# A Multi-Level Auto-Adaptive Noise-Filtering Algorithm for Land ICESat-2 Photon-Counting Data

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Areas and Datasets

#### 2.1.1. Forest

#### 2.1.2. Desert

#### 2.1.3. Grassland

#### 2.1.4. City

#### 2.2. Manually Annotated ICESat-2 Truth Reference Dataset

#### 2.3. Methods

#### 2.3.1. Overview

#### 2.3.2. Coarse Denoising

_{unit}× h

_{unit}. The parameter l

_{unit}determines the fineness of coarse denoising, and the parameter h

_{unit}determines the size of the potential photons region. All photons will be divided into grid cells to realize the data gridding of geolocated photons, as shown in Figure 4a. The size of the grid cell can be decided in two ways. One is set as a fixed percentage, and the grid cell size adaptively changes with the data:

#### 2.3.3. Fine Denoising

_{1}and c

_{2}of the ellipse is less than the length of the long axis of the ellipse 2a, the point q is in the search ellipse of the point p, as shown in Figure 6. The distance d from point q to the two foci of the ellipse with core point p as the center is calculated by Equation (3):

_{1}and c

_{2}are calculated by the following:

_{1}and c

_{2}of the ellipse will be as shown in Equations (7) and (8):

#### 2.4. Evaluation Indicators

## 3. Results

#### 3.1. Coarse Denoising Results

#### 3.2. Overall Denoising Result

#### 3.2.1. Forest

#### 3.2.2. Desert

#### 3.2.3. Grassland

#### 3.2.4. City

## 4. Discussion

#### 4.1. The Discussion of Coarse denoising result

#### 4.2. The Discussion of MLANF Denoising Result

- Forest: Three methods all have a lower precision in CF region. The DBSCAN algorithm misclassifies some noise photons as signal photons in CF. The DRAGANN algorithm of ATL08 fails to identify some signal photons in AF and has a lower recall in the forest region. The MLANF algorithm performs well in terms of precision and recall.
- Desert: The results of three algorithms in SD about three metrics are all greater than 99%. The DRAGANN algorithm of the ATL08 cannot identify the signal photons in the TD region, and the recall of it is only 53.43%. Therefore, the other denoising results of the two density-based methods perform well.
- Grassland: The grassland data all have lots of random noise photons, and their evaluation metrics are lower than those of the other land types. The HG data have a lower SNR than VG data, which seriously affects the accuracy of the three algorithms. As shown in Figure 26, the DBSCAN algorithm results have more errors of misclassification than the MLANF algorithm results. Compared with the other two methods, our method has the best data-denoising effect for the grassland-type data.
- City: In the SC study area, the precision of the MLANF algorithm is 98.22, which is better than that of the other two methods. And the DBSCAN algorithm has a higher recall rate, so its comprehensive evaluation index F-score is better than that of the other methods. Moreover, in the AC study area, the precision and recall value of our algorithm in this paper is high, so the comprehensive evaluation index F-score is the highest. In contrast, the DBSCAN algorithm and ATL08 have lower precision and recall values, so the quantitative evaluation results are lower than those of our method. Figure 27 shows the denoising results of the MLANF algorithm in the AC area, (b) and (c) show that the MLANF algorithm can accurately extract signal photons in areas with large terrain fluctuations. In conclusion, our method performs better in denoising selected city areas.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Geographical locations of eight datasets in this study: CF, woodland in the Congo region; AF, forest in the Brazilian Amazon; SD, Sahara Desert; TD, Taklamakan Desert, China; HG, steppe in Inner Mongolia, China; VG, steppe in Venezuela; SC, Shanghai, China; AC, Atlantic coastal urban agglomeration, northeast USA.

**Figure 3.**Flow chart of MLANF algorithm. It consists two steps: coarse denoising and fine denoising.

**Figure 4.**Coarse denoising: (

**a**) raw data with grids; (

**b**) cell photons counting result. The black points are raw photons and the grids in our coarse denoising step are red.

**Figure 5.**The equal scale detailed segment of photon distribution after the coarse denoising step (the scale unit is 150 m).

**Figure 6.**Determining whether a point is in the search model: (

**a**) point q is in the search ellipse, (

**b**) point q is outside the search ellipse. The black points are raw photons and the blue ellipse is the horizontal ellipse model.

**Figure 7.**Search ellipse based on adaptive change in slope. The black points are raw photons, the dotted ellipse is the horizontal ellipse model and the solid ellipse is our ellipse model with slope.

**Figure 9.**ICESat-2/ATLAS ground track and Google Earth satellite images over the Congo Forest. Blue line is the ATLAS ground track and two sampled segments within the yellow and green boxes are enlarged and illustrated in Figure 10a,b, respectively.

**Figure 10.**Comparison of detailed results of different signal photon extraction methods in the Congo Forest study area. (

**a**) Enlarged along-track segment corresponding to the green box in Figure 9 at along-track distances from 8 to 12 km. (

**b**) Corresponding to the yellow box in Figure 9, the along-track distance increases from 16 to 18 km.

**Figure 11.**ICESat-2/ATLAS ground track and Google Earth satellite images over the Amazon Forest. Blue line is the ATLAS ground track and two sampled segments within the yellow and green boxes are enlarged and illustrated in Figure 12a,b, respectively.

