Generating training data that is both correct and cheap — breaking the fidelity-versus-speed dilemma in single-photon LiDAR simulation.
Learning-based reconstruction needs large volumes of single-photon LiDAR data. Simulators that can supply it come in two flavors, and both are unsatisfying:
Poisson models are fast and closed-form, but they ignore dead time, so the data they produce is wrong in precisely the high-flux regime that matters.
Sequential models step through photon arrivals one at a time and are physically faithful, but they are orders of magnitude too slow to generate a dataset.
Two papers attack this gap from different directions.
Neural mapping
(Zhang et al., 2025) learns a direct mapping from scene and illumination parameters to the distorted photon-registration statistics. Instead of simulating the arrival process, the network predicts its outcome. The result is an ultrafast simulator that stays accurate at high flux.
Markov-renewal processes
(Zhang et al., 2025) takes the analytic route. Formulating registration as a Markov-renewal process yields, for the first time, closed-form predictions of the mean and variance of registered photon counts under dead time. Two ideas make it tractable:
A spectral truncation rule that computes the covariance statistics efficiently.
A proof of shift-invariance, which lifts the per-pixel model to full histogram-cube generation through a precomputed lookup table.
The generated cubes are statistically indistinguishable from the sequential gold standard, at a fraction of the cost.
Efficient simulation of photon registrations in single-photon LiDAR is essential for generating the large-scale training data that learning-based reconstruction demands, but physically faithful sequential simulators are far too slow. We learn a neural mapping from scene and illumination parameters directly to the distorted photon-registration statistics induced by dead time, yielding an ultrafast simulator that remains accurate in the high-flux regime.
@inproceedings{zhang2025ultrafast,title={Ultrafast High-Flux Single-Photon LiDAR Simulator via Neural Mapping},author={Zhang, Weijian and Weerasooriya, Hashan K. and Chan, Stanley H.},booktitle={IEEE International Conference on Image Processing (ICIP)},pages={2772--2777},year={2025},}
Single-photon LiDAR (SP-LiDAR) simulators face a dilemma: fast but inaccurate Poisson models or accurate but prohibitively slow sequential models. This paper breaks that compromise. We present a simulator that achieves both fidelity and speed by focusing on the critical, yet overlooked, component of simulation: the photon count statistics. Our key contribution is a Markov-renewal process (MRP) formulation that, for the first time, analytically predicts the mean and variance of registered photon counts under dead time. To make this MRP model computationally tractable, we introduce a spectral truncation rule that efficiently computes the complex covariance statistics. By proving the shift-invariance of the process, we extend this per-pixel model to full histogram cube generation via a precomputed lookup table. Our method generates 3D cubes indistinguishable from the sequential gold-standard, yet is orders of magnitude faster.
@article{zhang2025markovrenewal,title={Markov-Renewal Single-Photon LiDAR Simulator},author={Zhang, Weijian and Chennuri, Prateek and Weerasooriya, Hashan K. and Ma, Bole and Chan, Stanley H.},journal={arXiv preprint arXiv:2512.04924},year={2025},month=dec,doi={10.48550/arXiv.2512.04924},}