Parametric Modeling and Estimation of Photon Registrations for 3D Imaging

In single-photon light detection and ranging (SP-LiDAR) systems, the histogram distortion due to hardware dead time fundamentally limits the precision of depth estimation. To compensate for the dead time effects, the photon registration distribution is typically modeled based on the Markov chain self-excitation process. However, this is a discrete process and it is computationally expensive, thus hindering potential neural network applications and fast simulations. In this paper, we overcome the modeling challenge by proposing a continuous parametric model. We introduce a Gaussian-uniform mixture model (GUMM) and periodic padding to address high noise floors and noise slopes respectively. By deriving and implementing a customized expectation maximization (EM) algorithm, we achieve accurate histogram matching in scenarios that were deemed difficult in the literature.

Resolution Limit of Single-Photon LiDAR

Single-photon Light Detection and Ranging (LiDAR) systems are often equipped with an array of detectors for improved spatial resolution and sensing speed. However, given a fixed amount of flux produced by the laser transmitter across the scene, the per-pixel Signal-to-Noise Ratio (SNR) will decrease when more pixels are packed in a unit space. This presents a fundamental trade-off between the spatial resolution of the sensor array and the SNR received at each pixel. Theoretical characterization of this fundamental limit is explored. By deriving the photon arrival statistics and introducing a series of new approximation techniques, the Mean Squared Error (MSE) of the maximum-likelihood estimator of the time delay is derived. The theoretical predictions align well with simulations and real data.