**Figure 12.**Comparison of detailed results of different signal photon extraction methods in the Amazon Forest study area. (

**a**) Enlargement of the along-track segment corresponding to the green box in Figure 11 at the along-track distance from 6 to 8 km. (

**b**) Corresponding to the yellow box in Figure 11, the along-track distance increases from 16 to 18 km.

**Figure 13.**ICESat-2/ATLAS ground track over the Sahara Desert and Google Earth satellite images. Blue line is the ATLAS ground track and two sampled segments within the yellow and green boxes are enlarged and illustrated in Figure 14a,b, respectively.

**Figure 14.**Comparison of detailed results of different signal photon extraction methods in the Sahara Desert study area. (

**a**) Enlarged along-track segment corresponding to the green box in Figure 13 at along-track distances from 4 to 6 km. (

**b**) Corresponding to the yellow box in Figure 13, the along-track distance increases from 10 to 12 km.

**Figure 15.**ICESat-2/ATLAS ground track and Google Earth satellite images over the Taklamakan Desert. Blue line is the ATLAS ground track and two sampled segments within the yellow and green boxes are enlarged and illustrated in Figure 16a,b, respectively.

**Figure 16.**Detailed results of the comparison of different signal photon extraction methods in the Taklamakan Desert study area. (

**a**) Enlarged along-track segment corresponding to the green box in Figure 15 at along-track distances from 4 to 6 km. (

**b**) Corresponding to the yellow box in Figure 15, the along-track distance increases from 10 to 12 km.

**Figure 17.**ICESat-2/ATLAS ground track on Hulunbuir and Google Earth satellite images. Blue line is the ATLAS ground track and two sampled segments within the yellow and green boxes are enlarged and illustrated in Figure 18a,b, respectively.

**Figure 18.**Detailed results of the comparison of different signal photon extraction methods in the Hulunbuir grassland study area. (

**a**) Along-track segment corresponding to the green box in Figure 17 is enlarged at the along-track distance from 5 to 7 km. (

**b**) Corresponding to the yellow box in Figure 17, the along-track distance increases from 10 to 12 km.

**Figure 19.**ICESat-2/ATLAS ground track and Google Earth satellite image of the Venezuelan steppe. The surface consists of dense grasslands. Blue line is the ATLAS ground track and two sampled segments within the yellow and green boxes are enlarged and illustrated in Figure 20a,b, respectively.

**Figure 20.**Comparison of detailed results of different signal photon extraction methods in the study area of the Venezuelan steppe. (

**a**) Enlargement of the along-track segment corresponding to the green box in Figure 19 at along-track distances from 4 to 6 km. (

**b**) Corresponding to the yellow box in Figure 19, the along-track distance increases from 10 to 14 km.

**Figure 21.**ICESat-2/ATLAS ground track and Google Earth satellite image of Shanghai, China. The surface consists of artificial ground. Blue line is the ATLAS ground track and two sampled segments within the yellow and green boxes are enlarged and illustrated in Figure 22a,b, respectively.

**Figure 22.**Detailed results of the comparison of different signal photon extraction methods in the Shanghai study area. (

**a**) Along-track segment corresponding to the green box in Figure 21 is enlarged at the along-track distance from 4 to 6 km. (

**b**) Corresponding to the yellow box in Figure 21, the along-track distance increases from 15 to 17 km.

**Figure 23.**ICESat-2/ATLAS ground track and Google Earth satellite images of a cluster of cities along the Atlantic coast of the northeastern U.S. Blue line is the ATLAS ground track and two sampled segments within the yellow and green boxes are enlarged and illustrated in Figure 24a,b, respectively.

**Figure 24.**Comparison of detailed results of different signal photon extraction methods for the study area of the northeast Atlantic coastal urban group, USA. (

**a**) Along-track segment corresponding to the green box in Figure 23 is enlarged at along-track distances from 6 to 8 km. (

**b**) Corresponding to the yellow box in Figure 23, the along-track distance increases from 11 to 13 km.

**Figure 26.**Detailed results of MLANF algorithm and DBSCAN algorithm in Hulunbuir study area. (

**a**) MLANF algorithm results, (

**b**) details of MLANF algorithm results, (

**c**) DBSCAN algorithm results, (

**d**) details of DBSCAN algorithm results.

**Figure 27.**Details of MLANF algorithm results in northeast Atlantic coastal urban agglomeration study area, USA. (

**a**) MLANF algorithm results for the northeast Atlantic coastal urban agglomeration study area, USA, (

**b**) zoomed detailed results of the first yellow box in subplot (

**a**), (

**c**) zoomed detailed results of the second yellow box in subplot (

**a**).

Site | Geographical Location | Time (s) | Noise Rate (%) | Acquisition Date and Season | Beam | Local Time |
---|---|---|---|---|---|---|

