GM-APD laser radar range profile reconstruction method based on kurtosis factor and multi-scale analysis

Abstract

The invention discloses a GM-APD laser radar range profile reconstruction method based on a kurtosis factor and multi-scale analysis, relates to the technical field of laser radar detection imaging, and solves the problems that the prior art mostly depends on prior knowledge of template matching or hypothesis signal distribution and is difficult to adapt to a dynamic noise environment. According to the method, data cubes with different scales are generated by using a superpixel technology; a kurtosis factor-based echo signal distance parameter estimation method is adopted to analyze the significant difference between a target echo signal and background noise in kurtosis features, and a sliding window technology is combined with a dynamic threshold detection mechanism to realize accurate recognition of the target signal, so that accurate estimation of distance parameters is completed; and carrying out GM-APD laser radar range profile noise suppression based on multi-scale analysis, and the like. According to the method, the target edge definition and the noise suppression capability are remarkably enhanced. The improvement enables the high-precision range profile reconstruction of the photon counting radar in a low signal-to-background ratio sparse echo scene to be possible.

Description

Technical Field

[0001] The present invention relates to the field of laser radar detection imaging technology, and in particular to a GM-APD laser radar range image reconstruction method based on kurtosis factor and multi-scale analysis. Background Art

[0002] Array lidar overcomes the limitations of traditional single-point detection and point-by-point scanning methods. It achieves fast, high-resolution imaging through parallel acquisition, offering significant advantages in topographic mapping, urban infrastructure modeling, and military reconnaissance systems. Array lidar utilizes flood illumination, dispersing the laser energy over a wide area in the far field. This significantly reduces the optical power density per unit area, resulting in sparse target echoes and hindering long-range detection. Geiger-Mode Avalanche Photodiode (Gm-APD) lidar, based on avalanche breakdown characteristics, can detect echo signals at the single-photon level. This allows for the extraction of weak echoes even at extremely low light flux, addressing the sparse echo problem associated with long-range detection. GM-APDs are single-photon detectors with a 0 / 1 output. A single detection cannot distinguish signal from noise, requiring multi-frame accumulation to recover the target waveform. However, because GM-APDs utilize a first-photon triggering mechanism, photon pile-up is prone to occur in the presence of strong background noise, causing the target echo signal to be overwhelmed by the noise, severely impacting the quality of range image reconstruction.

[0003] Long-range detection using GM-APD array lidar systems faces inherent technical challenges under sparse echo conditions. Traditional hardware enhancements (such as increasing transmit power and expanding the receiving aperture) are difficult to achieve due to the physical limitations of semiconductor manufacturing processes and nonlinear cost increases. Under these conditions, the combined effects of spatiotemporal sparsity and solar background noise further weaken the echo signal-to-background ratio, rendering traditional point-by-point detection algorithms completely ineffective. Modern signal processing paradigms offer alternative solutions: methods based on advanced estimation theory can extract effective lidar signals under extreme environmental attenuation conditions. The core challenge stems from the problem of temporal undersampling during signal acquisition—limited integration time or the Poissonian photon count distribution caused by atmospheric scattering can violate the Nyquist sampling criterion. To address this issue, existing research has demonstrated that a Markov Random Field framework based on spatial correlation priors can achieve significant improvements by compensating for temporal undersampling through spatial redundancy. Within this context, a unified methodology for sparse echo signal extraction is emerging: by modeling the reconstructed image as a Markov random field, high-quality target reconstruction is achieved by leveraging inter-pixel spatial correlation as prior information. In this framework, spatial sampling effectively compensates for the shortcomings of temporal sampling. However, under high noise floor conditions, the coupling of photon pile-up effects and spectral interference makes accurate time-of-flight (TOF) extraction highly complex. This problem is particularly prominent in scenarios with the combined constraints of low light flux and low signal-to-background ratio.

[0004] In the pursuit of high-quality imaging using GM-APD array lidar systems, the simultaneous optimization of signal photon utilization efficiency and noise suppression capabilities is a key challenge. Hardware-centric improvements struggle to balance these two technical constraints, so the development of advanced algorithmic systems has become a key breakthrough. A typical example is a spatially consistent hierarchical Bayesian framework proposed by Yao et al. based on Markov Chain Monte Carlo (MCMC) sampling. While this framework significantly improves reconstruction accuracy through probabilistic modeling, the complex computational process of its iterative optimization mechanism limits its real-time application. To address this issue, Xu Feihu et al. innovatively combined a sparse Poisson intensity reconstruction algorithm (SPIRAL-TAP) with a non-local neural network, successfully achieving 45 km-level 3D reconstruction under the extreme condition of SBR = 0.1, marking a significant breakthrough in this hybrid algorithmic framework. Meanwhile, Goyal et al. took a different approach, proposing a "signal-noise separation photon efficient active imaging algorithm" based on temporal asynchrony. This algorithm effectively separates noise signals through a temporal discriminator, but its reliance on a simplified spatial statistical model of superpixels results in blocky artifacts in the reconstructed image. To address this shortcoming, Chen Songmao et al. introduced a multi-scale non-local regularization method. By fusing local spatial correlation with global image prior information, they achieved high-quality, artifact-free reconstruction at PPP = 0.8. However, existing research has not yet thoroughly analyzed the temporal distribution characteristics of photons, especially in the presence of strong background noise. The robustness verification system for the algorithm is still incomplete and urgently needs systematic exploration.

