Fractional order total variation GM-APD laser radar range image denoising algorithm

Abstract

The present application relates to the technical field of image data processing, and more particularly to a kind of based on fractional order total variation GM-APD laser radar range image denoising algorithm.The algorithm includes the following steps: step S1, original data is estimated by maximum likelihood estimation algorithm pixel by pixel distance parameter, realize the extraction of GM-APD range image;Step S2, introduce fractional order differential operator to construct FOTV model, obtain the spatial relationship and similarity relationship between pixels using spatial kernel function and value domain kernel function to optimize fractional order differential operator, construct FOTVGM-APD laser radar denoising model based on spatial kernel function and value domain kernel function;Step S3, split Bregman algorithm is used for range image denoising.The present application realizes the suppression of GM-APD laser radar range image lost information and distance abnormal value noise, while retaining target details and contour information.

Description

Technical Field

[0001] This invention relates to the field of image data processing technology, and in particular to a denoising algorithm for range images of fractional-order total variation GM-APD lidar. Background Technology

[0002] LiDAR is widely used in topographic mapping, forestry exploration, autonomous driving, and military defense. GM-APD (Geiger-Mode of Avalanche Photodiodes) lidar can detect single-photon level echo signals, enabling the detection of weak signals at long distances. However, because GM-APD uses a single-photon detection system, there is a detection dead time within the detection cycle, resulting in lost information in the acquired range image. Furthermore, under low signal-to-background ratio (the ratio of target echo photons to background noise photons within a gate), the target echo signal is easily submerged in noise, leading to a large amount of range anomaly noise in the range image. Therefore, to reconstruct high-quality range images, it is urgent to develop an effective range image denoising algorithm. In recent years, GM-APD lidar range image denoising algorithms have mostly adopted the approach of constructing an energy variance with a regularization term, transforming the denoising problem into an optimization problem, and using numerical solution methods for iterative solving. Global filtering methods are used to achieve range image denoising, but global filtering methods struggle to balance noise removal with the preservation of target details and edges. Fractional differential operators take into account more neighborhood information, can linearly enhance mid-frequency signals in images, nonlinearly preserve low-frequency signals, and can better preserve detail information while suppressing range image noise.

[0003] There are many methods for range image denoising. Maximum likelihood estimation (MLE) is an algorithm that estimates the most probable parameter values ​​from observation data. In GM-APD range image reconstruction, MLE is used to estimate the peak probability density of GM-APD detection, thereby reconstructing the target range image. The split Bregman algorithm is an algorithm for solving sparse optimization problems. Based on the Bregman iteration idea and splitting technique, it can efficiently solve optimization problems with sparsity constraints. In the literature of Xie Da et al.'s GM-APD LiDAR depth image restoration algorithm based on fractional-order total variational regularization, a combination of these two algorithms is presented to solve the sparse reconstruction problem in image processing. However, in practice, it has been found that under low signal-to-background ratio conditions, the acquired range image contains a large amount of range anomaly noise and missing information. Therefore, it is difficult to retain target details and contour information while suppressing missing information and range anomaly noise, resulting in an unsatisfactory denoising effect. Summary of the Invention

[0004] This invention provides a range image denoising algorithm based on fractional-order total variational GM-APD lidar to overcome the problem that existing technologies have a large amount of range anomaly noise and missing information in the range image obtained under low signal-to-background ratio conditions.

[0005] To achieve the above objectives, this invention provides a range image denoising algorithm based on fractional-order total variation GM-APD lidar, comprising the following steps:

[0006] Step S1: The distance parameters of the raw data are estimated pixel by pixel using the maximum likelihood estimation algorithm to extract the GM-APD distance image;

[0007] Step S2: Introduce fractional differential operators, use spatial kernel functions and range kernel functions to obtain spatial relationships and similarity relationships between pixels, optimize fractional differential operators, and construct a FOTVGM-APD lidar denoising model based on spatial kernel functions and range kernel functions;

[0008] Step S3: Use the split Bregman algorithm to denoise the range image.

