Satellite-borne photon counting laser radar point cloud denoising method and device and storage medium

Abstract

The invention discloses a satellite-borne photon counting laser radar point cloud denoising method and device and a storage medium, and the method comprises the steps: segmenting and delimiting a window in a calculation unit in an orbit direction, and calculating a maximum difference window; the method comprises the following steps: respectively taking a window above and below a signal window, defining the three windows as potential signal windows, and removing noise outside the potential signal windows to serve as first-step coarse de-noising; the product of the calculated average noise density and the circle area is used as the minimum neighborhood point number of a DBSCAN algorithm, and second-step coarse denoising is carried out on potential signal window photons; and constructing a minimum neighborhood point number under the influence of different signal-to-noise ratios, and performing fine denoising by using a clustering method based on a density space. The method not only considers the signal-to-noise ratio as a dynamic adjustment parameter, but also combines the data distribution characteristics, can perform adaptive adjustment in a mountainous area with large terrain gradient and high vegetation coverage, and reduces the subjectivity caused by manual determination of a clustering threshold.

Description

Technical Field

[0001] The present invention belongs to the field of ecological remote sensing, and in particular relates to a spaceborne photon counting lidar point cloud denoising method based on dynamic signal-to-noise ratio and data distribution characteristics. Background Art

[0002] The ICESat-2 spaceborne lidar satellite uses multi-beam micropulse photon counting altimetry technology. Due to its higher detection frequency and sensitivity in single-photon ranging mode, it is currently widely used for measuring vegetation height in forested areas. Complex mountainous terrain and dense vegetation cover reduce signal intensity, significantly increasing the difficulty of point cloud denoising. Traditional and improved algorithms are not well adapted to this unique terrain. Therefore, developing point cloud denoising algorithms suitable for densely forested mountainous areas is a cutting-edge and hot topic of research both domestically and internationally. Density-based spatial clustering algorithms are one effective denoising method, but the elliptical search range is ambiguous, and the manual determination of the minimum neighborhood point count threshold is highly subjective and empirical. Therefore, a new technical solution is needed to address this issue. Summary of the Invention

[0003] The purpose of the present invention is to provide a point cloud denoising method for spaceborne photon counting lidar based on dynamic signal-to-noise ratio and data distribution characteristics. The method uses the characteristics of signal-to-noise density difference to estimate the terrain slope of adjacent segments and thus optimize the elliptical search range. Based on the spatial distribution characteristics of photons, an equation for determining the minimum number of neighborhood points under the influence of different signal-to-noise ratios is constructed, thereby solving the aforementioned problems existing in the prior art.

[0004] In order to achieve the above object, the present invention specifically adopts the following technical solutions: A method for denoising a spaceborne photon counting lidar point cloud based on dynamic signal-to-noise ratio and data distribution characteristics, characterized by comprising the following steps: Step 1: Divide the calculation unit range of 1 km along the track into 5 200-meter segment intervals. In each segment interval, every 50 meters along the elevation direction is used as a window. Calculate and count the adjacent windows with the maximum photon number difference. ; Step 2, in the signal window Take a window above and below as the potential signal window , removing the noise outside the potential signal window is used as the first step of coarse denoising.

[0005] Step 3: Use the average noise density The product of the circle area is used as the minimum number of neighborhood points for the DBSCAN algorithm. Perform the second step of coarse denoising; Step 4: Normalize the signal-to-noise ratio. Based on the empirical rule theory, introduce the signal-to-noise ratio As a dynamic adjustment parameter, it adapts to changes in window signal strength The value is refined for denoising.

[0006] In step 1, the segment interval, window, and maximum difference window of each 1km calculation unit are defined. The specific steps include: Step 11: Set the segment interval and divide the single calculation unit into five 200-meter segment intervals, recorded as (in ).

[0007] Step 12: In each segment In the definition window is (in , and the height interval of each window is 50 meters).

[0008] Step 13, calculate the difference in the number of photons in adjacent windows. and , the difference in the number of photons in adjacent windows can be expressed as:

[0009] Where, and Window and The number of photons in Indicates the absolute value of the difference in the number of photons in adjacent windows.