[0005] Current research suggests that statistically based signal extraction methods have the potential to distinguish target echoes from noise. However, existing methods often rely on template matching or assume prior knowledge of signal distribution, making them difficult to adapt to dynamic noise environments. Therefore, there is an urgent need for an algorithm that combines spatiotemporal statistical properties with multiscale analysis to achieve high-precision range image reconstruction under conditions of extremely low photon flux and strong background noise.

[0006] In summary, existing technologies still have significant deficiencies in signal extraction and image reconstruction under low signal-to-background ratio and sparse photon conditions. An innovative method is urgently needed to improve the performance of GM-APD array lidar systems in extreme detection scenarios. Summary of the Invention

[0007] In order to solve the problems that the existing technologies mostly rely on template matching or assume prior knowledge of signal distribution, are difficult to adapt to dynamic noise environments, and further have significant deficiencies in signal extraction and image reconstruction under low signal-to-background ratio and sparse photon conditions, the present invention provides a GM-APD lidar range profile reconstruction method based on kurtosis factor and multi-scale analysis to achieve high-precision depth reconstruction of photon counting radar in extreme sensing scenarios.

[0008] A GM-APD lidar range profile reconstruction method based on kurtosis factor and multi-scale analysis is implemented by the following steps:

[0009] Step 1: Generate data cubes of different scales using superpixel technology;

[0010] Step 2: Use the kurtosis factor-based echo signal distance parameter estimation method to analyze the difference in kurtosis characteristics between the target echo signal and the background noise signal. Use the sliding window technology combined with the dynamic threshold detection mechanism to achieve accurate identification of the target signal. Finally, by extracting the local maximum value characteristics of the target echo signal, the distance parameter is accurately estimated.

[0011] Step 3: Perform noise suppression on the GM-APD lidar range image based on multi-scale analysis, and obtain a high-precision range image by judging and replacing pixel noise.

[0012] Beneficial effects of the present invention:

[0013] The proposed multi-scale analysis (MSA) framework based on kurtosis factor drive significantly improves the reconstruction quality and robustness of range images under the low signal-to-noise ratio and sparse photon conditions of GM-APD array radar systems. It has the following specific advantages:

[0014] 1. The GM-APD lidar range profile reconstruction method described in this invention utilizes innovative signal identification through kurtosis analysis: A signal extraction method using the kurtosis factor is developed to distinguish Gaussian target echoes from uniformly distributed noise. This method eliminates reliance on traditional matched filtering methods and adaptively identifies the presence of signals through inherent statistical characteristics, significantly enhancing robustness in low SBR environments.

[0015] 2. The GM-APD lidar range profile reconstruction method described in this invention uses multi-scale fusion for spatiotemporal enhancement: By combining kurtosis-based signal localization with a multi-scale framework, the algorithm effectively combines coarse-scale contour information with fine-scale details. This layered approach compensates for temporal undersampling by exploiting spatial redundancy, achieving superior noise suppression while maintaining edge integrity.

[0016] 3. Compared to traditional multi-scale analysis range profile reconstruction methods, the GM-APD lidar range profile reconstruction method described in this invention significantly improves target fidelity, peak signal-to-noise ratio, and structural similarity, significantly enhancing target edge clarity and noise suppression. This advancement enables high-precision range profile reconstruction for photon counting radars in low signal-to-background ratio and sparse echo scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1This is a flow chart of a GM-APD laser radar range profile reconstruction method based on kurtosis factor and multi-scale analysis according to the present invention;

[0018] Figure 2 Generate a schematic diagram for the superpixel data cube;

[0019] Figure 3 This is the schematic diagram of the MSA algorithm;

[0020] Figure 4 This is an ideal distance image effect diagram for simulating car data;

[0021] Figure 5 To simulate range image data using the MSA algorithm, SBR = 0.1: (a) O = 1; (b) O = 2; (c) O = 4 range image; (d) reconstructed range image;

