Photon counting laser radar denoising method based on improved DENCLUE

Abstract

The photon counting laser radar denoising method based on the improved DENCLUE comprises the following steps: selecting a research area, and obtaining a global positioning point cloud data set of the research area; noise points away from the sea surface are eliminated; the data set is divided into four quadrants, the number of point cloud data in each quadrant is calculated, and if the number is smaller than a noise point threshold value, the point cloud data is marked as a noise point; if the size is between the noise point threshold value and the minimum clustering size, carrying out improved DENCLUE clustering processing on the point cloud in the quadrant; if the quadrant is larger than the preset minimum clustering size, dividing the quadrant again until the former two conditions are met; the de-noising using the improved DENCLUE is to determine a density core using a simulated annealing algorithm. The method has small dependence on parameters, has a remarkable effect in the aspect of ICESat-2 data denoising, and provides an effective new method for shallow sea remote sensing water depth detection.

Description

Technical Field

[0001] The invention relates to a photon counting laser radar data denoising method based on improved DENCLUE, and belongs to the technical field of laser radars, in particular to the technical field of laser radar data processing. Background Art

[0002] Shallow waters play a vital role in the economic development of coastal areas as a key base for global fisheries and a focal point for many economic activities, including fishing, maritime transport, tourism and leisure activities. Accurate, high-resolution and continuous seafloor topography measurements are recognized as a key element in coastal area management and are also essential for the protection and management of coral reefs. Since the first demonstration of airborne green wavelength lidar technology for measuring water depth in 1969, bathymetric lidar technology has become an indispensable tool for surveying and mapping nearshore waters.

[0003] With the continuous advancement of water color remote sensing technology, the use of hyperspectral satellite image data to invert nearshore shallow water depth information has become a widely used technology. LiDAR data has attracted much attention due to its high application value in the ocean field, especially in applications such as shallow water bathymetry and coral reef management. The ICESat-2 LiDAR satellite launched by the National Aeronautics and Space Administration (NASA) in September 2018 has shown significant application potential in the field of shallow water bathymetry. Combining ICESat-2 and hyperspectral image data to invert nearshore water depth has become a hot research direction in the field of water color remote sensing. However, ICESat-2 data is affected by factors such as the atmosphere and sea surface, and there is a large amount of noise data, which brings challenges to the accuracy and availability of the data and limits its application in precise oceanographic research. Therefore, how to effectively retain the sea surface point cloud and seabed point cloud data in ICESat-2 and remove noise points has become a crucial topic in this field.

[0004] Current spatial clustering methods, such as Density-Based Spatial Clustering of Applications with Noise (DBSCAN) and Ordering points to identify the clustering structure (OPTICS), have performed well in ICESat-2 data denoising and have been widely used. Zhong et al. proposed a two-step denoising method combining the DBSCAN clustering algorithm and a two-dimensional window filter. First, the DBSCAN algorithm was used for preliminary denoising, and then a two-dimensional window filter was applied to further denoise the preprocessed underwater photon data. Gao et al. proposed an improved difference, regression and Gaussian adaptive nearest neighbor filtering method to improve the denoising performance of photon cloud data by combining large-scale and small-scale search radii, and effectively distinguish signal photons from noise photons. Zhu et al. proposed the OPTICS algorithm with elliptical search, and distinguished signal point clouds from noise by the maximum inter-class variance, achieving good denoising effects on point cloud data in forest areas. Yin et al. proposed an adaptive OPTICS algorithm, which effectively improved the denoising accuracy of ICESat-2 laser photon data by combining histogram threshold coarse denoising and K nearest neighbor with DBSCAN fine denoising. Tang et al. proposed an innovative multi-level adaptive denoising algorithm. The algorithm first uses the OPTICS algorithm for preliminary denoising to remove randomly distributed noise photons; then, according to the slope change of the forest terrain, the size of the elliptical search domain is automatically adjusted to perform refined denoising. Liu et al. proposed an adaptive clustering and kernel density estimation method, which adapts to the distribution characteristics of photons in ICESat-2 data by determining input parameters (the semi-major axis and semi-minor axis of the horizontal elliptical neighborhood, and the minimum number of points), and then uses the core distance and reachable distance values ​​to determine the classification threshold to distinguish signal photons from noise photons. Zheng et al. proposed a filtering method combining density and distance, removing low-density noise through an adaptive elliptical filter, and then using a distance-based filter to eliminate high-density noise clusters, thereby extracting pure seafloor signal photons from ICESat-2 data.

