{"ID":2866762,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.20500","arxiv_id":"2509.20500","title":"Real-Time Markov Modeling for Single-Photon LiDAR: $1000 \\times$ Acceleration and Convergence Analysis","abstract":"Asynchronous single-photon LiDAR (SP-LiDAR) is an important imaging modality for high-quality 3D applications and navigation, but the modeling of the timestamp distributions of a SP-LiDAR in the presence of dead time remains a very challenging open problem. Prior works have shown that timestamps form a discrete-time Markov chain, whose stationary distribution can be computed as the leading left eigenvector of a large transition matrix. However, constructing this matrix is known to be computationally expensive because of the coupling between states and the dead time. This paper presents the first non-sequential Markov modeling for the timestamp distribution. The key innovation is an equivalent formulation that reparameterizes the integral bounds and separates the effect of dead time as a deterministic row permutation of a base matrix. This decoupling enables efficient vectorized matrix construction, yielding up to $1000 \\times$ acceleration over existing methods. The new model produces a nearly exact stationary distribution when compared with the gold standard Monte Carlo simulations, yet using a fraction of the time. In addition, a new theoretical analysis reveals the impact of the magnitude and phase of the second-largest eigenvalue, which are overlooked in the literature but are critical to the convergence.","short_abstract":"Asynchronous single-photon LiDAR (SP-LiDAR) is an important imaging modality for high-quality 3D applications and navigation, but the modeling of the timestamp distributions of a SP-LiDAR in the presence of dead time remains a very challenging open problem. Prior works have shown that timestamps form a discrete-time Ma...","url_abs":"https://arxiv.org/abs/2509.20500","url_pdf":"https://arxiv.org/pdf/2509.20500v1","authors":"[\"Weijian Zhang\",\"Hashan K. Weerasooriya\",\"Prateek Chennuri\",\"Stanley H. Chan\"]","published":"2025-09-24T19:22:02Z","proceeding":"eess.SP","tasks":"[\"eess.SP\"]","methods":"[]","has_code":false}