[0022] Figure 6 To simulate the range image data using the MSA algorithm, SBR = 0.05: (a) O = 1; (b) O = 2; (c) O = 4 range image; (d) reconstructed range image;

[0023] Figure 7 This is the principle diagram of the MSA kurtosis-driven recovery algorithm;

[0024] Figure 8 Schematic diagram of the results of range image recovery using different algorithms;

[0025] Figure 9 Effect diagram of range image restoration for different SBR and frame numbers;

[0026] Figure 10 These are renderings of four different target scenarios;

[0027] Figure 11 In the figure, (a) is the reference distance image of building 1, and (b) is the reference distance image of building 2;

[0028] Figure 12 for Figure 11 Restored distance images of the buildings in the figure; where (a) is the distance image of building 1 restored by MSA; (b) is the distance image of building 1 restored by the method of the present invention; (c) is the distance image of building 2 restored by MSA; (d) is the distance image of building 2 restored by the suggestion. DETAILED DESCRIPTION

[0029] Specific implementation method 1. Combination Figure 1 and Figure 2This embodiment describes a GM-APD lidar range profile reconstruction method based on kurtosis and multi-scale analysis. First, the signal photon distribution is reconstructed using a photon number inversion model. Second, the kurtosis factor (fourth-order statistical moment) is used to distinguish target echoes from noise and extract range parameters. Finally, a multi-scale analysis framework is used to fuse edge and detail information from images of different resolutions to achieve high-fidelity 3D reconstruction. This enables high-precision imaging at long distances and in strong noise environments.

[0030] The specific process of the reconstruction method described in this embodiment is as follows:

[0031] Step 1: Generate data cubes of different scales using superpixel technology;

[0032] In the single-photon image reconstruction algorithm, constructing superpixels is an effective method to enhance the robustness of the algorithm. The principle is as follows Figure 1 As shown in the figure, the square signal represents the photon signal reflected from the target, the circular signal represents noise, and each row represents the histogram of a different pixel within the superpixel. The superpixel histogram generated by summing the histograms of all pixels within the superpixel will produce a peak due to the aggregation of signals, thus avoiding the interference of noise and "empty" pixels on signal extraction.

[0033] In this embodiment, a scaling matrix H with a dimension of O (O×O sliding window) is used to convolve Q to form a superpixel;

[0034]

[0035] Where Q represents the signal data cube collected M×N×T, where M×N represents 64×64 pixels and T represents the number of statistical frames.

[0036]

[0037] Where Q' is the new data cube generated by convolving the data cube Q with the scaling matrix H.

[0038] Step 2: Using a kurtosis-based echo signal distance parameter estimation method, we analyze the significant differences in kurtosis between the target echo signal and background noise, and employ a sliding window technique combined with a dynamic threshold detection mechanism to accurately identify the target signal. Furthermore, we extract the local maximum features of the target echo signal to accurately estimate the distance parameter. The specific steps are as follows:

[0039] Step 21: extract the kurtosis feature of the target echo signal and the kurtosis feature of the background noise signal; and use them as theoretical kurtosis features respectively;

[0040] First, the kurtosis feature of the target echo signal is extracted;

[0041] The assumed laser pulse energy distribution can be expressed as:

[0042]

[0043] Among them, n is related to the shape of the laser pulse; when n = 1, the fitting effect is the best. When n is 1, the pulse width is p w =3.5τ, τ is the key reference parameter for calculating pulse width.

[0044] Integrate the laser pulse energy distribution S(t) to obtain the total energy;

[0045]

[0046] The probability density function f(t) of the laser pulse energy distribution can be expressed as:

[0047]

[0048] Where t is time, the energy distribution equation of the target echo received by the detector is:

[0049]

[0050] Among them, t d is the pulse laser flight time, E r is the laser echo pulse energy amplitude;

[0051] The number of received target echo photons N(t) is:

[0052]

[0053] Where λ is the laser wavelength, h is Planck's constant, and c is the speed of light. Normalizing N(t) yields the probability density function n(t) of the number of target echo photons, N(t), as follows:

[0054]

[0055] Calculate the kurtosis factor to obtain the echo photon number curve characteristics;

[0056]

[0057] Where μ is the population mean, K 4 is the fourth-order central moment, K 2 is the variance. Since the number of echo photons is distributed in (0, +∞), the domain of the above equation can be simplified to (0, +∞) and modified as follows:

[0058]

[0059] Finally, the kurtosis characteristics of the target echo signal are obtained, that is, the theoretical kurtosis characteristics of the target echo signal;

[0060] Secondly, the kurtosis feature of the background noise signal is extracted, that is, the theoretical kurtosis feature of the background noise signal;

[0061] Set the width to T g Within the gate of , the noise photons exhibit a uniform temporal distribution, producing the theoretical kurtosis characteristic of the background noise signal:

[0062]

[0063] Among them, T N Is the gate front T N time bins, n noise (t) is the spatial distribution of noise photons.