[0010] Step 14: Repeat step 13 in each 200-meter segment. Calculate the difference in the number of photons in each window and find the largest difference:

[0011] Where, Indicates the maximum absolute value of the difference in the number of photons in adjacent windows, Indicates the window label corresponding to the maximum absolute value of the difference in the number of photons in adjacent windows.

[0012] We will label it as The window is defined as the signal window .

[0013] In step 2, the potential signal window and the potential noise window are divided, the noise density and signal density are calculated, and the minimum number of neighborhood points of the spatial clustering algorithm is preliminarily set. , complete the first step of coarse denoising, the specific steps include: Step 21, in the window labeled Signal Window Take a window above and below and , these three windows are defined as potential signal windows (PSW); the window outside the potential signal window is regarded as potential noise window (PNW), which is defined as:

[0014] Where, is the potential signal window, is the potential noise window; Assume that the total number of photons in the first segment is , the total number of photons in the potential signal window is , the total number of photons in the potential noise window is , defined as:

[0015] Where, This is the number of remaining photons after the first step of coarse denoising. This is the number of noise photons removed in the first step; Step 22, set Potential noise window The number of noise photons in , the area of ​​the window is ; Then, the window The amount of noise per unit area is the noise density for:

[0016] For all potential noise windows, the number of potential noise windows is , the average value of the noise density It can be expressed as:

[0017] Similarly, Potential signal window The number of signals per unit area is the signal density , the area of ​​the window is ; Then, the window The number of signals per unit area is the signal density for:

[0018] For all potential signal windows, the average value of the signal density Expressed as:

[0019] Where, These are the labels of the potential signal windows; Step 23: The number of noise points obtained by multiplying the average noise density and the circle area is used as the minimum number of neighborhood points. , with the minimum number of neighborhood points is a parameter, the minimum number of neighborhood points for:

[0020] Where, is the area of ​​the circle;

[0021] Where, is the radius of the circle.

[0022] Based on the first step of coarse denoising, the DBSCAN clustering algorithm is used to perform the second step of coarse denoising, and the amount of noise removed is , defined as:

[0023] Where, is the number of remaining photons after the second step of coarse denoising using the DBSCAN clustering algorithm; In step 4, the dynamic minimum number of neighborhood points is calculated based on statistical empirical rules and the distribution characteristics of photon data and the signal-to-noise ratio. , the specific steps include: Step 41: Count each photon point by continuously adjusting the direction angle of the elliptical search domain The maximum number of neighboring photons The frequency of the number of intervals and the frequency of the number of intervals The maximum number of neighborhood photons obtained Sum frequency Draw a quantity-frequency histogram and perform Gaussian fitting on the drawn histogram data to obtain the best mean and standard deviation .

[0024] Step 42, specifically, calculate the signal-to-noise ratio of each 200-meter segment within each 1 km calculation unit. , and its calculation formula is:

[0025] Where, and are the average values ​​of signal and noise density within the segmented interval respectively; Step 43, consider the signal-to-noise ratio for clustering parameters The influence of the normalized signal-to-noise ratio is used to Scaling to between 0 and 1, the calculation formula is as follows:

[0026] Where, and It indicates the minimum and maximum values ​​of the signal-to-noise ratio within each 1km calculation unit.

[0027] Step 44, use the normalized signal-to-noise ratio to adjust the multiple:

[0028] Where, is the benchmark value, To control the parameters of the signal-to-noise ratio, we make the fold change proportional to the signal-to-noise ratio and keep it within a reasonable range. is 1, is 2.

[0029] Step 45, keep Adjust within a reasonable range and calculate the dynamics using the following formula :

[0030] Step 46, based on the coarse denoising in the second step, the improved DBSCAN algorithm (optimized ellipse search angle, based on the signal-to-noise ratio and data distribution characteristics) is used. Parameters) for fine denoising, the amount of noise removed is , defined as:

[0031] Where, This is the number of remaining photons after the third step of fine denoising using the improved DBSCAN clustering algorithm.