[0005] At present, the main spatial clustering denoising methods for ICESat-2 and other lidar data are DBSCAN and OPTICS algorithms, but the denoising effects of these two clustering methods depend on the selection of parameters, and different parameters produce different denoising effects. The DENCLUE algorithm does not rely on the algorithm parameter settings and has shown sufficient accuracy and robustness in point cloud classification. This paper improves the traditional DENCLUE algorithm and applies the improved DENCLUE algorithm to ICESat-2 radar data denoising, effectively improving the denoising accuracy. Summary of the invention

[0006] The purpose of the present invention is to provide a photon counting laser radar denoising method based on improved DENCLUE to overcome the shortcomings of the prior art.

[0007] The photon counting laser radar denoising method based on improved DENCLUE is characterized by comprising the following steps: 1) Select the research area and obtain the global positioning point cloud dataset of the research area; 2) Eliminate noise points far from the sea surface: The sea surface is directly identified by the method of high frequency statistics, and the point cloud data within the range of 5 meters above the sea surface and 50 meters below the sea surface are directly classified as noise point clouds; 3) Data segmentation: For the denoised data set, first determine the upper, lower, left, and right boundaries of the data in terms of along-track distance and height, calculate the center point, divide the data set into four quadrants, and calculate the number of point cloud data in each quadrant; If the number of point clouds in a quadrant is less than the preset noise point threshold noise_number, all point clouds in the quadrant are marked as noise points; If the number of point clouds in a quadrant is between noise_number and min_number, the point clouds in the quadrant can be clustered using improved DENCLUE. If the number of point clouds in a quadrant is greater than the preset minimum cluster size min_number, the quadrant is divided again to form four smaller quadrants, and the number of point clouds in each quadrant is repeatedly counted until the previous two conditions are met; 4) Use improved DENCLUE for denoising: The improved DENCLUE uses a simulated annealing algorithm to determine the density core.

[0008] In step 3), min_number is calculated by dividing the total number of data points in the point cloud by the maximum distance of the point cloud along the track, and the result is rounded to the nearest multiple of 5, and this value does not exceed 50; noise_number is half of min_number, and is also rounded to the nearest multiple of 5, and its maximum value is also limited to 50.

[0009] In step 4), for each data point p [ i ]=( x i , y i ), use kernel density estimation to calculate its local density. The kernel density estimation uses the Gaussian kernel function, and the formula is as follows: (1) in, p [ j ]=( x j , y j ) are other points in the data set, h is the bandwidth parameter; n is the total number of point clouds in the dataset; After calculating the kernel density of each point, the simulated annealing algorithm is used to find the density attractor and calculate the new density estimate ρ accordingly; the simulated annealing algorithm accepts or rejects the new solution according to the Metropolis criterion of formula 2 to find the global optimal solution or a solution close to the global optimal solution; where Δρ is the energy difference, which is the change in density here, and T is the temperature parameter of simulated annealing; according to the Metropolis criterion, the calculated result of the probability P(accept) is between [0,1], indicating the probability of accepting the new solution; if P(accept)>0.5, that is, close to 1, the new solution is accepted; if P(accept)≤0.5, that is, close to 0, the new solution is rejected; (2) For every pair of density attractors p [ i ]and p [ j ], by calculating the Euclidean distance between them and comparing it to the sum of their respective radii to determine whether they are adjacent; when the distance between two attractors does not exceed the sum of their radii, an edge is drawn between the corresponding nodes of the graph, symbolically connecting the two adjacent attractors; this process ultimately constructs a graph in which the nodes represent density attractors and the edges map the proximity between them; with the graph constructed, further in-depth analysis is performed to identify and define clusters.