[0009] Step S2 includes: Step S21, introducing a fractional differential operator; Step S22, using spatial kernel functions and range kernel functions to obtain spatial and similarity relationships between pixels and optimizing the fractional differential operator; Step S23, constructing a FOTV denoising model based on spatial kernel functions and range kernel functions.

[0010] Furthermore, in step S21, the process of introducing the fractional differential operator is as follows:

[0011] Let the function f(x) be defined on the interval [a, b], n-1 ≤ α < n, where n is a positive integer. Then it is said that:

[0012]

[0013] For the Grumwald-Letnikov (GL) fractional derivative,

[0014] in [·] represents the floor function, and h represents the differential step size.

[0015] On the interval [a, t], using the same partition h = 1, The discrete form is expressed as:

[0016]

[0017] Extending this concept to functions of two variables:

[0018]

[0019]

[0020] N represents the number of terms in the polynomial. From equations (3) and (4), the v-order fractional differential coefficients can be obtained. for:

[0021]

[0022] Furthermore, in step S22, a spatial kernel function and a range kernel function are introduced to obtain the spatial relationship and similarity relationship between pixels and reconstruct the fractional differential operator:

[0023] First, we introduce the spatial kernel function:

[0024]

[0025] Where, σ s The variance of the spatial kernel function;

[0026] Secondly, a range kernel function is introduced:

[0027]

[0028] Where, σ r Let Variance be the range kernel function, then the new fractional differential operator is:

[0029]

[0030]

[0031] Where M is the number of rows (columns) of the GM-APD focal plane array.

[0032] make The above formula can be written in the following form:

[0033]

[0034] The matrix B′ has the following form:

[0035]

[0036] Furthermore, in step S23, a FOTV denoising model based on a spatial kernel function and a range kernel function is constructed. This model is as follows:

[0037] First, we introduce the FOTV denoising model:

[0038]

[0039] In the formula, u is the range image to be denoised, and g is the input noisy range image. Next, an auxiliary variable z is introduced, transforming the original denoising problem into:

[0040]

[0041] z and Since the function is convex and differentiable, the constrained problem is transformed into an unconstrained optimization problem.

[0042]

[0043] In the formula, γ is the penalty function, and an auxiliary variable b is introduced. The solution is as follows:

[0044]

[0045] The subproblem requires solving u and z simultaneously, and can be decomposed into:

[0046]

[0047] like Then the iteration ends, and the denoised distance image u = u is output. k+1 Otherwise, continue iterating until convergence.

[0048] Furthermore, step S1 includes: step S11, constructing the impulse response function of GM-APD; step S12, constructing the log-likelihood function related to the arrival time of the signal photon; and step S13, searching and solving the likelihood function within the entire range gating gate to obtain the target distance information.

[0049] Compared with the prior art, the advantages of the present invention are:

[0050] 1. This invention relates to a GM-APD lidar denoising model based on fractional total variation (FOTV). It utilizes spatial and domain kernel functions to obtain spatial and similarity relationships between pixels, optimizing the fractional differential operator. By combining the fractional differential operator, domain kernel function, and spatial kernel function, the FOTV model is improved, resulting in a novel FOTV GM-APD lidar range image denoising algorithm. First, the target range image is obtained through maximum likelihood estimation. Then, the FOTV denoising model is introduced, and its fractional differential operator is reconstructed using domain and spatial kernel functions to obtain the FOTVGM-APD lidar denoising model based on these functions. Finally, the range image is denoised using a split Bregman algorithm, achieving the preservation of target details and contour information while suppressing lost information and range anomaly noise.

[0051] 2. In step S21, a fractional differential operator is introduced. The fractional differential operator can enhance the edge information and preserve the detail information of the image while denoising the image. In step S22, a spatial kernel function and a range kernel function are introduced to obtain the spatial relationship and similarity relationship between pixels, reconstruct the fractional differential operator, and introduce it into the FOTV denoising model. This new model can remove noise while preserving the detail information and edge information of the image, thereby obtaining better image denoising and smoothing effects.