[0032] Beneficial effects of the present invention: The present invention provides a method for denoising point clouds of spaceborne photon counting lidar based on dynamic signal-to-noise ratio and data distribution characteristics. First, the potential signal window is found within a 200-meter segmented interval by using the signal-to-noise density difference characteristic, the signal density and noise density are calculated, and the noise outside the potential signal window is removed as the first step of coarse denoising; then the average noise density is used to calculate the noise density. The product of the circle area is used as the minimum number of neighborhood points for the DBSCAN algorithm. Perform the second step of coarse denoising; then calculate the terrain slope of adjacent segments based on the distribution characteristics of photons along the slope direction ,by Limit the ellipse search angle to the interval range, and then optimize the search range of the elliptical domain; finally, based on the empirical rule theory, the signal-to-noise ratio is introduced As a dynamic adjustment parameter, it adapts to changes in window signal strength Based on photon density and terrain slope, the present invention realizes the point cloud denoising process under the influence of signal-to-noise ratio, reduces the subjectivity brought by artificial determination of the minimum number of neighborhood points of the clustering threshold, and makes up for the defects of the current point cloud denoising in complex mountainous areas, making the density-based spatial clustering algorithm more universal. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 This is a flow chart of a method for denoising a point cloud of a spaceborne photon counting lidar based on dynamic signal-to-noise ratio and data distribution characteristics provided by the present invention; Figure 2 It is a division diagram of the computing unit, segmented interval, and window in a specific embodiment; Figure 3 This is the first step of the rough denoising of the window photon point cloud in the specific embodiment; Figure 4 This is the second step coarse denoising image of the window photon point cloud in a specific embodiment; Figure 5 It is a denoised image of the window photon point cloud in a specific embodiment. DETAILED DESCRIPTION

[0034] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0035] It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0036] Example 1

[0037] This embodiment provides a method for denoising a point cloud of a spaceborne photon counting lidar based on dynamic signal-to-noise ratio and data distribution characteristics. The denoising flow chart is as follows: Figure 1 As shown, the following steps are included: S1. Define the segmentation interval, window and maximum interpolation window of the calculation unit. The specific method is: Every 1 km along the track direction is regarded as a calculation unit, and each calculation unit is divided into five 200 m segmented intervals. In each segmented interval, every 50 m along the elevation direction is regarded as a window, and the window with the maximum photon number difference is calculated and counted as the signal window.

[0038] The length of the calculation unit, the length of the segment, and the elevation data of the window are not limited to 1 km, 200 m, and 50 m data. 1 km, 200 m, and 50 m are only specific embodiments.

[0039] Taking the Tunxi River Basin as an example, step S1 includes: S1.1. Log in to the ICESat-2 official website and select an ATL03 data file for the Tunxi River Basin to download.

[0040] S1.2. Draw a scatter plot based on the extracted photon height h_ph and along-track distance along_track_x. Divide the scatter plot into 1 km calculation units, 20 m segment intervals, and 50 m windows. Calculate and count the window with the maximum photon number difference as the signal window. ,like Figure 2 shown.

[0041] S2. Based on the potential signal window, remove the noise outside the potential signal window as the first step of coarse denoising: The specific method of step S2 is: In the window labeled Signal Window Take a window above and below and , these three windows are defined as potential signal windows (PSW); the window outside the potential signal window is regarded as potential noise window (PNW), which is defined as:

[0042] Where, is the potential signal window, Potential noise window.

[0043] Assume that the total number of photons in the first segment is , the total number of photons in the potential signal window is , the total number of photons in the potential noise window is , defined as:

[0044] Where, This is the number of remaining photons after the first step of coarse denoising. This is the number of noise photons removed in the first step.

[0045] After completing the first step of denoising, Figure 3 shown.

[0046] S3, based on the DBSCAN algorithm, the product of noise density and circle area is used as The parameters are used to perform the second step of coarse denoising on the potential signal window photons: Step S3 includes: Using the calculated average noise density The product of the circle area is used as the minimum number of neighborhood points for the DBSCAN algorithm. The second step of coarse denoising is performed, such as Figure 4 shown.

[0047] S3.1、Set Potential noise window The number of noise photons in , the area of ​​the window is ; Then, the window The amount of noise per unit area is the noise density for:

[0048] For all potential noise windows, the number of potential noise windows is , the average value of the noise density Expressed as:

[0049] Similarly, Potential signal windows The number of signals per unit area is the signal density , the area of ​​the window is ; Then, the window The number of signals per unit area is the signal density for:

[0050] For all potential signal windows, the average value of the signal density Expressed as:

[0051] Where, are labels of potential signal windows, respectively.