[0010] Potential clusters are revealed by identifying each connected component in the graph, each of which may correspond to a cluster. Within each connected component, the center of the cluster is determined by finding the point with the highest density, and all points within the component are considered members of the same cluster.

[0011] In step 4), for ICESat-2 ATL03 data, the bandwidth h is automatically calculated based on the standard deviation of the selected point cloud multiplied by 0.2.

[0012] The DENCLUE (Density Clustering) used in the present invention is an advanced clustering algorithm that relies on kernel density estimation to identify cluster structures in data. This algorithm defines clustering as the local maximum of a probability density function and distributes data points through a method called "hill climbing" so that all data points that tend to the same local maximum are classified into the same cluster. Unger et al. combined the core idea of ​​the DENCLUE method with the improved DBSCAN algorithm to effectively extract geometric patterns such as traffic lanes from LIDAR point clouds. Experimental results show that this method is superior to existing clustering techniques in terms of accuracy and robustness.

[0013] The present invention proposes an improved DENCLUE algorithm, which has low dependence on parameters and exhibits superior denoising performance when processing complex data sets. The method first performs frequency statistics on the data to identify and eliminate data far away from the signal point area; then, partition processing is performed on the remaining data, laying the foundation for the application of the simulated annealing algorithm, which replaces the traditional hill climbing method and is used to denoise the partitioned data. By denoising and refraction correction of ICESat-2 data, and comparing the accuracy with the in-situ observed water depth data, the results show that the correlation coefficient between the denoised ICESat-2 data and the in-situ data exceeds 0.9, and the average relative error is less than 1%. These results show that the improved DENCLUE algorithm proposed in the present invention has a significant effect on ICESat-2 data denoising, and provides an effective new method for shallow sea remote sensing water depth detection. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 This is a schematic diagram of the ATL03 data of the Great Barrier Reef 1.

[0015] Figure 2 This is a schematic diagram of the ATL03 data of the Great Barrier Reef 2.

[0016] Figure 3 This is the ATL03 data diagram of Ganquan Island.

[0017] Figure 4 This is a schematic diagram of ATL03 data for Oahu.

[0018] Figure 5 It is to improve the DENCLUE algorithm process.

[0019] Figure 6 Schematic diagram of the DENCLUE algorithm data segmentation method of the present invention.

[0020] Figure 7It is a comparison chart of the denoising results of the Great Barrier Reef 1, where (a) is the denoising result of the Great Barrier Reef 1 using the DENCLUE algorithm, (b) is the denoising result of the Great Barrier Reef 1 using the DBSCAN algorithm, and (c) is the confidence-based classification result of the Great Barrier Reef 1.

[0021] Figure 8 It is a comparison chart of the denoising results of the Great Barrier Reef 2, where (a) is the denoising result of the Great Barrier Reef 2 using the DENCLUE algorithm, (b) is the denoising result of the Great Barrier Reef 2 using the DBSCAN algorithm, and (c) is the confidence-based classification result of the Great Barrier Reef 2.

[0022] Fig. 9 The following is a comparison chart of the denoising results of Ganquan Island, where (a) is the denoising result of the DENCLUE algorithm of Ganquan Island, (b) is the denoising result of the DBSCAN algorithm of Ganquan Island, and (c) is the confidence-based classification result of Ganquan Island.

[0023] Fig.10 The following is a comparison chart of the denoising results of Oahu, where (a) is the denoising result of the DENCLUE algorithm on Oahu, (b) is the denoising result of the DBSCAN algorithm on Oahu, and (c) is the confidence-based classification result on Oahu.

