Multiscale Quadtree for denoising spaceborne photon-counting LiDAR
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摘要: 第二代星载激光雷达冰、云和陆地测高卫星（Ice, Cloud, and Land Elevation Satellite-2, ICESat-2）在获取浅海岛礁水深信息方面具有极大潜力。然而受大气散射、太阳辐射和仪器噪声等因素影响，造成获取的ICESat-2星载激光光子中存在大量噪声。针对上述问题，本文提出一种基于多尺度分析的四叉树星载激光雷达去噪方法。首先，使用高斯核函数和K折交叉验证的方法绘制光子核密度曲线（Kernel Density Estimation, KDE），并设置阈值来分离海面光子和海底光子；其次，利用自适应参数的DBSCAN（Density-Based Spatial Clustering of Applications with Noise）算法去除海底异常光子，获得粗略去噪结果。最后，对海底光子划分窗口，从不同尺度使用预判断四叉树算法提取出精确的海底信号光子。研究选取典型岛礁的ICESat-2卫星数据，通过与实测水深数据对比，决定系数（R2）分别达到95%和98%，均方根误差（RMSE）分别达到1.01 m和0.77 m。结果表明，该方法能够准确提取水下地形信息，为浅海水下地形反演奠定基础。Abstract: Ice, Cloud, and Land Elevation Satellite-2 (ICESat-2) has excellent potential for obtaining water depth information around islands and reefs. However, due to the influence of laser, atmospheric scattering and other factors, ICESat-2 data contains a lot of noise. Combining multiscale analysis with the quadtree algorithm, we propose a new photon-counting LiDAR denoising method to discard the large amount of noise in ICESat-2 data. First, Kernel Density Estimation (KDE) is performed using a Gaussian kernel function and the K-fold cross validation to set threshold values that separate sea surface photons from seafloor photons. Second, abnormal photons are removed using the Density-Based Spatial Clustering of Applications with Noise (DBSCAN) with adaptive parameters, yielding rough denoising results. Finally, for the seafloor photon partition window, accurate seafloor signal photons are extracted across multiple scales using the pre-judgment quadtree. The study used ICESat-2 photon-counting data from typical islands and reefs, comparing it with in situ water depth measurements. The coefficient of determination (R²) in the study area reaches 95% and 98%, with root mean square errors (RMSE) of 1.01 m and 0.77 m, respectively. The results show that the proposed method can accurately extract underwater topographic information, providing a solid foundation for the inversion of shallow marine topography.
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Key words:
- bathymetry /
- ICESat-2 /
- photon classification /
- kernel density estimation /
- multiscale analysis /
- quadtree
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图 7 不同光子密度的去噪结果（蓝色点代表海面光子，红色点代表海底光子，灰色点代表噪声光子）
Fig. 7 Denoising results of different photon densities blue points represent sea surface photons, red points represent seafloor photons, and gray points represent noise photons
图 8 不同海底地形的去噪结果（蓝色点代表海面光子，红色点代表海底光子，灰色点代表噪声光子）
Fig. 8 Denoising results of different seafloor terrains blue points represent sea surface photons, red points represent seafloor photons, and gray points represent noise photons
表 1 实验区域
Tab. 1 Experimental area
序号 研究区域 采集时间 航迹 波束 范围 (a) 东岛 2023-08-07 19:59:02 0743 GT3L 16°39′54″～16°41′07″N (b) 华光礁 2022-07-15 14:36:12 0362 GT1R 16°13′33″～16°14′37″N (c) 蜈支洲岛 2022-06-28 03:40:53 0095 GT3R 18°18′52″～18°19′01″N (d) 别克斯岛 2020-07-17 13:08:31 0339 GT1L 18°07′26″～18°07′48″N (e) 瓦胡岛 2022-09-02 06:13:30 1105 GT3R 21°17′08″～21°18′04″N (f) 埃林吉纳埃环礁 2022-09-08 08:22:27 1198 GT2R 11°07′12″～11°08′06″N 
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表 2 精度评价结果（东岛、蜈支洲岛和别克斯岛）
Tab. 2 Accuracy verification results (Dong Island, Wuzhizhou Island, and Vieques Island)
实验区域 指标 实验方法 ATL03 DBSCAN Quadtree 本文方法 东岛 OA/% 94.7 94.5 94.1 97.8 F1/% 97.2 97.1 96.9 98.9 FPR/% 48.3 48.3 34.7 23.1 蜈支洲岛 OA/% 94.1 96.0 93.7 98.5 F1/% 85.3 91.9 86.9 96.9 FPR/% 0.2 4.8 5.7 1.8 别克斯岛 OA/% 83.6 93.4 93.1 95.3 F1/% 80.0 92.9 92.5 95.4 FPR/% 0.0 1.7 0.6 8.3
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表 3 精度评价结果（华光礁、瓦胡岛和埃林吉纳埃环礁）
Tab. 3 Accuracy verification results (Huaguang Reef, Oahu Island, and Ailinginae Atoll)
实验区域 指标 实验方法 ATL03 DBSCAN Quadtree 本文方法 华光礁 OA/% 95.1 95.8 96.3 99.3 F1/% 97.4 97.8 98.0 99.6 FPR/% 73.9 45.8 17.5 2.6 瓦胡岛 OA/% 96.2 94.5 96.8 97.7 F1/% 98.0 97.1 98.3 98.8 FPR/% 79.8 41.9 25.8 15.7 埃林吉纳埃环礁 OA/% 97.9 98.4 98.5 98.7 F1/% 98.9 99.2 99.3 99.4 FPR/% 55.3 28.2 13.6 1.0
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表 4 不同算法的去噪精度比较
Tab. 4 Comparison of denoising accuracy of different algorithms
研究区域 方法 指标 R²/% RMSE/m MAE/m MRE/% 点数量 东岛 DBSCAN算法 89.0 1.03 0.77 7.53 627 Quadtree算法 75.0 1.35 0.80 7.88 618 本文方法 95.0 1.01 0.77 7.26 696 瓦胡岛 DBSCAN算法 97.0 0.99 0.76 15.64 477 Quadtree算法 96.0 1.28 0.85 16.87 486 本文方法 98.0 0.91 0.69 10.72 596
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