[0052] S3.2. The number of noise points obtained by multiplying the average noise density and the circle area is used as the minimum number of neighborhood points. , with the minimum number of neighborhood points is a parameter, the minimum number of neighborhood points for:

[0053] Where, is the area of ​​the circle;

[0054] Where, is the radius of the circle.

[0055] S3.3, with the minimum number of neighborhood points As the clustering parameter, the DBSCAN clustering algorithm is used to perform the second step of coarse denoising, and the amount of noise removed is ; After the second step, the number of remaining photons is obtained:

[0056] Where, is the number of remaining photons after the second step of coarse denoising using the DBSCAN clustering algorithm.

[0057] S4, introduce the signal-to-noise ratio parameter to construct the Calculate the formula and use density-based spatial clustering method for fine denoising; Step S4 includes: S4.1. Count each photon point by continuously adjusting the direction angle of the elliptical search domain The maximum number of neighboring photons The frequency of the number of intervals and the frequency of the number of intervals The maximum number of neighborhood photons obtained Sum frequency Draw a quantity-frequency histogram and perform Gaussian fitting on the drawn histogram data to obtain the best mean and standard deviation .

[0058] S4.2. Specifically, within each 1km calculation unit, calculate the signal-to-noise ratio of each 200m segment interval , and its calculation formula is:

[0059] Where, and are the average values ​​of signal and noise density within the segmented interval, respectively.

[0060] S4.3. Considering the minimum number of neighborhood points for clustering parameters based on signal-to-noise ratio The influence of the normalized signal-to-noise ratio is used to Scaling to between 0 and 1, the calculation formula is as follows:

[0061] Where, and They represent the minimum and maximum signal-to-noise ratio within each 1km calculation unit.

[0062] S4.4. Use normalized signal-to-noise ratio to adjust the fold:

[0063] Where, is the benchmark value, To control the parameters of the signal-to-noise ratio, we make the fold change proportional to the signal-to-noise ratio and keep it within a reasonable range. is 1, is 2.

[0064] S4.5. Dynamically calculate the minimum number of neighborhood points using the following formula :

[0065] S4.6, based on the second step of coarse denoising, with the minimum number of neighborhood points As the clustering parameter, the DBSCAN algorithm is used for fine denoising, and the amount of noise removed is ; After fine denoising, the final number of remaining photons is obtained:

[0066] Where, is the number of remaining photons after the third step of fine denoising based on the DBSCAN clustering algorithm.

[0067] Maximum number of neighboring photons in step S4.1 The method of determining is: The search angle range is determined, and an elliptical neighborhood is used to search for the maximum number of neighboring photon points of each photon point within the search angle range.

[0068] Calculate the terrain slope of adjacent segment intervals. Assume that two adjacent segment intervals and , each segment interval has a signal window , the slope of adjacent segment intervals is defined as , that is, the maximum possible distribution angle of signal photons in adjacent signal windows is:

[0069] Where, and Two adjacent segment intervals correspond to signal windows Center height; Indicates the horizontal distance between two adjacent segment intervals, i.e. 200 meters; Since the distribution of signal photons along the slope direction is random, As the signal photon distribution angle range, the search angle of the elliptical domain is optimized, that is, the optimized search angle range is:

[0070] Where, is the search angle range.

[0071] Based on the DBSCAN clustering algorithm, is the center of the ellipse, and its Ellipse distance Defined as:

[0072]

[0073] in,

[0074] Where, and are the major and minor axes of the ellipse, respectively. For forest vegetation covered areas, a=6b is usually taken, and for crop growing areas, a=9b is taken. is the direction angle of the elliptical search domain, and Points The horizontal and vertical coordinates of and Points The horizontal and vertical coordinates of .

[0075] By continuously rotating the elliptical domain and calculating the number of photon points at each angle, the maximum number of neighborhood photon points of each photon point in the search interval is explored, thereby improving the accuracy and efficiency of photon point cloud analysis.

[0076] For a given point and angle parameters ,function Indicates the number of points in the dataset that meet the following conditions: Belong to the dataset ;point with dot The distance between ) is less than or equal to 1.