[0024] Fig.11 Comparison chart of the accuracy analysis of in-situ measured water depths, where (a) is the accuracy evaluation result of the Great Barrier Reef 1, (b) is the accuracy evaluation result of Ganquan Island, and (c) is the accuracy evaluation result of Oahu Island. DETAILED DESCRIPTION

[0025] The ICESat-2 data is used as an example below to better illustrate the technical solution of the present invention.

[0026] 1. ICESat-2 Data The ICESat-2 satellite was launched by NASA on September 15, 2018. It completes an orbital cycle every 91 days, covering the global latitude range of 88°N to 88°S. It is equipped with an advanced terrain laser altimeter system, which uses photon counting technology to emit low-energy 532nm blue-green light pulses at a frequency of 10kHz. In addition, the pulse width of ATLAS is only 1.5 ns, the center spacing of the footprint is about 0.7 m, and the coverage area of ​​each footprint is 17 m. The ATLAS system simultaneously emits three pairs of laser pulses, with the center spacing of two adjacent pairs of laser pulses being 3.3 km. In each pair of laser pulses, there is a strong pulse and a weak pulse, with a center spacing of 90 m between them and an energy ratio of about 4:1.

[0027] Currently, ICESat-2 provides four layers of data products, including Level-1, Level-2, Level-3A and Level-3B, which combine raw telemetry data with complex processed products to provide researchers with rich information resources. In particular, the Level-2 product, the ATL 03 global positioning point cloud dataset, records point cloud data information in detail, including latitude, longitude and altitude, providing valuable data resources for high-precision measurements of the Earth's surface topography. The data can be downloaded from the NASA website at: https: / / search.earthdata.nasa.gov / search.

[0028] 2. Study area To ensure the reliability of the algorithm proposed in this study, the following key factors were considered in the selection of the study area: water depth conditions, terrain undulation, degree of interference from human activities, and the time of data collection. Based on these criteria, this study finally selected Ganquan Island, the Great Barrier Reef, and Oahu as experimental research areas. Specifically, the water depth of Great Barrier Reef Area 1 does not exceed 5 meters, the terrain is relatively flat, and it is basically not disturbed by human activities; the water depth of Great Barrier Reef Area 2 is less than 10 meters, the terrain is slightly undulating, and there is little impact from human activities; the water depth of Ganquan Island does not exceed 15 meters, the terrain undulations are more obvious, and it is less affected by human activities; the water depth of Oahu can reach up to 20 meters, the terrain undulations vary significantly, and it is greatly affected by human activities. In addition, in order to evaluate the impact of data collection time on the results, this study specially selected ATL03 data at different times: Great Barrier Reef 1: ATL03_20230630070939_01542008_006_02.h5, such as Figure 1 As shown; Great Barrier Reef 2: ATL03_20230408111340_02761908_006_02.h5, such as Figure 2 As shown; Ganquan Island: ATL03_20220317202009_13071401_006_01.h5, such as Figure 3 As shown; Oahu: ATL03_20230630154820_01602001_006_02.h5, such as Figure 4 As shown; The specific trajectory distribution of the four sets of data is also as follows Figure 1-Figure 4 shown.

[0029] 3. In situ observation data In this study, field bathymetric data were used for verification. Digital elevation model data of the Great Barrier Reef, lidar data of Oahu and Ganquan Island, and multibeam bathymetry data of Wuzhizhou Island were obtained. The assessment data of the Great Barrier Reef of Australia is a high-resolution digital elevation model developed by Geoscience Australia with a resolution of 30 meters. This dataset is based on years of ocean mapping and integrates shipborne multi-beam and single-beam echo sounder data, airborne lidar bathymetry data, and satellite-derived seafloor bathymetry data collected from 2010 to 2020. Its elevation is based on the WGS-84 coordinate system. The Ganquan Island data is a composite product of lidar bathymetry data and multi-beam bathymetry data. Among them, the lidar bathymetry data is obtained by the airborne Optech Aquarius bathymetry system with a flight altitude of about 300m; the multi-beam bathymetry data is obtained by the R2SONIC2024 shallow water multi-beam system, and the comprehensive bathymetry accuracy of the dataset is about 35cm. The assessment data for Oahu in the Hawaiian Islands comes from shallow water depth information obtained by Optech using airborne lidar technology in 2013. The lidar system operates in the 532 nm blue-green band and has a root mean square error of 0.3 m.

