, while a Gaussian distribution is applied to represent peaks generated by target reflections. To enhance image quality, the Levenberg-Marquardt (LM) algorithm is combined with total variation (TV) regularization, significantly improving target reconstruction accuracy and clarity in fog conditions.

The photon echo data collected in foggy environments are analyzed using a Gamma-Gaussian mixture model to reconstruct depth and intensity images. Three-dimensional image reconstruction (Fig. 7) is performed using the peak value method, maximum likelihood estimation (MLE) algorithm, and the proposed LM-TV algorithm. Comparative analysis demonstrates that the LM-TV algorithm outperforms traditional methods, reducing the root mean square error (RMSE) of the depth image by 1.0231 and increasing the structural similarity index (SSIM) of the intensity image by 0.5485 (Table 1). These results highlight the effectiveness of the LM-TV method in fog penetration imaging, delivering more accurate and robust target reconstruction.

In this paper, TCSPC technology is utilized to obtain photon echo data in the time domain under foggy conditions. A Gamma-Gaussian mixture model is employed to separate fog echo signals from target reflections, enabling precise depth and intensity to be extracted using the LM algorithm. Compared to the peak value method, the LM algorithm reduces the RMSE of the reconstructed depth image by 0.9475 and improves the SSIM of the reconstructed intensity image by 0.4720. The integration of TV regularization with the LM algorithm further reduces the RMSE of the depth image by an additional 0.0756 and enhances the SSIM by 0.0765. When compared to the MLE algorithm, the combined LM-TV method achieves a reduction in RMSE of 0.4788 and an improvement in SSIM by 0.4563. These findings demonstrate that the hybrid LM-TV algorithm significantly outperforms traditional methods, offering a more accurate and robust solution for target reconstruction in foggy environments.