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The Ice, Cloud, and Land Elevation Satellite-2 (ICESat-2) is the world's first satellite-borne photon-counting laser altimeter with unprecedented detection performance. Noise removal is an important process applied to raw data and determines the quality of the end product. Assuming that the sparse spatial distribution of noise photons makes them more easily isolated than signal photons, we propose a noise-removal algorithm without input parameters based on quadtree isolation. MATLAS was used to evaluate the performance of our algorithm. We compare our algorithm to the improved density-based spatial clustering of applications with noise (DBSCAN) algorithm. Experimental results show that our algorithm accurately extracts signal photons from raw data and is superior to the improved DBSCAN in accuracy and time efficiency. This novel algorithm makes it possible to efficiently remove noise from photon-counting light detection and ranging (LiDAR) data.