[0030] 4. Use improved DENCLUE denoising 4.1 Overall Process The single-photon laser radar system carried by the ICESat-2 satellite contains a large amount of noise data in the point cloud data of the ocean area. The DENCLUE algorithm can adapt to complex data distribution structures, and is particularly suitable for complex data sets where natural data distribution may be composed of multiple different density areas. This is particularly important when processing non-uniformly distributed data sets, while DBSCAN and OPTICS may not perform well on such data sets. In addition, the DENCLUE algorithm is less sensitive to parameters, which makes it easier to adjust and use in practical applications. The DBSCAN algorithm is very sensitive to the selection of parameters, and although the OPTICS algorithm provides a method that does not require a preset number of clusters, there are still certain difficulties in parameter selection. Therefore, the present invention uses the DENCLUE algorithm to denoise ICESat-2, but during the day, atmospheric scattering causes a particularly large number of noise points above the sea surface, and spatial clustering is difficult to remove such noise, so the present invention adds the idea of ​​frequency statistics and block classification to improve the accuracy of the DENCLUE clustering algorithm. After data partitioning, the original DENCLUE algorithm is difficult to completely remove the noise points near the seabed signal point cloud. Therefore, the DBSCAN algorithm is added to remove the noise point cloud around the signal point cloud to achieve the purpose of precise denoising. The overall process is as follows: Figure 5 shown.

[0031] 4.2 Data Partitioning ICESat-2 ATL03 data contains a large amount of noise data, which is usually located far away from the sea surface and the seabed. At the same time, the amount of sea surface signal point cloud data is huge, and the sea surface fluctuation generally does not exceed 5 meters. ICESat-2's underwater detection capability usually does not exceed 50 meters. Therefore, the sea surface can be directly identified by the method of high frequency statistics, and the point cloud data within 5 meters above the sea surface and 50 meters below the sea surface can be directly classified as noise point cloud.

[0032] After excluding the noise points far from the sea surface, the distribution of the remaining noise points shows a certain regularity. However, the effect of using the DENCLUE clustering algorithm to denoise these data is not ideal. In view of this, the present invention proposes a new method for data partitioning, which can make the signal point cloud in a small area show an obvious structured distribution by segmenting the data, so as to more effectively identify and remove noise points (such as Figure 6 As shown). The present invention first determines the four upper, lower, left and right boundaries of the data in terms of along-track distance and height, thereby calculating the center point and dividing the data set into four quadrants. Then, the algorithm calculates the number of point cloud data in each quadrant. If the number of data in a quadrant is less than the preset noise point threshold (noise_number), all point clouds in the quadrant are marked as noise points. If the number of data is greater than the preset minimum cluster size (min_number), the quadrant is divided again to form four smaller quadrants, and the number of point clouds in each quadrant is repeatedly counted. If the number of data in a quadrant is between noise_number and min_number, the point cloud in the quadrant can be DENCLUE clustered. In this algorithm, min_number is calculated based on the total number of data points in the point cloud divided by the maximum distance of the point cloud along the track, and the nearest multiple of 5 is taken as the result, but this value will not exceed 50. Noise_number is half of min_number, and also takes the nearest multiple of 5, and its maximum value is also limited to 50. This setting is intended to provide a dynamically adjusted threshold for the clustering algorithm to adapt to point cloud data of different scales and distributions.