[0064] Step 2: Use the sliding window method to obtain the kurtosis characteristics of the target echo signal and background noise signal observation data. The process is as follows:

[0065] First, obtain the GM-APD lidar observation data, and perform histogram statistics on the observation data to obtain the statistical histogram K(t);

[0066] According to the photon number inversion method, combined with the histogram of the observed data, the number of photons in each time interval is obtained:

[0067]

[0068] Where i is the time bin of the gate, K(i) is the frequency of the i-th interval in the histogram, and K total is the sum of the trigger frequencies for each interval in the histogram.

[0069] Next, the number of photons N s (t) is converted into a discrete sequence and then normalized. The photon count is converted into a unit sum by normalization to obtain the normalized photon number discrete sequence n s [i];

[0070] Then, the sliding window method is used to calculate the kurtosis factor sequence of the photon number data; that is, the kurtosis factor characteristics of the target echo signal in the observation data;

[0071]

[0072] Among them, μ j is the total average signal in the sliding window; j and w are the starting position and width of the sliding window respectively. According to the above formula, the size of the sliding window is physically affected by the laser pulse width p. w=3.5τ, ensuring the complete echo time profile capture while excluding the noise-dominated area.

[0073] Finally, the kurtosis factor of the background noise signal in the observed data is calculated as follows:

[0074]

[0075] Among them, μ noise is the overall average noise signal, T N Is the gate front T N Time bin, T N The choice of is highly dependent on the target scenario and its value can be based on system design parameters or mission requirements (e.g., measurement range), or established by system calibration using strong a priori information from known scenarios.

[0076] Step 2: Set the dynamic threshold to detect the target echo signal. The process is as follows:

[0077] The adaptive threshold θ combines this noise characteristic with the signal kurtosis q d =6 combined:

[0078]

[0079] Among them, σ noise is the standard deviation of the noise, and C is the confidence coefficient.

[0080] To determine the adaptive threshold θ, the standard deviation of the noise σ noise Must be switched from T N Estimated in time bins:

[0081] in,

[0082]

[0083] Finally, the kurtosis-driven single photon echo signal target distance parameter extracts the kurtosis factor sequence Q d [i], the echo signal detection formula is:

[0084]

[0085] Among them, {a i} is the target echo signal sequence.

[0086] Step 24: Extract the maximum value of the target echo signal to complete the distance parameter estimation. The process is as follows:

[0087] If D is taken as the direct distance between the target and the detection system, the difference between the maximum echo signal value and the abscissa index of the starting position must be obtained.

[0088] First, the maximum value of the probability density function n(t) can be calculated, that is, the maximum echo signal value; it can be expressed as follows:

[0089]

[0090] Next, the difference between the maximum echo signal value and the abscissa index of the starting position can be calculated as:

[0091] (t d +1)-t d = 1. Target echo signal distance sequence {d i}for:

[0092] {d i}={a i +1}

[0093] The target echo signal distance parameter d is:

[0094] d=argmax(Q d [i])

[0095] i∈{d i}

[0096] Step 25: Obtain range images at different scales.

[0097] Traversal Pixels obtain range images at different scales.

[0098] Step 3: The noise suppression of the GM-APD laser radar range image based on multi-scale analysis combines the contour information of the low-resolution image with the detail features of the high-resolution image, optimizes the range image through pixel noise judgment and noise replacement, retains the edge contour of the range image and suppresses noise. The specific method is as follows:

[0099] Step 3.1: Noise discrimination: calculate the gradient of the eight-neighborhood sliding window and set the threshold to detect noise pixels;

[0100] First, the fractional gradient judgment method is used to judge the noise;

[0101] Generally speaking, noise is a maximum or minimum point in an image, and an image is usually composed of continuous pixels with little difference. Some extreme points are not noise points, but edge points on the image. In order to enable us to detect noise more accurately and retain image edge information, this implementation introduces a fractional gradient judgment method.

[0102] To determine whether it is a noise point, it is necessary to calculate the fractional gradient of the eight directions of the point. Assume is the gradient of f(x,y) in the α direction, where x and y determine the coordinates of the pixel point, where α = 0°, 45°, 90°, 135°, 180°, 225°, 270°, 315°; v is the fractional order. The directional gradient is calculated as follows:

[0103]

[0104] in,

[0105] a0=1;

[0106] a1=-v;

[0107]

[0108] Let the threshold be T. If the derivative values ​​in the eight directions are all greater than the threshold T, then this point can be judged as a noise point; otherwise, it means that the current pixel point is a signal point.