[0052] 2. Monte Carlo simulation and experimental results show that, under the same signal-to-background ratio (SBR) and statistical frame count, the target restoration accuracy of the algorithm proposed in this invention is improved by at least 5.11%, and the peak signal-to-noise ratio (PSNR) is improved by at least 24.6%. The method proposed in this invention can achieve denoising of GM-APD lidar range images under low SBR conditions. Attached Figure Description

[0053] Figure 1 This is a schematic diagram of the overall algorithm flow.

[0054] Figure 2 The simulated target distance image is set.

[0055] Figure 3 K and PSNR are the evaluation metrics for different fractional orders under 20 frames.

[0056] Figure 4 The distance image simulation analysis diagrams for different SBRs under 20 frames are plotted for the algorithm proposed in this invention and the comparison algorithms TV, FOTV, and BF.

[0057] Figure 5 The denoising results are shown for different signal-to-background ratios across 20 frames.

[0058] Figure 6 The K-curve graphs for different signal-to-background ratios at 20 frames are plotted for the algorithm proposed in this invention and the comparison algorithms TV, FOTV, and BF.

[0059] Figure 7 PSNR curves for different signal-to-background ratios under 20 frames were plotted for the algorithm proposed in this invention and the comparison algorithms TV, FOTV, and BF.

[0060] Figure 8 Simulation analysis of distance images with different frame numbers when SBR is 0.5.

[0061] Figure 9 K-curves were plotted for the proposed algorithm and the comparison algorithms TV, FOTV, and BF at different frame counts with SBR=0.5.

[0062] Figure 10PSNR curves for the proposed algorithm and comparison algorithms TV, FOTV, and BF at different frame counts with SBR=0.5 are plotted.

[0063] Figure 11 This is a diagram of a lidar system.

[0064] Figure 12 This is a diagram of the target scene for the imaging experiment.

[0065] Figure 13 This is the ideal target range image for the imaging experiment.

[0066] Figure 14 The result of the TV denoising algorithm is shown in the image.

[0067] Figure 15 The image shows the result of the FOTV denoising algorithm.

[0068] Figure 16 The image shows the result of the BF denoising algorithm.

[0069] Figure 17 This is a diagram showing the denoising result of the algorithm of this invention.

[0070] Figure 18 This is a quantitative assessment of the quality of reconstructed distance images using various metrics.

[0071] Figure 19 The image shows the denoising result of the proposed algorithm at 100 frames and an SBR of 0.8.

[0072] Figure 20 The image shows the denoising results of the algorithm of this invention at 100 frames and an SBR of 0.8.

[0073] Figure 21 This provides a quantitative evaluation of the quality of the reconstructed range image using two denoising algorithms. Specific implementation methods

[0074] To make the objectives and advantages of the present invention clearer, the present invention will be further described below with reference to the accompanying drawings and embodiments; it should be understood that the specific embodiments described herein are only for explaining the present invention and are not intended to limit the present invention.

[0075] like Figure 1 As shown, a range image denoising algorithm based on fractional-order total variation GM-APD lidar specifically includes the following steps:

[0076] Step S1: The distance parameters of the raw data are estimated pixel by pixel using the maximum likelihood estimation algorithm to extract the GM-APD distance profile.

[0077] Step S11, the process of constructing the impulse response function of the GM-APD is as follows:

[0078] First, construct the pulsed laser emission model:

[0079]

[0080] Where f(t) is the laser pulse waveform and τ is the laser pulse width.

[0081] The expression for the Impulse Response Function (IRF) of the GM-APD, without considering noise photons caused by background light and detector dark counting, is as follows:

[0082]

[0083] Where f(t0|t) is the impulse response function of GM-APD, and t0 is the flight time of the target photon to be estimated.

[0084] Step 12, the process of constructing the log-likelihood function related to the arrival time of the signal photon is as follows: First, define the relationship between the flight time of the target photon and the target distance:

[0085]

[0086] Where z is the target distance and c is the speed of light.

