A single-photon denoising method based on alternating horizontal and vertical division

Abstract

The application relates to a single-photon denoising method based on alternating horizontal and vertical division, and relates to the technical field of photon data processing. The original photon data is uniformly pretreated, the influence of uneven photon distribution is eliminated by dynamically adjusting the along-track coordinate, an alternating horizontal and vertical division strategy is adopted, vertical division and horizontal division are recursively executed, the distance between the photons on both sides of the division line and the division line is ensured to be equal, until the termination condition is met, the number of times of photon division is counted, and the optimal threshold is adaptively selected by combining the maximum between-class variance method to filter out noise photons. Through dynamic selection of the division line for alternating horizontal and vertical division, the statistical characteristics of the number of times of photon division are combined, and the maximum between-class variance method is used to adaptively determine the threshold of the best division, so that efficient separation of signal photons and noise photons can be realized.

Description

Technical Field

[0001] This invention relates to the field of photonic data processing technology, specifically a single-photon denoising method based on alternating horizontal and vertical partitioning. Background Technology

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

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

[0004] Furthermore, existing methods often employ fixed thresholds or simple statistical thresholds, failing to fully utilize the inter-class distribution characteristics of photon partitioning times, thus exhibiting poor adaptability. For these reasons, a more flexible and efficient photon denoising method is urgently needed. Summary of the Invention

[0005] To address the shortcomings of the prior art, this invention provides a single-photon denoising method based on alternating horizontal and vertical division. This method dynamically selects dividing lines to perform alternating horizontal and vertical divisions, and combines the statistical characteristics of the number of times a photon is divided with the maximum inter-class variance method to adaptively determine the optimal division threshold, thereby achieving efficient separation of signal photons and noise photons.

[0006] To achieve the above objectives, 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: Acquire raw photon data, perform homogenization preprocessing, calculate the global background photon count rate mean μ, and statistically analyze 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 closer to the average global background photon count rate, so as to eliminate the influence of uneven photon distribution.

[0008] Step 2: Based on the original photon data after homogenization preprocessing, an alternating horizontal and vertical partitioning strategy is adopted. Each partitioning ensures that the distance between the photons on both sides of the partitioning line and the partitioning line is equal. In the first partitioning, the photons are partitioned parallel to the x-axis to obtain two sub-regions. In the second partitioning, the photons in the sub-regions are partitioned parallel to the y-axis. The above two partitioning processes are repeated to perform recursive partitioning until each sub-region contains only two or fewer photons or reaches a preset depth.

[0009] Step 3: Count the number of times each photon is divided. Based on the distribution of the number of times the photon is divided, use the maximum inter-class variance method to determine the optimal division threshold. Photons with a division count lower than the threshold are judged as noise and filtered out to achieve the output of the denoising result.

[0010] Furthermore, in step one, the distance along the track is dynamically adjusted using the following formula:

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

[0012] In the formula, x adjusted This represents the adjusted value, x represents the original value, and Δ represents the adjustment amount.

[0013] Furthermore, the formula for calculating the average global background photon count rate μ is as follows:

[0014]

[0015] In the formula, N total L represents the total number of photons. track This represents the distance along the track.

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

[0017] Furthermore, in step three, the threshold calculation formula is as follows:

[0018]

[0019] In the formula, k * Let represent the final threshold, k represent the threshold value, L-1 represent the maximum value of the threshold value, ω0 and ω1 represent the proportion of photons with layer values ​​less than t and greater than or equal to t, respectively, and μ0 and μ1 represent the average layer values ​​of photons with layer values ​​less than t and greater than or equal to t, respectively.

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

[0021] 1. This invention proposes an alternating horizontal and vertical division strategy based on dynamic mean division lines to ensure the photon distance and balance on both sides of the division line, thereby improving the division balance and accuracy. Through a dynamic homogenization preprocessing algorithm, the photon density difference along the track direction is eliminated, improving the division robustness and achieving efficient separation of signal photons and noise photons.

[0022] 2. This invention uses the maximum inter-class variance method for traversal optimization, adaptively determines the optimal threshold, and combines the inter-class distribution characteristics of the number of photon partitioning to achieve threshold adaptability. No manual intervention is required, which solves the problems of redundant calculation and poor surface adaptability caused by existing methods relying on manual parameters and fixed partitioning patterns.

[0023] 3. The partitioning mode of this invention adapts to different photon distributions, reduces the sensitivity of the fixed quadtree structure to complex surfaces, and reduces recursive complexity through unidirectional partitioning. It is suitable for large-scale photon data processing. Combined with homogenization preprocessing and dynamic threshold selection, it is especially suitable for scenarios such as polar ice sheet monitoring, vegetation biomass estimation, and marine topographic mapping, and has the advantages of high precision and high efficiency. Attached Figure Description

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

[0025] Figure 2 This is a comparison diagram of photon distribution before and after homogenization preprocessing in the embodiment;

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

[0027] Figure 4 This is a schematic diagram of the node structure with alternating horizontal and vertical divisions in the embodiment;

[0028] Figure 5 This is a diagram showing the noise reduction effect in the embodiment. Detailed Implementation

[0029] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the invention, not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

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

[0031] Step 1: Acquire raw photon data (including longitude, latitude, and elevation), perform homogenization preprocessing, and calculate the average global background photon count rate. Where, N total L represents the total number of photons. track The distance along the track is used, and the local background photon count rate μ is calculated by window (e.g., every 50 shots). local The distance along the track is dynamically adjusted using the following formula:

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

[0033] In the formula, x adjusted The value represents the adjusted value, x represents the original value, and Δ represents the adjustment amount, which ranges between [a, b] and is optional, a = 0.05m and b = 0.2m.