[0109] Step 32: Pixel replacement: Use the corresponding pixels of the low-scale image (O=2, 4) to replace the noise pixels; that is, when O=2 L-1 , use the corresponding pixels of the scale image L=2,3 to replace the noise pixels of the scale image L=1, and output the final high-precision distance image z;

[0110] Step 4: Calculate the evaluation indicators target restoration degree RD, peak signal-to-noise ratio PSNR and structural similarity SSIM respectively to evaluate the reconstruction method described in this embodiment.

[0111] Specific implementation method 2: Figures 3 to 9 As shown, this embodiment is a simulation experiment of a GM-APD laser radar range profile reconstruction method based on kurtosis factor and multi-scale analysis described in the specific embodiment 1:

[0112] In this embodiment, the Monte Carlo method is used to simulate the GM-APD radar signal under low light conditions. The evaluation indicators in step 4, target reduction degree RD, peak signal-to-noise ratio PSNR and structural similarity SSIM, are used to evaluate the method described in the first embodiment, and the method of the present invention is compared with the multi-scale analysis MSA algorithm. The principle of the MSA algorithm is as follows: Figure 3 shown.

[0113] A model vehicle 40 m away from the system was used in the simulation, e.g. Figure 4 shown.

[0114] The number of photons per pixel (PPP) is defined as:

[0115]

[0116] where N s(t) is the signal photon distribution function, T is the detection period, and M r and M c are the number of rows and columns in the GM-APD array, respectively.

[0117] SBR is calculated as:

[0118]

[0119] Where N is the background noise photon count, calculated as where N v (t) is the background noise photon distribution function.

[0120] like Figure 5 As shown, Figure 5 Simulated range image data for the MSA algorithm, when SBR = 0.1: (a) distance maps of O = 1, (b) O = 2, (c) O = 4; (d) reconstructed range image. Figure 6 Simulated range image data for the MSA algorithm, when SBR = 0.05: (a) O = 1; (b) O = 2; (c) range image of O = 4; (d) reconstructed range image. Figure 7 This is a schematic diagram of the kurtosis-driven algorithm of the present invention.

[0121] Reconstruction was performed using MATLAB 2024b on a workstation equipped with an AMD Ryzen 97945HX CPU and 16GB RAM. The proposed method was evaluated using 100 accumulated frames for statistical analysis under photon sparse conditions of PPP = 0.1802 and SBR = 0.08. The reconstructions between MSA and the proposed method were compared, as shown in Figure 2. Figure 8 shown.

[0122] exist Figure 8 Among them, (a) MSA, O=1; (b) MSA, O=2; (c) MSA, O=4; (d) MSA, reconstructed distance image; (e) the method of the present invention, O=1; (f) the method of the present invention, O=2; (g) the method of the present invention, O=4; (h) the method of the present invention, reconstructed distance image.

[0123] When using MSA for simulations of low SBR and PPP, only a small amount of target information is obtained ( Figure 8 (ac)); the target outline is missing in (a) and (b), and (c) contains considerable noise. The reconstructed range image in (d) contains a lot of noise and holes, and the target details are incomplete. In the simulation, a series of images with different resolutions were obtained using the method of the present invention and different sliding window sizes. Figure 8 (g) by combining Figure 8 The complete profile information of (e) and (f) is compared with that from Figure 8(g) The detailed information is combined to complete the "empty" pixel to complete the Figure 8 (h) Then the range image is obtained. Therefore, the range image combines the effective image information of different scales. Figure 8 Compared with the high-resolution (64×64) range image in (g), Figure 8 (h) Most of the lost target parts are recovered. Figure 8 (e) and Figure 8 Compared to the low-resolution range image in (f) (16×16 and 32×32, respectively), it also provides more vehicle details and clearer edge contours. As shown in Table 1, compared with MSA, our proposed algorithm significantly improves RD, PSNR, and SSIM. Table 1 shows the evaluation results of different algorithms on range image indicators.

[0124] Table 1

[0125]

[0126] Under severe photon confinement conditions, conventional MSA exhibits serious defects: the initial decomposition stage, e.g. Figure 8 (a)-(c) in Fig. 3 show fragmented target outlines and amplified noise artifacts, which ultimately lead to incomplete reconstruction of residual gaps, such as Figure 8 In contrast, using dynamic window mapping, our adaptive multi-scale framework strategically integrates complementary spatial frequency information: the coarse-scale mapping preserves the structural continuity such as Figure 8 (e)e-(f) in , while fine-scale processing restores local details, such as Figure 8 (g) in [1]; finally reconstructed through hierarchical feature fusion; as Figure 8 (h) in the figure. This method achieves comprehensive gap filling, enhanced edge definition, and perceptually coherent detail recovery, outperforming MSA in both qualitative object representation and quantitative metrics. As shown in Table 1, the reconstruction time for the method of the present invention is 0.86 seconds, while the MSA method of this embodiment takes 0.83 seconds. Despite a slight increase in processing time, the method described in this embodiment demonstrates superior performance in terms of RD, PSNR, and SSIM.

