Single-photon denoising method based on alternating transverse and longitudinal division

Abstract

The invention discloses a single photon denoising method based on alternating transverse and longitudinal division, and relates to the technical field of photon data processing. Performing homogenization preprocessing on original photon data, and eliminating the influence of non-uniform photon distribution by dynamically adjusting along-track coordinates; recursively executing vertical division and horizontal division by adopting an alternating transverse and longitudinal division strategy, and ensuring that the sum of distances between photons on two sides of a division line and the division line is equal until a termination condition is met; counting the number of times that photons are divided, and adaptively selecting an optimal threshold value to filter noise photons in combination with a maximum between-class variance method. According to the method, the division lines are dynamically selected to perform transverse and longitudinal alternate division, and the optimal division threshold is adaptively determined by adopting the maximum between-class variance method in combination with the statistical characteristics of the number of times of division of photons, so that efficient separation of signal photons and noise photons can be realized.

Description

Technical Field

[0001] The present invention relates to the technical field of photon data processing, and specifically to a single-photon denoising method based on alternating horizontal and vertical partitioning. Background Art

[0002] Laser altimetry satellites, such as ICESat-2, obtain surface photon data through photon-counting laser altimeters. However, due to the influence of solar background light and instrument noise, the data contains a large number of noise photons.

[0003] Existing denoising methods, such as clustering algorithms, waveform statistics methods, and local feature calculation methods, have problems of relying on input parameters and poor adaptability to surface types. The traditional quadtree method distinguishes signal and noise photons by recursively dividing into four sub-regions. Although it does not require input parameters, its fixed partitioning mode does not consider the distance balance of the photon spatial distribution, which may lead to computational redundancy or insufficient adaptability to photon data with specific distributions.

[0004] In addition, existing methods mostly use fixed thresholds or simple statistical thresholds, and do not fully utilize the inter-class distribution characteristics of the number of photon partitions, so the adaptability is poor. For the above reasons, there is an urgent need for a more flexible and efficient photon denoising method at present. Summary of the Invention

[0005] To solve the deficiencies in the background art, the present invention provides a single-photon denoising method based on alternating horizontal and vertical partitioning. It dynamically selects the partitioning line for horizontal and vertical alternating partitioning, combines the statistical characteristics of the number of times photons are partitioned, and adaptively determines the optimal partitioning threshold using the maximum inter-class variance method, capable of efficiently separating signal photons and noise photons.

[0006] To achieve the above object, the present invention adopts the following technical solution: A single-photon denoising method based on alternating horizontal and vertical partitioning, comprising the following steps:

[0007] Step 1: Obtain the original photon data, perform homogenization preprocessing, calculate the global background photon count rate mean μ, and statistically calculate the local background photon count rate μ local , and eliminate the influence of uneven photon distribution by dynamically adjusting the along-track distance to make the local background photon count rate approach the global background photon count rate mean;

[0008] Step 2: Based on the original photon data after homogenization preprocessing, adopt an alternating horizontal and vertical partitioning strategy. Each time of partitioning ensures that the sum of the distances between the photons on both sides of the partitioning line and the partitioning line is equal. When initially partitioning, the photons are partitioned parallel to the x-axis to obtain two sub-regions. When secondarily partitioning, the photons in the sub-regions are partitioned parallel to the y-axis. Repeat the above two partitioning processes to perform recursive partitioning until each sub-region contains less than two photons or reaches the preset depth;

[0009] Step 3: Count the number of times each photon is divided. Based on the distribution of the number of times photons are divided, use the Otsu method to determine the threshold for the optimal division. Photons with a division count lower than the threshold are determined as noise and filtered out to output the denoising result.

[0010] Further, in the above Step 1, the along-track distance is dynamically adjusted using the following formula:

[0011] x adjusted = x + Δ·sgn(μ - μ local )

[0012] where x adjusted represents the adjusted value, x represents the original value, and Δ represents the adjustment amount.

[0013] Further, the calculation formula for the mean value μ of the global background photon count rate is as follows:

[0014]

[0015] where N total is the total number of photons, and L track is the along-track distance.

[0016] Further, the adjustment amount Δ ∈ [a, b], where a = 0.05 m and b = 0.2 m.

[0017] Further, in the above Step 3, the threshold solving formula is as follows:

[0018]

[0019] where k * represents the final threshold, k represents the threshold, L - 1 represents the maximum value of the threshold, ω0 and ω1 respectively represent the ratios of photons with layer values less than t and greater than or equal to t, and μ0 and μ1 respectively represent the mean values of the photon layer values with layer values less than t and greater than or equal to t.

