Markov-renewal LIDAR Simulator Predicts Count Statistics with Analytical Fidelity and Speed

Single-photon LiDAR simulators traditionally face a difficult trade-off between speed and accuracy, relying on either fast but imprecise models or slow, meticulously detailed simulations. Researchers Weijian Zhang, Prateek Chennuri, and Hashan K. Weerasooriya, along with Bole Ma and Stanley H. Chan from Purdue University, overcome this limitation with a new simulator that delivers both fidelity and computational efficiency. The team achieves this breakthrough by focusing on the underlying statistics of photon counts, formulating a Markov-renewal process that analytically predicts key characteristics under realistic dead time conditions. This innovative approach, combined with a spectral truncation rule for managing complex data, allows the simulator to generate three-dimensional data cubes that are indistinguishable from those produced by the established, yet slow, sequential method, but at significantly increased speed. This advancement finally unlocks the potential for large-scale, physically accurate data generation, which is crucial for developing and training advanced learning-based single-photon LiDAR reconstruction techniques.

The team addressed limitations in existing simulators, which often struggle to accurately model the statistical nature of photon counts, particularly in low-light conditions or with complex noise. Consequently, scientists developed MaRS, a new framework designed to provide more realistic simulations of the photon arrival process. MaRS is based on a Markovian model of photon arrival, allowing for efficient and realistic simulation. The team also investigated the impact of bin resolution on both accuracy and efficiency, providing guidance on selecting an appropriate resolution for different applications.

The framework was compared against existing simulators to demonstrate its advantages. To evaluate accuracy, the authors created a dataset and a deep learning network, specifically a U-Net architecture, to perform reflectivity estimation, incorporating a dual-branch feature extraction mechanism to capture both spatial and temporal information. Results demonstrate that MaRS consistently outperforms existing simulators in terms of accuracy, especially in challenging low-light conditions and with complex noise. Experiments on reflectivity estimation show that models trained with MaRS-generated data achieve superior performance.

This study highlights the importance of realistic simulation for developing and validating algorithms for photon counting applications. This work represents a significant advancement in photon counting simulation, providing a more accurate and flexible framework for modeling the photon arrival process. This work overcomes this challenge by accurately modeling photon count statistics, a previously overlooked component in simulation fidelity. Scientists formulated a Markov-renewal process (MRP) to analytically predict the mean and variance of registered photon counts under dead time, providing a tractable path to accurate simulation without per-photon iteration. To implement this theoretical framework, the team introduced a spectral truncation rule that efficiently computes the complex covariance statistics inherent in the MRP model.

This innovation allows for a significant reduction in computational burden while preserving accuracy. By proving the shift-invariance of the process, researchers extended the per-pixel model to generate full 3D histogram cubes using a precomputed lookup table, enabling full parallelization of the simulation. Experiments demonstrate that MaRS generates histogram cubes indistinguishable from the sequential gold-standard, yet achieves orders of magnitude faster computation. Unlike autoencoder-based methods requiring retraining for each dead-time setting, MaRS provides a unified and flexible framework for synthesizing entire histogram cubes with improved statistical fidelity across varying operating conditions. This breakthrough enables the generation of large-scale, physically-faithful datasets essential for training modern deep learning pipelines for SP-LiDAR reconstruction, resolving a critical bottleneck in the field.

Statistical Simulation Achieves Fast, Accurate LiDAR Data

This research delivers a breakthrough in simulating Single-Photon LiDAR (SP-LiDAR) data, achieving both high fidelity and computational speed. Previous simulators faced a trade-off between accuracy and efficiency. Scientists have developed a new simulator that overcomes this limitation by focusing on the underlying statistics of photon counts, specifically addressing the impact of detector dead time. The team formulated a Markov-renewal process (MRP) that analytically predicts the mean and variance of registered photon counts, even with dead time effects. To make this model computationally feasible, they introduced a spectral truncation rule, efficiently capturing the complex covariance statistics.

Crucially, they proved the process is shift-invariant, allowing them to extend per-pixel calculations to generate full 3D histogram cubes using a precomputed lookup table. Experiments demonstrate that this method generates cubes indistinguishable from the sequential gold-standard, yet operates at significantly faster speeds. Measurements confirm the accuracy of this approach, with the spectral truncation rule precisely matching ground-truth variance predictions while reducing computational demands. Validation across diverse settings shows that retaining only the five dominant eigenmodes of the system accurately captures the full correlation structure. Researchers developed a novel simulator grounded in a Markov-renewal process that accurately predicts the statistical behaviour of registered photon counts, even under conditions of detector dead time. Crucially, this simulator achieves accuracy comparable to the gold-standard sequential method, but operates over six orders of magnitude faster. The key to this advancement lies in a combination of analytical modelling and computational efficiency. By directly formulating the photon statistics and incorporating detector dead time, the team avoids the approximations inherent in previous approaches. A spectral truncation scheme further accelerates covariance computation, while a scalable synthesis pipeline enables efficient data generation.