[0087] Photon flight time t in a single pixel i，j Related depth z i，j The log-likelihood function is:

[0088]

[0089] Among them, U i，j It is the set of flight times within a single-pixel gating gate.

[0090] Step 13, the process of searching and solving the likelihood function within the entire distance gating gate to obtain the target distance information is as follows:

[0091] The distance parameter z ranges from the time interval starting at the gate to the bins-1 time interval. T is the gate length, Δ is the minimum time resolution for counting, and the last time interval is discarded because the number of untriggered counts is accumulated in the last time interval. Then, the likelihood function for different parameters is calculated, and the estimated echo position z can be obtained by finding the parameter value corresponding to the maximum value of the likelihood function. pos .

[0092] z pos =argmax z (L Z )

[0093] By repeating the above process and performing maximum likelihood estimation pixel by pixel, the three-dimensional distance image g can be extracted.

[0094] Step S2 introduces a fractional differential operator, uses spatial and range kernel functions to obtain spatial and similarity relationships between pixels, optimizes the fractional differential operator, and constructs a FOTVGM-APD lidar denoising model based on spatial and range kernel functions, including the following specific steps:

[0095] Step S21: Introduce a fractional differential operator. This operator can consider more neighborhood information, balance the frequency components in the range image, improve the accuracy of subsequent range image reconstruction, and preserve the edge detail information of the image. The process of introducing the fractional differential operator is as follows:

[0096] Let the function f(x) be defined on the interval [a, b], n-1 ≤ α < n, where n is a positive integer. Then it is said that:

[0097]

[0098] For the Grumwald-Letnikov (GL) fractional derivative,

[0099] in [·] represents the floor function, and h represents the differential step size.

[0100] On the interval [a, t], using the same partition h = 1, The discrete form is expressed as:

[0101]

[0102] Extending this concept to functions of two variables:

[0103]

[0104]

[0105] N represents the number of terms in the polynomial. From the above equation, we can obtain the v-th order fractional differential coefficients. for:

[0106]

[0107] Step S22: Due to the range anomalous noise and missing information generated by the GM-APD lidar, the diffusion coefficient of the fractional-order total variation differential equation is small at the range abrupt change point, making it impossible to calibrate the range anomalous noise and missing information generated by the GM-APD lidar. Therefore, a spatial domain kernel function and a value domain kernel function are introduced to obtain the spatial relationship and similarity relationship between pixels and reconstruct the fractional-order differential operator. The specific process is as follows:

[0108] First, we introduce the spatial kernel function:

[0109]

[0110] Where, σ s The variance of the spatial kernel function;

[0111] Secondly, a range kernel function is introduced:

[0112]

[0113] Where, σ r Let Variance be the range kernel function, then the new fractional differential operator is:

[0114]

[0115]

[0116] Where M is the number of rows (columns) of the GM-APD focal plane array.

[0117] make The above formula can be written in the following form:

[0118]

[0119] The matrix B′ has the following form:

[0120]

[0121] Step S23: Based on the fractional total variation (FOTV) GM-APD LiDAR denoising model, spatial and range kernel functions are introduced to obtain the spatial and similarity relationships between pixels. The fractional differential operator is optimized to construct the FOTV denoising model based on the spatial and range kernel functions. The specific process is as follows:

[0122] First, we introduce the FOTV denoising model:

[0123]

[0124] In the formula, u is the range image to be denoised, and g is the input noisy range image. Next, an auxiliary variable z is introduced, transforming the original denoising problem into:

[0125]

[0126] z and Since the function is convex and differentiable, this constrained problem is transformed into an unconstrained optimization problem:

[0127]

[0128] In the formula, γ is the penalty function, and an auxiliary variable b is introduced. The solution is as follows:

[0129]

[0130] The subproblem requires solving u and z simultaneously, and can be decomposed into:

[0131]

[0132] like Then the iteration ends, and the denoised distance image u = u is output. k+1 Otherwise, continue iterating until convergence.

[0133] Step S3: Use the split Bregman algorithm to denoise the range image.