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

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

[0036] Initial division: The photon is divided perpendicularly to the x-axis to obtain two sub-regions, ensuring that the distance between the photon and the dividing line on both sides of the dividing line is equal;

[0037] Secondary division: Divide the photons in the two sub-regions horizontally along the y-axis to ensure that the distances between the photons on both sides of the dividing line and the dividing line are equal;

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

[0039] The classification criteria can be expressed as follows:

[0040]

[0041] In the formula, X represents D k The quadrant space in D k Let D' represent the set of quadrants that can be partitioned in the k-th layer. k Let represent the set of the k-th quadrant.

[0042] Step 3: Count the number of times each photon is divided. Record the number of times each photon is divided during its journey from the root node to the leaf node. Based on the distribution of photon division counts, use the Otsu's method to determine the optimal division threshold. Photons with a division count below the threshold are judged as noise and filtered out to achieve the denoising result output. The threshold calculation formula is as follows:

[0043]

[0044] In the formula, k * Let represent the final threshold, k represent the threshold value, L⁻¹ represent the maximum value of the threshold value, and ω₀ and ω₁ represent the proportions of photons with layer values ​​less than t and greater than or equal to t, respectively. p(i) represents the proportion of photons with a layer value of i within the window, and μ0 and μ1 represent the average layer values ​​of photons with layer values ​​less than t and greater than or equal to t, respectively.

[0045] Example

[0046] Data from the ICESat-2ATL03 satellite was acquired. This data, stored in HDF5 file format, contains information such as the longitude, latitude, and altitude of photons. This data was then read and prepared for further processing.

[0047] Since the photon distribution in ATL03 data is often non-uniform, it is necessary to perform homogenization preprocessing before denoising. The photon distribution before and after processing is then 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 homogenization preprocessing, the photon distribution is more balanced.

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

[0049] The vertical dividing line s satisfies:

[0050]

[0051] The horizontal dividing line s satisfies:

[0052]

[0053] The number of times each sub-region is divided is counted. By counting the number of divisions, we can better understand the distribution of the data and provide a basis for the subsequent selection of the optimal threshold.

[0054] In the initial partitioning, the unpartitioned photon data is horizontally divided to obtain upper and lower sub-regions. In the second partitioning, each of the upper and lower sub-regions is independently vertically divided, resulting in two distinct left and right sub-regions. This alternating horizontal and vertical partitioning continues. After two horizontal partitionings and one vertical partitioning, if a sub-region contains only one photon and its partitioning count has not reached the partitioning threshold (assuming the threshold is 4), this photon is considered a noise photon. After three horizontal partitionings and two vertical partitionings, if a sub-region contains only one photon but its partitioning count has reached the partitioning threshold, this photon is considered a signal photon.

[0055] Next, the maximum inter-class variance (MOV) method is used to select the optimal threshold for denoising. The algorithm iterates through all possible thresholds, calculates the inter-class variance, and selects the threshold that maximizes the inter-class variance as the optimal splitting threshold. Figure 4 As shown, the node structure with alternating horizontal and vertical divisions is illustrated. Initially, there is only one root node representing the undivided region. Then, the root node undergoes a horizontal division, dividing the region into upper and lower sub-regions, which can also be called internal nodes. By alternating horizontal and vertical divisions and appropriately selecting thresholds, signal photons and noise photons can be effectively separated.

[0056] Finally, data denoising is performed based on the selected threshold, and the processed result is output. Figure 5 As shown, the final denoising effect is displayed. The horizontal axis represents the distance along the track, the vertical axis represents the photon height, blue represents signal photons, and red represents noise photons.

[0057] In summary, through steps such as homogenization preprocessing, alternating horizontal and vertical segmentation, statistical analysis of the number of segmentations, threshold selection using the maximum inter-class variance method, and output of denoising results, effective denoising processing of photon data was achieved, significantly improving the accuracy and adaptability of photon denoising. This provides 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] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered illustrative and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of the equivalents of the claims are intended to be included within the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

[0059] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider 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 division, characterized by: The method comprises the following steps: Step one: Obtain the original photon data, make uniform preprocessing, calculate the global background photon counting rate mean μ, and count the local background photon counting rate μ according to the window local By dynamically adjusting the distance along the track to make the local background photon counting rate approach the global background photon counting rate mean, the influence of uneven photon distribution is eliminated; Step two: based on the original photon data after homogenization preprocessing, adopt the strategy of alternating horizontal and vertical division, ensure the distance between the photons on both sides of the division line and the division line is equal each time, divide the photons parallel to the x-axis to obtain two sub-regions in the first division, divide the photons of the sub-regions parallel to the y-axis in the second division, repeat the above two division processes to perform recursive division until each sub-region contains two or fewer photons or reaches a preset depth; Step three: count the number of times each photon is divided, based on the distribution of the number of times the photon is divided, determine the optimal division threshold value by using the maximum inter-class variance method, and filter out the photons with a division number below the threshold value to determine noise, and output the denoising result.

2. The single-photon denoising method based on alternating horizontal and vertical division according to claim 1, wherein: In the step one, the distance along the track is dynamically adjusted by 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 division according to claim 2, characterized in that: The calculation formula of the global background photon counting rate mean μ is as follows: where N is the total number of photons, L is the distance along the track, and total is the total number of photons, L is the distance along the track, and 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 is in the range of [a, b], a = 0.05 m, and b = 0.2 m.

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

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