[0033] 4.3 Improvements to DENCLUE Since the present invention performs partition processing on the data, in order to better process and adapt to the partition processing method, the present invention improves the DENCLUE algorithm to make it more adaptable to the partition processing data results. The original DENCLUE algorithm uses the hill climbing method to determine the density core, and the improved DENCLUE uses the simulated annealing algorithm to determine the density core. The simulated annealing algorithm helps the algorithm to jump out of the local optimal solution, increase the possibility of finding the global optimal solution, and can effectively avoid falling into the local optimal solution.

[0034] For each data point p[i](xi,yi), kernel density estimation is used to calculate its local density. Kernel density estimation uses the Gaussian kernel function, and the formula is as follows: (1) Among them, p[j](x j ,y j ) are the other points in the dataset and h is the bandwidth parameter. For ICESat-2 ATL03 data, the bandwidth h is automatically calculated based on the standard deviation of the selected point cloud multiplied by 0.2.

[0035] After calculating the kernel density of each point, we use the simulated annealing algorithm to find the density attractor and calculate the new density estimate ρ based on it. The simulated annealing algorithm accepts or rejects new solutions according to the Metropolis criterion (Formula 2) to find the global optimal solution or a solution close to the global optimal solution. Among them, Δρ is the energy difference (here, the change in density), and T is the temperature parameter of simulated annealing.

[0036] (2) For each pair of density attractors p[i] and p[j], we determine whether they are adjacent by calculating the Euclidean distance between them and comparing it to the sum of their respective radii. When the distance between two attractors does not exceed the sum of their radii, we draw an edge between the corresponding nodes of the graph, symbolically connecting the two adjacent attractors. This process ultimately builds a graph where the nodes represent density attractors and the edges map their proximity.

[0037] As the graph is constructed, further analysis is performed to identify and define clusters. Potential clusters are revealed by identifying each connected component in the graph, each of which may correspond to a cluster. Within each connected component, the center of the cluster is determined by finding the point with the highest density, and all points within that component are considered members of the same cluster.

[0038] 5. Accuracy evaluation method The present invention compares and analyzes the ICESat-2 data after denoising and refraction correction in the three study areas with the in-situ bathymetric data to evaluate the effect of data processing. The mean absolute error (MAE), root mean square error (RMSE), mean relative error (MRE) and correlation coefficient (COR) are calculated according to formulas (3) to (6). r 2 ).

[0039] , (3) , (4) , (5) , (6) In the formula The data is retrieved from ICESat-2; data, n is the total number of point clouds.

[0040] In the formula a is the data inverted by ICESat-2; b is the data inverted by ICESat-2 data, n is the total number of point clouds.

[0041] 6. Denoising results and accuracy evaluation 6.1 Denoising Results In order to verify the effectiveness of this denoising method, the denoising results based on the improved DENCLUE are compared with the denoising results of the DBSCAN algorithm and the classification results based on confidence. Figure 7-Figure 10 As shown. The DENCLUE algorithm shows its unique advantages. In the denoising results of the Great Barrier Reef 1, the signal points (red points) show a trend of gradually decreasing from about 50 meters to about 40 meters in elevation, forming a relatively obvious continuous band distribution, while the noise points (black points) are relatively scattered, mainly distributed on the upper and lower sides of the signal points. In the denoising results of the Great Barrier Reef 2, the signal points are mainly concentrated in the elevation range of about 50 meters, showing a relatively flat distribution, while the noise points are distributed more evenly in elevation, but the number is small. In the denoising results of Oahu, the DENCLUE algorithm also retains continuous seabed signal points, which is similar to the denoising results of the DBSCAN denoising algorithm. In the denoising results of Oahu, the signal points show a distribution from 0 meters to about 50 meters in elevation, which is relatively flat overall, and the noise points are widely distributed in elevation, but the number is small. Through these analyses, it can be seen that the DENCLUE algorithm can accurately identify and extract signal points, effectively remove noise interference, and retain the core features of the data when processing scenes with relatively continuous signal point distribution and obvious characteristics. The performance of the DBSCAN algorithm depends significantly on two key parameters: the neighborhood radius and the minimum number of points. Improper parameter selection may lead to significant differences in denoising results. In order to solve this problem, the present invention uses DBSCAN to denoise the data in the appropriate field radius and minimum point cloud in the four study areas. In the ICESat-2ATL03 algorithm theoretical basis document, when the point cloud confidence is 3 and 4, the point cloud can be considered to be a signal point. Therefore, the classification result based on confidence is that the confidence levels of 3 and 4 are signal points, and the point clouds with confidence levels of 0, 1, and 2 are noise points.