[0134] To verify the denoising performance of the proposed algorithm, this invention uses the Monte Carlo method to simulate the range profile of a GM-APD lidar and performs simulation analysis. The simulated target range profile is set as follows: Figure 2 As shown.

[0135] Simulation analysis parameter settings: The laser single-pulse emission energy is set to 1.25 × 10⁻⁶. -9 J, with a laser wavelength of 1064nm, a laser pulse width of 5ns, a detector array of 64×64, a detector time resolution of 1ns, a round-trip atmospheric attenuation coefficient of 0.8×0.8, a target diffuse reflectance of 0.3, a receiver transmittance of 90%, a transmitter transmittance of 80%, a gating gate width of 200m, and a target position within the gating gate of 60m. Simulated range images were processed using TV, FOTV, BF, and the algorithm proposed in this invention under different SBRs and frame numbers. Each simulation experiment was repeated 1000 times, and the simulation results were evaluated by averaging the target fidelity and peak signal-to-noise ratio.

[0136] Simulation Analysis Experiment 1: To investigate the impact of fractional order on the denoising performance of low SBR simulation data, fractional orders were set to 0.1, 0.3, 0.5, 0.7, 1, 1.2, 1.5, 1.8, and 2, with a statistical frame count of 20 frames and an SBR of 0.3. 1000 sets of Monte Carlo simulations were conducted. The average values ​​of target restoration and peak signal-to-noise ratio (PSNR) were used to evaluate the range image quality. When the fractional order was 0.7, the values ​​of K and PSNR were the highest, resulting in the best denoising performance. Figure 3 As shown.

[0137] Simulation Analysis Experiment 2: To verify the denoising performance of the proposed algorithm with the same number of frames and different SBRs, this invention sets the number of frames to 20, and the SBRs to 0.3, 0.4, 0.5, 0.6, and 0.7. K and PSNR are used to evaluate the denoising performance of the algorithm. The single Monte Carlo simulation results for 20 frames with different SBRs are shown in the figure below. Figure 4 As shown.

[0138] Depend on Figure 4 As can be seen, when SBR = 0.3, the target location in the range image processed by TV, FOTV, and BF algorithms has a large amount of noise, and the completeness and contour information of the target are poor. The algorithm proposed in this invention filters out most of the noise at the target location and can roughly identify the target's contour information, but the target's internal structure is incomplete. When SBR = 0.4, the range image processed by TV, FOTV, and BF algorithms has roughly recovered the complete target, but noise still exists, and the smoothness of the range image is poor. The algorithm proposed in this invention not only recovers the target relatively completely but also has little difference from the standard image and has a good denoising effect. When SBR = 0.8, the target in the range image processed by TV, FOTV, and BF algorithms is complete and has good smoothness, but a small amount of noise still exists. The algorithm proposed in this invention still ensures a good denoising effect.

[0139] Simulation Analysis Experiment 3: To verify the stability of the denoising performance of the proposed algorithm under different SBRs at the same frame rate of 20 frames, 1000 Monte Carlo experiments were conducted on TV, FOTV, BF, and the proposed algorithm respectively. K, PSNR, and SSIM were used to evaluate the distance profiles after processing by each algorithm. The mean values ​​of each index are shown below. Figure 5 As shown.

[0140] like Figure 6 As shown, the above Figure 5 The K-curves of the data were plotted for 20 frames at different signal-to-background ratios (SBRs). As the SBR increased, the K-value of each algorithm improved to varying degrees. The algorithm proposed in this invention outperformed the comparison algorithms in K-value across all SBRs. When the SBR was 0.4, the K-values ​​of the TV, FOTV, and BF algorithms were all less than 85%, while the target K-value of the algorithm proposed in this invention reached 95.49%. This demonstrates that the proposed algorithm has good denoising performance. When the SBR was 0.5, the K-value of the algorithm proposed in this invention reached 0.9865, which is at least 5.11% higher than the other comparison algorithms.