[0077]

[0078] In layman's terms, this formula calculates In, all The number of points whose distance does not exceed 1, that is, the number of photon points inside the ellipse.

[0079] Next, define the range of direction angles:

[0080] Where, Indicates the minimum value rounded down. Indicates the maximum value rounded up.

[0081] In angle Points within range The maximum number of neighboring photons in the elliptical search domain The calculation is as follows:

[0082] Where, Indicates lower point of angle The number of photons in the elliptical search domain.

[0083] Example 2 This embodiment provides a device for calculating flow generation. The device includes a processor and a memory. The memory stores a program or instruction, which is loaded and executed by the processor to implement the spaceborne photon counting lidar point cloud denoising method of embodiment 1.

[0084] Example 3 This embodiment provides a computer-readable storage medium, which may be a non-volatile computer-readable storage medium or a volatile computer-readable storage medium. The computer-readable storage medium stores instructions. When the instructions are executed on a computer, the computer executes the spaceborne photon counting lidar point cloud denoising method of embodiment 1.

[0085] Those skilled in the art will clearly understand that the technical solution of the present invention, or the portion that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes instructions for causing a computer device (which may be a personal computer, server, or network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk.

[0086] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any improvements and optimizations made by those skilled in the art without departing from the scope of the present invention should be considered as within the scope of protection of the present invention.

Claims

1. A method for denoising point cloud of spaceborne photon counting lidar based on dynamic signal-to-noise ratio and data distribution characteristics, characterized in that: The following steps are involved: Step 1: along the track direction, according to the set distance as the calculation unit, segment and delineate the window in the calculation unit, and calculate the maximum difference window; Step 2. In the window labeled Signal Window Take a window above and below and , these three windows are defined as potential signal windows, and the noise removal outside the potential signal windows is taken as the first step of coarse denoising; Step 3 uses the calculated average noise density The product of the circle area is used as the minimum number of neighborhood points for the DBSCAN algorithm. , perform the second step of coarse denoising on the potential signal window photons; Step 4: Normalize the signal-to-noise ratio and construct the minimum number of neighborhood points under different signal-to-noise ratios , and use density-based spatial clustering method for fine denoising.

2. The method for denoising a point cloud of a spaceborne photon counting laser radar according to claim 1, characterized in that: In step 1, the method for calculating the maximum difference window is: Calculate the difference in the number of photons in adjacent windows. and , the difference in the number of photons in adjacent windows is expressed as: In the formula, and The windows are and The number of photons in Represents the absolute value of the difference in the number of photons in adjacent windows; Calculate the difference in the number of photons for each window and find the largest difference: In the formula, Represents the maximum absolute value of the difference in the number of photons in adjacent windows, Indicates the window label corresponding to the maximum absolute value of the difference in the number of photons in adjacent windows.

3. The method for denoising a point cloud of a spaceborne photon counting laser radar according to claim 1, characterized in that: In step 1, the distance set in the calculation unit is 1 km; the number of segments in the calculation unit is 5, which is recorded as ,in .

4. The method for denoising a point cloud of a spaceborne photon counting laser radar according to claim 3, characterized in that: The number of windows in the computational unit is: In the definition window is ,in , and the height interval of each window is 50 meters.

5. The method for denoising a point cloud of a spaceborne photon counting laser radar according to claim 1, characterized in that: The step 2 comprises: In the window labeled Signal Window Take a window above and below and , these three windows are defined as potential signal windows; the windows outside the potential signal windows are regarded as potential noise windows: In the formula, is the potential signal window, is the potential noise window; Assume that the total number of photons in the first segment is , the total number of photons in the potential signal window is , the total number of photons in the potential noise window is : In the formula, This is the number of remaining photons after the first step of coarse denoising. This is the number of noise photons removed in the first step.