Congo Forest (CF) | 9°38′–9°50′N, | 150~153 | 33.42 | 9 May 2021, in summer | Strong | day |

22°38′–22°42′E | ||||||

Amazon Rainforest (AF) | 4°57′–5°12′N, | 78~81 | 0.62 | 23 October 2021, in autumn | Strong | night |

62°39′–62°33′E | ||||||

Sahara Desert (SD) | 22°51′–22°58′N, | 63~65 | 0.99 | 15 July 2021, in summer | Strong | night |

6°55′–6°57′E | ||||||

Taklimakan Desert (TD) | 40°21′–40°30′N, | 282~284 | 0.53 | 31 July 2021, in summer | Weak | night |

82°22′–82°26′E | ||||||

Hulunbuir grassland (HG) | 9°38′–9°50′N, | 349~351 | 62.39 | 19 September 2021, in summer | Weak | day |

22°38′–22°42′E | ||||||

Venezuela grassland (VG) | 7°58′–8°12′N, | 125~128 | 17.22 | 22 May 2021, in summer | Strong | day |

68°14′–68°18′E | ||||||

Shanghai, China (SC) | 30°48′–30°56′N, | 449~451 | 5.74 | 5 December 2021, in winter | Strong | night |

121°22′–121°26′E | ||||||

Atlantic coastal urban area, USA (AC) | 53°22′–53°30′N, | 206~208 | 55.06 | 13 May 2021, in summer | Weak | night |

75°10′–75°18′E |

Data Name | Signal Photon Ratio | Noise Photon Ratio | Signal Photon Ratio (after Coarse Denoising) | Noise Photon Ratio (after Coarse Denoising) | Outlier Photon Ratio |
---|---|---|---|---|---|

CF | 66.58% | 33.42% | 66.58% | 6.84% | 26.58% |

AF | 99.38% | 0.62% | 99.32% | 0.00% | 0.68% |

SD | 99.01% | 0.99% | 99.01% | 0.46% | 0.53% |

TD | 99.47% | 0.53% | 99.47% | 0.03% | 0.50% |

HG | 37.61% | 62.39% | 37.61% | 2.47% | 59.93% |

VG | 82.78% | 17.22% | 82.78% | 13.86% | 3.35% |

SC | 94.26% | 5.74% | 91.72% | 0.00% | 8.28% |

AC | 44.94% | 55.06% | 44.94% | 8.45% | 46.62% |

Data Name | Precision (%) | Recall (%) | F-score (%) | ||||||
---|---|---|---|---|---|---|---|---|---|

DBSCAN | MLANF | ATL08 | DBSCAN | MLANF | ATL08 | DBSCAN | MLANF | ATL08 | |

CF | 94.54 | 95.01 | 96.42 | 97.57 | 99.17 | 99.10 | 96.03 | 97.04 | 97.74 |

AF | 99.95 | 99.94 | 99.39 | 92.37 | 98.19 | 70.31 | 96.02 | 99.06 | 82.36 |

SD | 99.97 | 99.98 | 99.98 | 99.93 | 99.94 | 99.98 | 99.95 | 99.96 | 99.98 |

TD | 99.98 | 99.96 | 99.96 | 99.92 | 99.95 | 53.43 | 99.95 | 99.95 | 69.63 |

HG | 75.77 | 94.01 | 97.96 | 98.09 | 99.83 | 99.03 | 85.50 | 96.83 | 98.49 |

VG | 89.06 | 96.30 | 95.40 | 99.02 | 94.23 | 77.53 | 93.78 | 95.25 | 85.54 |

SC | 95.39 | 98.22 | 96.70 | 98.24 | 93.19 | 86.36 | 96.80 | 95.64 | 91.24 |

AC | 90.83 | 96.40 | 93.19 | 96.18 | 99.16 | 99.29 | 93.43 | 97.76 | 96.14 |

Average | 93.19 | 97.48 | 97.38 | 97.67 | 97.96 | 85.63 | 95.18 | 97.69 | 90.14 |

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**MDPI and ACS Style**

Liu, J.; Liu, J.; Xie, H.; Ye, D.; Li, P.
A Multi-Level Auto-Adaptive Noise-Filtering Algorithm for Land ICESat-2 Photon-Counting Data. *Remote Sens.* **2023**, *15*, 5176.
https://doi.org/10.3390/rs15215176

**AMA Style**

Liu J, Liu J, Xie H, Ye D, Li P.
A Multi-Level Auto-Adaptive Noise-Filtering Algorithm for Land ICESat-2 Photon-Counting Data. *Remote Sensing*. 2023; 15(21):5176.
https://doi.org/10.3390/rs15215176

**Chicago/Turabian Style**

Liu, Jun, Jingyun Liu, Huan Xie, Dan Ye, and Peinan Li.
2023. "A Multi-Level Auto-Adaptive Noise-Filtering Algorithm for Land ICESat-2 Photon-Counting Data" *Remote Sensing* 15, no. 21: 5176.
https://doi.org/10.3390/rs15215176