[0127] To further verify the performance of the proposed method under different SBRs and frame rates, we set PPP = 0.1802; SBR = 0.05, 0.08, and 0.1; and image frame rate = 50, 80, and 100, and reconstructed the target range image. The results were compared with the MSA results in Table 1.

[0128] The proposed method shows superior reconstruction fidelity under photon-starved conditions, effectively suppresses noise artifacts, and achieves complete target boundary recovery with enhanced edge sharpness. Figure 9As shown. Comparison with MSA reveals the inherent advantage of the method of the present invention in maintaining structural consistency between different SBRs (0.05-0.1) and frame integration counts (50-100). Multiple Monte Carlo experiments were performed to systematically evaluate the stability of the algorithm and quantitative recovery performance using RD, PSNR and SSIM. As shown in Table 2, Table 2 is an evaluation table of range image indicators under different signal-to-noise ratios and frame numbers, demonstrating the statistical stability of the method of the present invention.

[0129] Table 2

[0130]

[0131] As can be seen from Table 2, the algorithm proposed in this paper achieves the key indicators of system performance enhancement compared with the traditional MSA. Under moderate noise conditions (SBR = 0.08, 80 frames), the framework shows a substantial improvement of 34.22% RD, 11.11% PSNR, and 23.92% SSIM, confirming its robustness in photon-limited environments, especially under suboptimal signal background conditions. To verify the robustness of the proposed method under low signal photon and high background noise conditions, 1,000 independent Monte Carlo trials were performed for each experimental combination of SBR (0.01, 0.04, 0.06, 0.1, 1), PPP (0.0180, 0.0360, 0.0540, 0.1802, 0.9008) and number of frames (30, 50, 100, 150, 200, 250, 300, 400) to ensure statistical stability. The recovery results are compared using three metrics: ARD, APSNR, and ASSIM. The experimental results show that the proposed method is resilient to both quantum-confined signal conditions and complex background interference, while maintaining compatibility with actual radar systems.

[0132] Specific implementation method 3: Combination Figures 10 to 12 This embodiment is described as a performance verification of a GM-APD laser radar range profile reconstruction method based on kurtosis factor and multi-scale analysis described in Specific Embodiment 1. The specific process is as follows:

[0133] In this embodiment, a 64×64 array GM-APD laser radar is built to verify the performance of the method of the present invention.

[0134] Experimental equipment: 1064nm fiber laser, 64×64 array GM-APD camera, transmit and receive optical paths with a transmittance of 0.9, with transmit and receive fields of view of 0.8°×0.8° respectively. Maximum laser output energy of 100uJ, pulse width of 5ns, and repetition rate of 10kHz. The GM-APD lidar system parameters are shown in Table 3.

[0135] Table 3

[0136]

[0137] Key timing parameters of GM-APD array detectors include avalanche buildup time (<10 ps), quenching time (<5 ns), and dead time (<100 ns), which together define their minimum detectable period. For our high-repetition-rate lidar system (20 kHz, pulse interval = 50 μs), these characteristics ensure precise temporal photon counting with negligible dead-time effects. A quantum efficiency of 20% at 1064 nm and a dark count rate of 3.4 kHz further establish the detector's operational boundaries for sparse echo detection and directly inform our multi-frame accumulation strategy (100 frames) and sliding window kurtosis analysis (window width = 10 ns) to overcome spatiotemporal sparsity constraints.

[0138] The LiDAR system uses a GM-APD as a detector. The transmitting optical system first illuminates the target area with laser light, generating an optical feedback signal that activates the GM-APD's timing function. After the laser light is diffusely reflected from the target surface, the receiving optical system focuses the light signal onto the GM-APD's focal plane, at which point the GM-APD stops timing. A readout circuit then converts the laser photon's time-of-flight into digital form and transmits the data to a host computer for signal processing. After algorithmic processing, the data is displayed as a depth image.