[0020] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0021] 1. The present invention proposes an alternating horizontal and vertical division strategy based on a dynamic mean division line, ensuring the balance of the photon distances on both sides of the division line, improving the division balance and accuracy. Through a dynamic uniform preprocessing algorithm, the photon density difference in the along-track direction is eliminated, improving the division robustness, and achieving an efficient separation of signal photons and noise photons;

[0022] 2. The present invention traverses and optimizes using the Otsu method, adaptively determines the optimal threshold, and realizes threshold adaptability by combining the between-class distribution characteristics of the number of photon divisions, without manual intervention, solving the problems of redundant calculation and poor surface adaptability caused by the dependence on manual parameters and fixed division modes in existing methods;

[0023] 3. The division mode of the present invention adapts to different photon distributions, reduces the sensitivity of the fixed quadtree structure to complex surfaces, and the single-direction division reduces the recursive complexity, making it suitable for large-scale photon data processing. Combining uniform preprocessing and dynamic threshold selection, it is especially suitable for scenarios such as polar ice sheet monitoring, vegetation biomass estimation, and ocean terrain mapping, with the advantages of high precision and high efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 is the flowchart of the method of the present invention;

[0025] Figure 2 is the comparison diagram of photon distributions before and after uniform preprocessing in the embodiment;

[0026] Figure 3 is the schematic diagram of the construction process of alternating horizontal and vertical division in the embodiment;

[0027] Figure 4 is the schematic diagram of the node structure of alternating horizontal and vertical division in the embodiment;

[0028] Figure 5 is the denoising effect diagram in the embodiment. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0029] Next, the technical solutions in the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0030] As Figure 1 shown, a single-photon denoising method based on alternating horizontal and vertical division includes the following steps:

[0031] Step 1: Obtain the original photon data (including longitude, latitude, and elevation), perform uniform preprocessing, and calculate the global background photon count rate mean wherein, N total is the total number of photons, L track is the along-track distance, and the local background photon count rate μ local is statistically calculated according to a window (such as every 50 shots), and the along-track distance is dynamically adjusted using the following formula:

[0032] xadjusted = x + Δ·sgn(μ - μ local ), Δ ∈ [a, b]

[0033] Wherein, x adjusted represents the adjusted value, x represents the original value, Δ represents the adjustment amount, and its range is between [a, b]. Optionally, a = 0.05 m and b = 0.2 m.

[0034] By dynamically adjusting the distance along the track to make the local background photon count rate approach the global background photon count rate mean, the original photon data is preprocessed uniformly to eliminate the influence of uneven photon distribution.

[0035] Step 2: Based on the original photon data after uniform preprocessing, recursively perform alternating horizontal and vertical partitioning, specifically:

[0036] Initial partitioning: Vertically partition the photons parallel to the x-axis to obtain two sub-regions, ensuring that the sum of the distances between the photons on both sides of the partitioning line and the partitioning line is equal;

[0037] Secondary partitioning: Horizontally partition the photons in the two sub-regions parallel to the y-axis respectively, ensuring that the sum of the distances between the photons on both sides of the partitioning line and the partitioning line is equal;

[0038] Recursive partitioning: Repeat the above two partitioning processes until each sub-region contains less than two photons or reaches the preset depth.

[0039] The partitioning criterion can be expressed as follows:

[0040]

[0041] Wherein, X represents the quadrant space in D k in, D k represents the set of quadrants that can be partitioned in the k-th layer, and D' k represents the k-th layer quadrant set.

[0042] Step 3: Count the number of times the photons are partitioned, record the number of times each photon is partitioned during the process from the root node to the leaf node, and based on the distribution of the number of times the photons are partitioned, use the maximum between-class variance method to determine the threshold for the best partitioning. Photons with a partitioning number lower than the threshold are determined as noise and filtered out to achieve the output of the denoising result. The threshold solving formula is as follows:

[0043]

[0044] Wherein, k * represents the final threshold, k represents the threshold, L - 1 represents the maximum value of the threshold, ω0 and ω1 respectively represent the ratios of the photons with layer values less than t and greater than or equal to t, Let \(p(i)\) represent the proportion of photons with an inner layer value of \(i\) in the window, and \(\mu_0\) and \(\mu_1\) represent the average layer values of photons with layer values less than \(t\) and greater than or equal to \(t\), respectively.

[0045] Embodiment

[0046] ICESat-2 ATL03 data is obtained from the ICESat-2 satellite. These data are stored in the HDF5 file format and contain information such as the longitude, latitude, and elevation of photons. Read these data and prepare for subsequent processing.

[0047] Since the photon distribution in ATL03 data is often uneven, before denoising processing, it is necessary to perform uniform preprocessing on the data. The photon distributions before and after processing are combined Figure 2 As shown, the left side is the original data and the right side is the adjusted data. It can be seen that after uniform preprocessing, the photon distribution is more balanced.

[0048] Next, the preprocessed data is processed using the method of alternating horizontal and vertical partitioning. The purpose is to alternately divide the data horizontally and vertically to ensure that the distances from the photons on both sides of the partitioning line to the partitioning line are equal, forming multiple sub-regions. The construction process of alternating horizontal and vertical partitioning is combined Figure 3 As shown, the partitioning depth of each photon data is obtained using the partitioning line, where:

[0049] The vertical partitioning line \(s\) satisfies:

[0050]

[0051] The horizontal partitioning line \(s\) satisfies:

[0052]

[0053] And the number of partitioning times for each sub-region is counted. By counting the number of partitioning times, the data distribution can be better understood, providing a basis for subsequent optimal threshold selection.

