Fast NLOS imaging at low sampling rates based on Poisson modeling

Existing non-line-of-sight (NLOS) imaging techniques face fundamental trade-offs under low sampling rates: direct methods enable rapid reconstruction but suffer significant degradation in image quality; iterative methods achieve high-quality reconstructions but incur prohibitive computational costs per frame; and deep learning approaches lack generalization capabilities. To overcome these limitations, this study proposes a parallelized Nesterov-accelerated proximal gradient descent algorithm, achieving an optimal balance of superior reconstruction quality, high computational speed, and low sampling rate, suitable for real-time NLOS imaging systems. Inspired by the light-cone transform theory, we formulate the NLOS reconstruction problem as a linear inverse problem and derive a convex optimization objective under Poisson noise assumptions. The optimization objective is solved using proximal gradient descent, with further integration of Nesterov acceleration enhancing the convergence rate from the conventional order 1/k to order 1/k squared, significantly reducing the required number of iterations. Moreover, parallel computing techniques are employed to achieve real-time algorithm execution on GPUs.We experimentally collected data with dimensions of 64×64×4096 to validate the imaging quality and computational speed performance of our method. Results demonstrate that at a low sampling rate of only 1.56%, the proposed algorithm significantly outperforms comparative algorithms in terms of peak signal-to-noise ratio (PSNR). Additionally, the GPU-based parallel computation achieves a reconstruction speed of 1 second per frame under the Poisson noise model, approaching the performance of representative direct methods such as LCT (0.44 s/frame), PB (3.7 s/frame), and FBP (1.16 s/frame).