[0139] Imaging experiment verification: In order to verify the performance of the method of the present invention, imaging experiments were conducted on building 1 at a distance of about 880 meters and building 2 at a distance of about 1080 meters during the day with strong sunlight. Figure 10 As shown, the experimental parameters are set as shown in Table 4;

[0140] Table 4

[0141]

[0142] The experimental parameters listed in Table 4, such as delay and gate width, were input into the GM-APD array radar system. The target building was detected and target echo data was acquired. Data for Building 1 was collected at 13:00 on May 19, 2023. Data for Building 2 was collected at 11:00 on December 24, 2024. Pixels containing target information were selected, and cumulative histograms were generated through multi-frame statistics. The SBR and PPP measurement procedure consists of three steps. First, the illumination laser source is turned off, and the GM-APD acquires background noise counts caused by ambient photons and detector dark counts to generate a noise count histogram. Next, the illumination laser source is turned on, and the GM-APD acquires total photon counts, which include signal photons and background noise, to generate a total count histogram. The signal count histogram is then derived by subtracting the noise count histogram from the total count histogram. Finally, the SBR is calculated as the ratio of signal counts to background noise counts, while the PPP is determined as the ratio of signal counts to the number of detected events. During the measurement process, multiple measurements are averaged to reduce statistical error. In the detection scenario of Building 1, the measured PPP and SBR were determined to be 0.85 and 0.1, respectively. In contrast, for Building 2, the PPP and SBR were significantly lower, at 0.1 and 0.01, respectively.

[0143] In order to quantitatively evaluate the superiority of the method proposed in this embodiment, a depth image without background noise should be obtained first as a reference. In this experiment, it is necessary to collect night detection data with visibility > 20km in the same scene and reconstruct it into a reference distance image. Building 1 was collected at 22:00 on May 19, 2023, with no solar background light noise and visibility of 25km. Building 2 was collected at 22:00 on December 24, 2024, with no solar background light noise and visibility of 25km. The reference distance image was obtained by reconstructing 5000 frames of data using the histogram statistical method, as shown in Figure 2. Figure 11 As shown, (a) is the reference distance image of building 1, and (b) is the reference distance image of building 2.

[0144] The statistical frame count for Building 1 was set to 200. Given that both the PPP and SBR of Building 2 were significantly lower than those of Building 1, the statistical frame count was appropriately increased to 400 while maintaining a high imaging frame rate. The depth images of the GM-APD lidar data collected under a daylight background were restored using the methods of the present invention.

[0145] from Figure 12 It can be seen from the figure that, compared with MSA, the method of the present invention can restore most areas of the target building, the target outline is obvious, and the noise points are reduced. Figure 12In the figure, (a) is the range image of building 1 restored using MSA; (b) is the range image of building 1 restored using the proposed method; (c) is the range image of building 2 restored using MSA; and (d) is the range image of building 2 restored using the proposed method. A quantitative evaluation of the processing results is shown in Table 5.

[0146] Table 5

[0147]

[0148] As shown in Table 5, under the conditions of PPP = 0.85 and SBR = 0.1, the proposed algorithm improves RD by 66.63%, PSNR by 24.75%, and SSIM by 43.95% compared to the MSA algorithm. Under the conditions of PPP = 0.05 and SBR = 0.053, the RD metric is emphasized more during range image reconstruction. In this study, the RD of the range image processed by the proposed method is 0.8091, while the RD of the range image processed by the MSA algorithm is only 0.3912. Furthermore, the proposed algorithm also demonstrates superior performance in terms of PSNR and SSIM metrics, highlighting its overall superiority. Compared to the MSA algorithm, the proposed method achieves improvements of RD, PSNR, and SSIM by 51.65%, 21.69%, and 54.48%, respectively.

[0149] The technical features of the above-mentioned embodiments can be combined arbitrarily. In order to make the description concise, not all possible combinations of the technical features in the above-mentioned embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0150] The above-described embodiments merely illustrate several implementations of the present invention, and while their descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the patent. It should be noted that a person skilled in the art would be able to make numerous variations and improvements without departing from the spirit of the present invention, all of which fall within the scope of protection of the present invention. Therefore, the scope of protection of the patent for this invention shall be determined by the appended claims.

Claims

1. A GM-APD lidar range profile reconstruction method based on kurtosis factor and multi-scale analysis, used to achieve high-precision range profile reconstruction for photon counting radar in extreme sensing scenarios; its characteristics are: The method is implemented by the following steps: Step 1: Generate data cubes of different scales using superpixel technology; Step 2: Use the kurtosis factor-based echo signal distance parameter estimation method to analyze the difference in kurtosis characteristics between the target echo signal and the background noise signal. Use the sliding window technology combined with the dynamic threshold detection mechanism to achieve accurate identification of the target signal. Finally, by extracting the local maximum value characteristics of the target echo signal, the distance parameter is accurately estimated. Step 3: Based on multi-scale analysis, GM-APD lidar range image noise is suppressed, and high-precision range images are obtained through pixel noise judgment and noise replacement.