[0042] The denoising effects of the improved DENCLUE denoising algorithm and the DBSCAN denoising algorithm are significantly stronger than the confidence-based classification results. In particular, the improved DENCLUE denoising algorithm shows better discrimination ability when dealing with noise between sea surface points and seabed points, effectively avoiding the situation where noise is misjudged as signal points. In addition, the algorithm can retain more signal point clouds when the data volume is small or the data depth is large, which is crucial for subsequent data analysis and processing. However, under the condition that the noise points are densely distributed during the day, the DBSCAN algorithm tends to mistakenly divide the noise-dense areas into signal points, which limits its application effect in high-noise environments. The following situation occurs mainly because the DENCLUE algorithm can effectively filter noise during the clustering process, especially when the data distribution is uneven. Through partition processing, DENCLUE can cluster in local areas, thereby reducing the impact of noise on the overall clustering results. However, DBSCAN may misjudge noise as signal points in a high-noise environment, resulting in a decrease in clustering effect.

[0043] 6.2 Accuracy Evaluation Because the data of the Great Barrier Reef 2 is located in the coral reef and the DEM changes quickly, the data of this area is not used for evaluation during verification. In order to further verify the accuracy of this method, the denoised data of the three study areas were refraction corrected and compared with the actual measured water depth data for accuracy evaluation. When the laser pulses emitted by ICESat-2 penetrate the water body, they will be refracted according to Snell's law. Therefore, before the water depth accuracy evaluation is performed, the ICESat-2 data must be refraction corrected. At present, the most widely used refraction correction method in ICESat-2 data is the refraction correction technology based on the mean sea level assumption proposed by Parrish et al. This study adopted this method for refraction correction. The measured water depth data of the three areas are all in the WGS-84 coordinate system, and the seabed point data of ICESat-2 in this coordinate system can be directly used for comparison.

[0044] When analyzing the data from the three study areas (e.g. Fig.11 ), most of the data fit closely to the 1:1 line, showing high consistency of the data. Although affected by seawater characteristics, refraction correction and terrain changes, the water depth data showed slight deviations. Especially in the Great Barrier Reef area, the small amount of noise points left over from the denoising process led to abnormal points in the accuracy assessment. Nevertheless, the correlation coefficients between the refraction-corrected ICESat-2 data and the in-situ water depth data exceeded 0.9, indicating a significant correlation. This result confirms the effectiveness of the improved DENCLUE denoising algorithm in retaining seafloor signal points, maintaining high data accuracy and reliability even in complex marine environments.

[0045] 7. Conclusion This paper proposes an improved DENCLUE algorithm, which aims to optimize the data processing process to improve the denoising performance. The method first performs frequency statistics on the data to identify and remove the data far away from the signal point area; then, the remaining data is partitioned to lay the foundation for the application of the simulated annealing algorithm, which replaces the traditional hill climbing method and is used to denoise the partitioned data. The improved DENCLUE algorithm is significantly better than the DBSCAN algorithm and the confidence-based classification method in denoising. It can not only effectively remove the noise between the sea surface points and the seabed points, but also better retain the sparsely distributed signal points, which is crucial to maintain data integrity.