6. The method for denoising a point cloud of a spaceborne photon counting laser radar according to claim 1, characterized in that: The step 3 comprises: Step 31, set Potential noise window The number of noise photons in , the area of ​​the window is ; Then, the window The noise density is the number of noises per unit area. for: For all potential noise windows, assume that the total number of potential noise windows is , the average value of the noise density It is expressed as: Similarly, Potential signal window The number of signals per unit area is the signal density , the area of ​​the window is ; Then, the window The number of signals per unit area is the signal density for: For all potential signal windows, the average value of the signal density It is expressed as: In the formula, They are the labels of the potential signal windows; Step 32: The number of noise points obtained by multiplying the average noise density by the circle area is used as the minimum number of neighborhood points. , minimum number of neighborhood points for: In the formula, is the area of ​​the circle; Step 33, with the minimum number of neighborhood points As the clustering parameter, the DBSCAN clustering algorithm is used for the second step of coarse denoising, and the amount of noise removed is ; After the second step, the remaining number of photons is obtained: In the formula, It is the number of remaining photons after the second step of coarse denoising using the DBSCAN clustering algorithm.

7. The method for denoising a point cloud of a spaceborne photon counting laser radar according to claim 1, characterized in that: The step 4 comprises: Step 41, by continuously adjusting the direction angle of the elliptical search domain, count each photon point The maximum number of neighboring photons , divide the quantity into intervals and count the frequency ; The maximum number of neighborhood photons that will be obtained Sum frequency Draw a number-frequency histogram and perform Gaussian fitting on the drawn histogram data to obtain the best mean and standard deviation ; Step 42, calculate the signal-to-noise ratio of each 200-meter segment interval: In the formula, is the signal-to-noise ratio, and are the average values ​​of signal and noise density in the segmented interval, respectively; Step 43, consider the minimum number of neighborhood points of the clustering parameter based on the signal-to-noise ratio The influence of Scaling to between 0 and 1, the calculation formula is as follows: In the formula, and They represent the minimum and maximum values ​​of the signal-to-noise ratio in each 1km calculation unit respectively; Step 44, use the normalized signal-to-noise ratio to adjust the multiple: In the formula, is the base value, To control the parameters of the influence of the signal-to-noise ratio, the fold change is proportional to the signal-to-noise ratio and remains within a reasonable range; Step 45, Keep Adjust within a reasonable range and calculate the dynamic minimum number of neighborhood points using the following formula : ; Step 46, based on the coarse denoising in the second step, the minimum number of neighborhood points As the clustering parameter, the DBSCAN algorithm is used for fine denoising, and the amount of noise removed is ; After fine denoising, the final number of remaining photons is obtained: In the formula, It is the number of remaining photons after the third step of fine denoising using the DBSCAN clustering algorithm.

8. The method for denoising a point cloud of a spaceborne photon counting laser radar according to claim 7, characterized in that: The maximum number of neighboring photons in step S41 The method of determining is: The slopes between adjacent segment intervals are defined by : In the formula, and The signal windows corresponding to two adjacent segment intervals are The center height of Indicates the horizontal distance between two adjacent segment intervals; According to the defined interval slope, determine the search angle range of the optimization ellipse domain: In the formula, is the search angle range; Based on the DBSCAN clustering algorithm, is the center of the ellipse, and its The ellipse distance is defined as: in, In the formula, and are the major and minor axes of the ellipse, is the direction angle of the elliptical search domain, and Points The horizontal and vertical coordinates of and Points The horizontal and vertical coordinates of By continuously rotating the ellipse and calculating the number of photon points at each angle, the maximum number of neighboring photon points of each photon point in the search interval is explored. The number of photons in the elliptical search domain The calculation formula is: In the formula, represents the photon point in the ellipse domain, Indicated in lower point of angle The number of photons in the elliptical search domain; Define the range of direction angles: In the formula, Indicates the minimum value to round down to. Indicates the maximum value rounded up; In Angle Points within range The maximum number of neighboring photons in the elliptical search domain The calculation of is as follows: In the formula, Indicated in lower point of angle The number of photons in the elliptical search domain.

9. A spaceborne photon counting laser radar point cloud denoising device, characterized in that: It comprises a processor and a memory; the memory stores a program or instruction, and the program or instruction is loaded and executed by the processor to implement the steps of the satellite-borne photon counting lidar point cloud denoising method as claimed in any one of claims 1 to 8.

10. A computer-readable storage medium storing a program or instruction, wherein the program or instruction, when executed by a processor, implements the steps of the method for denoising a space-borne photon counting lidar point cloud as claimed in any one of claims 1 to 8.

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