# A Directional Nearest Neighbor Distance-Based Algorithm for Signal Photon Extraction from Spaceborne Photon-Counting LiDAR in Shallow Waters

## TL;DR

This paper introduces a new algorithm to extract signal photons from satellite LiDAR data in shallow waters, improving bathymetry accuracy despite high noise.

## Contribution

The novel DNNDA algorithm uses directional photon distribution and spatial relationships for improved signal extraction in noisy environments.

## Key findings

- DNNDA achieves F1-scores exceeding 95% in seafloor photon extraction from ICESat-2 data.
- The algorithm reduces root-mean-square errors below 0.57 m when validated against high-precision bathymetry data in Puerto Rico.

## Abstract

The Ice, Cloud, and Land Elevation Satellite-2 (ICESat-2) employs a 532 nm laser with strong water-penetration capability, making it well suited for satellite-derived bathymetry in shallow waters; however, the effective denoising of photon-counting data remains essential due to strong solar background and intrinsic instrument noise. To address this challenge, this study proposes a novel photon denoising method, termed the Directional Nearest Neighbor Distance-based Algorithm (DNNDA), for robust extraction of signal photons from shallow-water ICESat-2 data. Unlike existing methods that rely heavily on density or terrain features and often degrade under high-noise conditions, DNNDA systematically exploits both scale-corrected spatial relationships and directional distribution characteristics of photons. By quantitatively characterizing the directional features of photon distributions and embedding this information into a density representation, DNNDA amplifies the density contrast between signal and noise photons, rendering the seafloor signal photons more distinct and easier to extract. An evaluation index was further designed to automate optimal parameter determination. Validation using multiple global ICESat-2 datasets demonstrates that DNNDA achieves superior seafloor photon extraction performance, with F1-scores exceeding 95%. Further regression analysis against high-precision CUDEM data in the Puerto Rico region yields root-mean-square errors below 0.57 m. By jointly correcting scale anisotropy and incorporating directional information, DNNDA enables reliable and adaptive signal photon extraction across local and global scales, providing a robust solution for shallow-water bathymetry in complex, high-noise environments.