[0046] Through the depth accuracy evaluation of the Great Barrier Reef, Ganquan Island and Oahu Island, it was found that the denoising method proposed in the present invention has an average relative error of less than 1% between the seabed data and the in-situ measured data, a determination coefficient of more than 0.9, an average absolute error of less than 1.0m, and a root mean square error of less than 1.5m. These accuracy evaluation indicators are significantly better than traditional denoising methods such as DBSCAN, proving the effectiveness and reliability of the improved DENCLUE algorithm in high-precision ICESat-2 data processing.

Claims

1. Photon counting lidar denoising method based on improved DENCLUE, characterized by The following steps are involved: 1) Select the research area and obtain the global positioning point cloud dataset of the research area; 2) Eliminate noise points far from the sea surface: The sea surface is directly identified by the method of high frequency statistics, and the point cloud data within the range of 5 meters above the sea surface and 50 meters below the sea surface are directly classified as noise point clouds; 3) Data segmentation: For the denoised data set, first determine the upper, lower, left, and right boundaries of the data in terms of along-track distance and height, calculate the center point, divide the data set into four quadrants, and calculate the number of point cloud data in each quadrant; If the number of point clouds in a quadrant is less than the preset noise point threshold noise_number, all point clouds in the quadrant are marked as noise points; If the number of point clouds in a quadrant is between noise_number and min_number, the point clouds in the quadrant can be clustered using improved DENCLUE. If the number of point clouds in a quadrant is greater than the preset minimum cluster size min_number, the quadrant is divided again to form four smaller quadrants, and the number of point clouds in each quadrant is repeatedly counted until the previous two conditions are met; 4) Use improved DENCLUE for denoising: The improved DENCLUE uses a simulated annealing algorithm to determine the density core.

2. The photon counting laser radar denoising method based on improved DENCLUE as claimed in claim 1, characterized in that In step 3), min_number is calculated by dividing the total number of data points in the point cloud by the maximum distance of the point cloud along the track, and the result is rounded to the nearest multiple of 5, and this value does not exceed 50; noise_number is half of min_number, and is also rounded to the nearest multiple of 5, and its maximum value is also limited to 50.

3. The photon counting laser radar denoising method based on improved DENCLUE as claimed in claim 1, characterized in that In step 4), for each data point p [ i ]=( x i , y i ), use kernel density estimation to calculate its local density. The kernel density estimation uses the Gaussian kernel function, and the formula is as follows: （1）， in, p [ j ]=( x j , y j ) are other points in the data set, h is the bandwidth parameter; n is the total number of point clouds in the dataset; After calculating the kernel density of each point, the simulated annealing algorithm is used to find the density attractor and calculate the new density estimate ρ accordingly. The simulated annealing algorithm accepts or rejects the new solution according to the Metropolis criterion of formula 2 to find the global optimal solution or a solution close to the global optimal solution. Among them, Δρ is the energy difference, which is the change in density in this case, and T is the temperature parameter of the simulated annealing. According to the Metropolis criterion, the calculated result of the probability P(accept) is between [0,1], indicating the probability of accepting the new solution. If P(accept) > 0.5, that is, close to 1, the new solution is accepted. If P(accept) ≤ 0.5, that is, close to 0, the new solution is rejected. （2） For every pair of density attractors p [ i ]and p [ j ], by calculating the Euclidean distance between them and comparing it with the sum of their respective radii to determine whether they are adjacent; when the distance between two attractors does not exceed the sum of their radii, an edge is drawn between the corresponding nodes of the graph, symbolically connecting the two adjacent attractors; this process ultimately constructs a graph in which the nodes represent density attractors and the edges map the proximity between them; as the graph is constructed, clusters are identified and defined.

4. The photon counting laser radar denoising method based on improved DENCLUE as claimed in claim 3, characterized in that In step 4), for ICESat-2 ATL03 data, the bandwidth h is automatically calculated based on the standard deviation of the selected point cloud multiplied by 0.2.

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