[0141] like Figure 7 As shown, the above Figure 5The PSNR curves for different signal-to-background ratios (SBRs) across 20 frames were plotted. As the SBR increases, the PSNR of each algorithm improves to varying degrees. The algorithm proposed in this invention outperforms the comparative algorithms in PSNR across all SBRs. When the SBR is 0.4, the PSNR of the TV, FOTV, and BF algorithms is less than 16, while the PSNR of the algorithm proposed in this invention reaches 20.6488. This demonstrates the good denoising performance of the proposed algorithm. When the SBR is 0.5, the PSNR of the algorithm proposed in this invention reaches 26.0541, which is at least 24.6% higher than the other algorithms.

[0142] Simulation Analysis Experiment 4: To verify the impact of different statistical frame numbers on the denoising performance of the proposed algorithm, simulation data with SBR=0.5 was selected. The processing results of TV, FOTV, BF, and the proposed algorithm at frame numbers of 20, 25, 30, 35, 40, 45, and 50 were investigated. Single Monte Carlo simulation data with different frame numbers and SBR=0.5 were also analyzed. The results are as follows: Figure 8 As shown.

[0143] like Figure 9 As shown, the above Figure 8 The K-curve graphs for different frame numbers with SBR=0.5 in the data show that the K values ​​of each algorithm improve to varying degrees as the number of statistical frames increases. When the number of statistical frames is 25, the K values ​​for TV, FOTV, and BF do not exceed 70%. In contrast, the K value of the algorithm in this paper reaches 0.8198, which is already able to remove noise in the range image quite well. When the number of imaging frames is 35, the K value of the algorithm proposed in this paper is improved by at least 13.58% compared with the other comparison algorithms.

[0144] like Figure 10 As shown, the above Figure 8 The PSNR curves for different frame numbers with SBR=0.5 in the data show that the PSNR of each algorithm improves to varying degrees as the number of statistical frames increases. When the number of statistical frames is 35, the PSNR of the algorithm proposed in this invention is improved by at least 24.55% compared with the other comparison algorithms.

[0145] The above analysis and experiments, through simulation analysis, verified the superiority of the algorithm proposed in this invention. The following will verify this through experiments, in which a lidar system was built. The lidar system is as follows... Figure 11 As shown.

[0146] Experimental equipment: 1064nm fiber laser, 64×64 array GM-APD camera, with transmit and receive fields of view of 0.9°×0.9° respectively, laser pulse output energy of 110uJ, pulse width of 10ns, and repetition frequency of 15kHz.

[0147] Imaging Experiment Verification: To verify the denoising performance of the proposed algorithm, an imaging experiment was conducted on a residential building complex ranging from 446.1m to 463.2m under strong sunlight. The target scene is shown in the image below. Figure 12 As shown.

[0148] Through the Figure 10 The target scene image was imaged and detected at night using peak picking, with a total of 5000 frames. Multi-frame statistical analysis was performed to obtain the ideal target distance image for the scene, as shown below. Figure 13 As shown.

[0149] In a daytime imaging experiment, with SBR set to 0.8, the average number of target photons detected by each pixel within the door / window was divided by the total number of photons within the door / window. At 100 frames per second, TV denoising, FOTV denoising, BF denoising, and the proposed algorithm were used to denoise the range image obtained by the maximum likelihood estimation method. The denoised range image is shown below. Figure 14 , Figure 15 , Figure 16 as well as Figure 17 As shown, Figure 18 These are the evaluation indicators.

[0150] like Figure 18 As shown, various metrics are used to quantitatively evaluate the quality of the reconstructed distance image. This is achieved through... Figure 14 , Figure 15 , Figure 16 as well as Figure 17 Comparing the denoising results, it can be seen that the TV, FOTV, and BF denoising algorithms remove some noise, but noise, missing information, and range anomaly noise still exist, and the denoised image loses target details and contour information. The algorithm of this invention utilizes spatial and domain kernel functions to obtain the spatial and similarity relationships between pixels, optimizes the fractional-order differential operator, and designs a novel FOTV GM-APD lidar range image denoising algorithm. This algorithm retains target details and contour information while suppressing missing information and range anomaly noise. The denoising method proposed in this invention improves target restoration accuracy by at least 4.29% and achieves a peak signal-to-noise ratio of 4.6969, both of which are superior to the compared algorithms, demonstrating that the denoising method proposed in this invention has excellent denoising performance for GM-APD range images.