[0054] During the initial partitioning, a horizontal partitioning is performed on the unpartitioned photon data to obtain upper and lower sub-regions. During the second partitioning, vertical partitioning is independently performed on the upper and lower sub-regions respectively to obtain two different left and right sub-regions, and then continue with alternating horizontal and vertical partitioning. After two horizontal partitions and one vertical partition, there is a sub-region with only one photon, and its partitioning times do not reach the partitioning threshold (assuming the partitioning threshold is 4 at this time), that is, this photon is considered a noise photon. After three horizontal partitions and two vertical partitions, there is a sub-region with only one photon, but its partitioning times reach the partitioning threshold, that is, this photon is considered a signal photon.

[0055] Next, the Otsu method is used to select the optimal threshold for denoising. The algorithm traverses all possible thresholds, calculates the between-class variance, and selects the threshold that maximizes the between-class variance as the optimal partitioning threshold. Combined with Figure 4 As shown, it shows the node structure of alternating horizontal and vertical partitioning. Initially, there is only one root node representing the unpartitioned area. Then, the root node undergoes a horizontal partition, dividing it into two sub-areas, the upper and lower ones, which can also be called internal nodes. By alternating horizontal and vertical partitioning and reasonably selecting the threshold, signal photons and noise photons can be effectively separated.

[0056] Finally, data denoising is performed according to the selected threshold, and the processed result is output. Combined with Figure 5 As shown, it shows the final denoising effect diagram. The horizontal axis is the along-track distance, the vertical axis is the photon height, the blue represents signal photons, and the red represents noise photons.

[0057] In summary, through steps such as homogenization preprocessing, alternating horizontal and vertical segmentation, division times statistics, Otsu method threshold selection, and denoising result output, effective denoising of photon data is achieved, significantly improving the accuracy and adaptability of photon denoising, providing a new solution for the efficient processing of laser altimetry satellite data. Experimental results show that this method has broad application prospects in fields such as ice sheet elevation measurement, sea ice thickness inversion, land elevation measurement, forest biomass estimation, and lake water level monitoring.

[0058] For those skilled in the art, it is obvious that the present invention is not limited to the details of the above exemplary embodiments, and without departing from the spirit or basic characteristics of the present invention, the present invention can be implemented in other specific forms. Therefore, in any aspect, the embodiments should be regarded as exemplary and non-limiting. The scope of the present invention is defined by the appended claims rather than the above description. Therefore, it is intended to embrace all changes within the meaning and scope of the equivalent conditions of the claims in the present invention. Any reference signs in the claims should not be regarded as limiting the claims involved.

[0059] In addition, it should be understood that although this specification is described according to embodiments, not every embodiment only contains an independent technical solution. This narrative way of the specification is only for clarity. Those skilled in the art should regard the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A single photon denoising method based on alternating horizontal and vertical partitioning, characterized in that: The following steps are involved: Step 1: Obtain the original photon data, perform homogenization preprocessing, calculate the global background photon count rate mean μ, and count the local background photon count rate μ by window local , by dynamically adjusting the distance along the track, the local background photon count rate is made close to the global background photon count rate mean, so as to eliminate the influence of uneven photon distribution; Step 2: Based on the original photon data after homogenization preprocessing, an alternating horizontal and vertical division strategy is adopted. Each division ensures that the distance between the photons on both sides of the division line and the division line is equal. In the first division, the photons are divided parallel to the x-axis to obtain two sub-areas. In the second division, the photons in the sub-areas are divided parallel to the y-axis. The above two division processes are repeated to perform recursive division until each sub-area contains less than two photons or reaches a preset depth; Step 3: Count the number of times each photon is divided. Based on the distribution of the number of times the photon is divided, the maximum inter-class variance method is used to determine the optimal division threshold. Photons with a division number lower than the threshold are judged as noise and filtered out to achieve denoising result output.

2. The single photon denoising method based on alternating horizontal and vertical partitioning according to claim 1, characterized in that: In step 1, the distance along the track is dynamically adjusted using the following formula: x adjusted =x+Δ·sgn(μ-μ local ) In the formula, x adjusted represents the adjusted value, x represents the original value, and Δ represents the adjustment amount.

3. The single photon denoising method based on alternating horizontal and vertical partitioning according to claim 2, characterized in that: The calculation formula of the global background photon count rate mean μ is as follows: Where N total is the total number of photons, L track is the distance along the track.

4. The single photon denoising method based on alternating horizontal and vertical division according to claim 2, characterized in that: The adjustment amount Δ∈[a,b], a=0.05m, b=0.2m.

5. The single photon denoising method based on alternating horizontal and vertical partitioning according to claim 1, characterized in that: In step 3, the threshold solution formula is as follows: In the formula, k * Represents the final threshold, k represents the threshold, L-1 represents the maximum value of the threshold, ω0 and ω1 represent the proportion of photons with layer values ​​less than t and greater than or equal to t, respectively, μ0 and μ1 represent the mean layer values ​​of photons with layer values ​​less than t and greater than or equal to t, respectively.

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