2. The GM-APD laser radar range profile reconstruction method based on kurtosis factor and multi-scale analysis according to claim 1, characterized in that: In step 1, superpixel technology is used to generate data cubes of different scales; Use the scale matrix H of dimension O to perform convolution operation on the data cube Q to generate data cubes Q' of different scales; Where Q is the acquired signal data cube.

3. The GM-APD laser radar range profile reconstruction method based on kurtosis factor and multi-scale analysis according to claim 1, characterized in that: The specific process of step 2 is: Step 21: extracting the kurtosis features of the target echo signal and the background noise signal; Step 22: Using the sliding window method to obtain the kurtosis characteristics of the target echo signal and the background noise signal in the observation data; Step 23: Set a dynamic threshold to detect the target echo signal; Step 24: Extract the maximum value of the target echo signal and complete the distance parameter estimation to obtain the range image at different scales.

4. The GM-APD laser radar range profile reconstruction method based on kurtosis factor and multi-scale analysis according to claim 3, characterized in that: In step 21, the kurtosis feature q of the target echo signal is extracted d , which can be expressed as follows: The kurtosis characteristic q of the background noise signal noise It can be expressed as follows: Where t is time, μ is the population mean, K 4 is the fourth-order central moment, K 2 is the variance, T g is the gate width, T N T before the gate N time bins, n(t) is the probability density function of the number of target echo photons N(t) obtained, n noise (t) is the spatial distribution of noise photons.

5. The GM-APD laser radar range profile reconstruction method based on kurtosis factor and multi-scale analysis according to claim 4, characterized in that: The number N(t) of the target echo photons is expressed as follows: Where, t d is the pulse laser flight time, λ is the laser wavelength, h is Planck constant, c is the speed of light, E r is the laser echo pulse energy amplitude, and τ is the reference parameter for calculating the pulse width.

6. The GM-APD laser radar range profile reconstruction method based on kurtosis factor and multi-scale analysis according to claim 3, characterized in that: The specific process of step 22 is as follows: First, the sliding window method is used to calculate the kurtosis factor sequence of the photon number data, that is, the kurtosis factor characteristics of the target echo signal in the observation data; Secondly, calculate the kurtosis factor of the background noise signal in the observation data, which is expressed as follows: Where μ j is the total average signal in the sliding window; j and w are the starting position and width of the sliding window respectively; μ noise is the overall average noise signal; n s [i] is the normalized discrete sequence of photon numbers.

7. The GM-APD laser radar range profile reconstruction method based on kurtosis factor and multi-scale analysis according to claim 6, characterized in that: First, perform histogram statistics on the observed data to obtain the histogram K(t); According to the photon number inversion method and the statistical histogram K(t), the number of photons in each time interval is obtained, which can be expressed as follows: Where i is the time bin of the gate, K(i) is the frequency of the i-th interval in the histogram, and T N T before the gate N Time bins, K total is the sum of the trigger frequencies of each interval in the histogram; Secondly, the number of photons N s (t) is converted into a discrete sequence and then normalized to obtain the normalized discrete sequence of photon number n s [i].

8. The GM-APD laser radar range profile reconstruction method based on kurtosis factor and multi-scale analysis according to claim 6, characterized in that: The specific process of steps two and three is as follows: According to the kurtosis characteristics of the target echo signal and background noise signal obtained in step 2.1, the adaptive threshold θ is set, which can be expressed as follows: Where σ noise is the standard deviation of the background noise signal, C is the confidence coefficient, q noise is the kurtosis characteristic of the background noise signal, q d is the kurtosis feature of the target echo signal; The standard deviation σ of the background noise signal is required noise In T N The estimation in each time bin is expressed as follows: Where, According to the kurtosis factor characteristic Q of the target echo signal in the obtained observation data d [i] and the kurtosis factor Q of the background noise signal noise , obtain the target echo signal sequence: In the formula, {a i } is the target echo signal sequence.

9. The GM-APD laser radar range profile reconstruction method based on kurtosis factor and multi-scale analysis according to claim 8, characterized in that: In step 24: calculate the maximum value of the probability density function n(t), and calculate the difference between the maximum value and the starting position coordinate index to obtain the target echo signal distance parameter d: d=argmax(Q d [i])。 10. The GM-APD laser radar range profile reconstruction method based on kurtosis factor and multi-scale analysis according to claim 1, characterized in that: The specific process of step three is: Step 3.1: Noise discrimination: calculate the gradient of the eight-neighborhood sliding window and set the threshold to detect noise pixels; Step 32: Pixel replacement, replacing noise pixels with corresponding pixels of the low-scale image; Step 3: Output the final high-precision distance image.

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