A novel nonparametric adaptive kernel density estimation method for removing nonrandom noise from ICESat-2 photon-counting LiDAR data

The Ice, Cloud, and Land Elevation Satellite-2 (ICESat-2) demonstrates significant advantages in retrieving surface elevation. However, its unique photon-counting detection mechanism and vertical profiling introduce substantial noise, particularly nonrandom noise from multiple scattering and specular reflections. These two noise types often coexist in large-scale regions, yet most existing parameterized algorithms are designed to address only one, limiting their denoising effectiveness in complex environments. To address this challenge, a robust nonparametric density estimation algorithm is proposed to efficiently remove nonrandom noise while ensuring accurate surface elevation retrieval. The proposed method adaptively determines the K nearest neighbors based on the photon distribution and employs Principal Component Analysis (PCA) to identify the orientation and axes of a search ellipse for adaptive bandwidth estimation. Local deviation factors are then computed, followed by adaptive thresholding along the track distance to extract high-quality signal photons. The proposed algorithm is tested on ICESat-2 datasets acquired under varying laser intensity levels, including glaciers characterized by multiple scattering, inland water affected by specular reflection, and sea ice where both types of nonrandom noise coexist. Experimental results demonstrate superior performance across diverse surface types, achieving an average F (the harmonic mean of Recall and Precision) of 0.9896. Elevation profiles fitted by our method closely align with manually labeled results, exhibiting an average bias of 0.003 m, an average MAE of 0.006 m, and an average RMSE of 0.010 m, outperforming the compared methods. Specifically, our method reduces the mean bias by approximately 86.96% compared to the specular return removal method, 57.14% compared to the multiple scattering removal method, and 95.00% compared to ICESat-2 data products. In conclusion, this study provides an effective and generalizable solution for eliminating nonrandom noise in highly reflective or scattering environments, demonstrating robust performance and high accuracy across diverse surface types and large-scale scene data.