[0151] To verify the advancement of the algorithm presented in this paper, based on the aforementioned experimental conditions, under 100 frames and an SBR of 0.8, the algorithm was compared with the proposed algorithm in the Geiger mode avalanche photodiode laser detection and range image restoration method based on fractional total variation regularization. The denoised range image is as follows: Figure 19 , Figure 20 , Figure 21 These are the evaluation indicators.

[0152] like Figure 21 As shown, various metrics are used to quantitatively evaluate the quality of the reconstructed distance image. This is achieved through... Figure 19 , Figure 20 Comparison of denoising results shows that while existing algorithms remove some noise, noise, missing information, and distance anomaly noise still exist, and the denoised image loses some target details and contour information. The algorithm of this invention, however, retains target details and contour information while suppressing missing information and distance anomaly noise. The denoising method proposed in this invention improves target restoration accuracy by at least 3.18% and peak signal-to-noise ratio by 0.2548, both of which are superior to the compared algorithms, while still maintaining excellent denoising performance.

[0153] The technical solution of the present invention has been described above with reference to the preferred embodiments shown in the accompanying drawings. However, it will be readily understood by those skilled in the art that the scope of protection of the present invention is obviously not limited to these specific embodiments. Without departing from the principles of the present invention, those skilled in the art can make equivalent changes or substitutions to the relevant technical features, and the technical solutions after these changes or substitutions will all fall within the scope of protection of the present invention.

[0154] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A range image denoising algorithm based on fractional-order total variation GM-APD lidar, characterized in that, Includes the following steps: Step S1: The distance parameters of the raw data are estimated pixel by pixel using the maximum likelihood estimation algorithm to extract the GM-APD distance image; Step S21: Introduce a fractional differential operator; Step S22: Optimize the fractional differential operator by obtaining the spatial and similarity relationships between pixels using spatial and range kernel functions; Step S23: Construct a FOTVGM-APD lidar denoising model based on spatial and range kernel functions. Step S22: Introduce spatial kernel function and range kernel function to obtain spatial and similarity relationships between pixels and reconstruct fractional differential operators: First, we introduce the spatial kernel function: in, The variance of the spatial kernel function; Secondly, a range kernel function is introduced: in, The variance of the kernel function is the range. For a noisy range image as input, the new fractional differential operator is: in, The number of rows or columns in the GM-APD focal plane array. For the distance image to be denoised, To find the number of terms in the summation; make The above formula can be written in the following form: Where the matrix The format is as follows: Step S3: Use the split Bregman algorithm to denoise the range image.

2. The range image denoising algorithm for fractional-order total variation GM-APD lidar as described in claim 1, characterized in that, In step S23, a denoising model for the FOTVGM-APD lidar is constructed based on spatial kernel functions and range kernel functions. This model is as follows: First, we introduce the FOTV denoising model: In the formula, For the distance image to be denoised, To input a noisy range image, secondly, auxiliary variables are introduced. The original noise reduction problem is transformed into: and Since the function is convex and differentiable, this constrained problem is transformed into an unconstrained optimization problem: In the formula To define the penalty function, introduce an auxiliary variable b and solve for it: Subproblems need to be solved simultaneously and Decomposed into: like Then the iteration ends, and the denoised distance image is output. Otherwise, continue iterating until convergence.

3. The range image denoising algorithm for fractional-order total variation GM-APD lidar according to claim 2, characterized in that, Step S1 includes: Step S11, constructing the impulse response function of GM-APD; Step S12: Construct the log-likelihood function related to the arrival time of the signal photon; Step S13: Search and solve the likelihood function within the entire distance gating gate to obtain the target distance information.

Images