Theoretical Signal Extraction Model of Spatial Density-Based Algorithms and Its Extraction Capacity Analysis for Photon-Counting Lidars

Photon-counting laser altimeter is an advanced remote sensing observation equipment, which provides detailed surface profile information, exemplified by the advanced topographic laser altimeter system (ATLAS) on Ice, Cloud, and land Elevation Satellite-2 (ICESat-2). However, the high sensitivity of a photon-counting laser altimeter introduces noisy geolocated photons, posing a tremendous challenge in signal extraction from noise photons with low signal-to-noise ratios (SNRs). An efficient signal extraction algorithm is critical for further applications of ICESat-2 data, and the spatial density-based algorithms perform well and have been verified in various scenarios, e.g., canopy and ground detection, sea-ice freeboard detection, and bathymetry. Currently, the geometric parameters in density-based algorithms are usually empirically determined, and the main challenge is to adaptively set the optimal geometric parameters in variable scenarios. In this study, a theoretical mapping model that correlates the performance metrics (e.g., number of true positive, false positive, and false negative photons) with the algorithm parameters and the lidar system parameters is derived. The performance of this model is verified using Monte Carlo simulated data of bare lands and vegetated areas with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$R^{2}$ </tex-math></inline-formula> exceeding 0.99, and also verified using ICESat-2 data over land, ocean, vegetation, and ice areas with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$R^{2}$ </tex-math></inline-formula> exceeding 0.94. Based on the model, the signal extraction capacity in different SNRs, channel numbers, and signal durations are discussed, offering a theoretical foundation for determining the optimal parameters to extract ICESat-2 signal photons and also for better designing hardware parameters of photon-counting laser altimeters.