Restoration of Streak Tube Imaging LiDAR 3D Images in Photon Starved Regime Using Multi-Sparsity Constraints and Adaptive Regularization

Streak Tube Imaging Lidar (STIL) offers significant advantages in long-range sensing and ultrafast diagnostics by encoding spatial-temporal information as streaks, and hence decodes 3D images using tailored algorithm. However, under low-photon conditions that caused either long-range or reduced exposure time, the reconstructed image suffer from low contrast, strong noise and blurring, hindering the application in various scenarios. To address this challenge, we propose a Multi-Sparsity Constraints and Adaptive Regularization (MSC-AR) algorithm based on the Maximum a Posteriori (MAP) framework, which jointly denoises and deblurs degraded streak images and efficiently solved using the Alternating Direction Method of Multipliers (ADMM). MSC-AR considers gradient sparsity, intensity sparsity, and an adaptively weighted Total Variation (TV) regularization along the temporal dimension of the streak image which collaboratively optimizing image quality and structural detail, thus better 3D restoration results in low-photon conditions. Experimental results demonstrate that MSC-AR significantly outperforms existing approaches under low-photon conditions. At an exposure time of 300 ms, it achieves millimeter-level RMSE and over 88% SSIM in depth image reconstruction, while maintaining robustness and generalization across different reconstruction strategies and target types.