Method for reconstructing range image of gm-apd lidar based on convex set projection

Abstract

The application discloses a GM-APD laser radar distance image reconstruction method based on convex set projection, and comprises the following steps: interpolating an original low-resolution image to obtain a high-resolution reference image; constructing a transformation model based on an image degradation model, and obtaining an estimated low-resolution image based on the transformation model and the high-resolution reference image; defining a constraint condition; calculating the residual error of the original low-resolution image and the estimated low-resolution image, and correcting the high-resolution reference image based on the residual error and the constraint condition to obtain a final high-resolution distance image. The application not only solves the problem of edge blurring of the original convex set projection algorithm, but also enhances the image edge structure and improves the image quality.

Description

Technical Field

[0001] This invention relates to the field of signal reconstruction and image processing technology, and in particular to a GM-APD lidar range image reconstruction method based on convex set projection. Background Technology

[0002] GM-APD (Geiger mode Avalanche Photo Diode) lidar is a type of lidar that uses a Geiger mode avalanche photodiode array as its detector. It boasts long detection range, strong anti-interference capabilities, and photon-level detection sensitivity. It is widely used in missile guidance, ground and air target identification, underwater target detection, and air-to-ground combat. However, when using GM-APD array lidar to detect and image long-range targets, the image resolution is limited by the size of the GM-APD array, making subsequent target identification and tracking difficult. Therefore, obtaining high-quality, high-resolution range images of targets is crucial for achieving long-range target identification and tracking.

[0003] Currently, research on range image super-resolution reconstruction algorithms mainly falls into three categories: interpolation-based, learning-based, and reconstruction-based methods. Interpolation-based methods are relatively simple and easy to operate, but they rely heavily on their own information, potentially blurring image edges and causing the interpolation results to deviate from reality. Learning-based methods yield more realistic reconstruction results with better image quality, but they heavily rely on external sample libraries, and the quality and quantity of samples directly affect the reconstruction results. Reconstruction-based methods incorporate prior knowledge into the constraint information, eliminating the need for a sample library and achieving good range image reconstruction results. A classic example is the POCS-based super-resolution reconstruction algorithm, which introduces multiple prior conditions to constrain the low-resolution image and then iteratively solves to obtain the reconstruction result. This algorithm is simple and feasible, but it can easily lead to over-smoothing of the image and blurred edges. Therefore, this invention proposes a GM-APD lidar range image reconstruction method based on convex set projection. Summary of the Invention

[0004] In view of the technical defects or improvement needs in the existing technology, the purpose of this invention is to propose a GM-APD lidar range image reconstruction method based on convex set projection.

[0005] This invention provides a GM-APD lidar range image reconstruction method based on convex set projection, comprising:

[0006] Interpolation is performed on the original low-resolution image to obtain a high-resolution reference image;

[0007] A transformation model is constructed based on the image degradation model, and an estimated low-resolution image is obtained based on the transformation model and the high-resolution reference image.

[0008] Define constraints; calculate the residual between the original low-resolution image and the estimated low-resolution image; and correct the high-resolution reference image based on the residual and the constraints to obtain the final high-resolution range image.

[0009] Optionally, a high-resolution reference image can be obtained by calculating the original low-resolution image using a bicubic interpolation method.

[0010] Optionally, the calculation formula for the transformation model is:

[0011]

[0012] In the formula, g(m1,m2,l) represents the low-resolution image of the l-th frame, f(n1,n2) represents the high-resolution reference image, n(m1,m2,l) represents noise, h(n1,n2;m1',m'2,l) represents the point spread function of the observed image at point (m1',m'2), (n1,n2) represents the x and y coordinates of the pixel in the reconstructed image, and (m1',m'2) represents the center coordinates of the point spread function.

[0013] Optionally, the process of estimating the low-resolution image based on the transformation model and the high-resolution reference image includes:

[0014] Constructing a fractional differential mask window based on GL fractional differential operators;

[0015] The high-resolution reference image is obtained by convolving the high-resolution reference image with the fractional-order differential mask window.

[0016] The estimated low-resolution image is obtained based on the convolutional high-resolution reference image and the normalized point spread function.

[0017] Optionally, the process of constructing a fractional-order differential mask window based on the GL fractional-order differential operator includes:

[0018] Define the formula for the fractional derivative of GL;

[0019] The image is divided into several directions, and the coefficients of the fractional derivative of GL are obtained based on these directions and the difference expression.

[0020] The fractional differential mask window is obtained based on the coefficients of the fractional derivative of GL;

[0021] The formula for the fractional derivative of GL is as follows:

[0022]

[0023] In the formula, This is represented as a fractional derivative, where G represents the definition of the fractional derivative in GL, α is the order of the fractional derivative, a and b represent the interval range, R represents the differential step size, and [] represents the floor function. The coefficients are generalized binomial coefficients. This is a gamma function.

[0024] Optionally, the formula for the fractional-order differential mask window is:

[0025]

[0026] In the formula, α is the order of the fractional-order mask window, -1 < α < 1, and A represents the fractional-order differential mask window.

[0027] Optionally, the formula for convolving the high-resolution reference image using the fractional-order differential mask window is as follows:

[0028] ref k x,y=A*ref n1,n2

[0029] In the formula, ref k x,y represent the high-resolution reference image after convolution, and ref n1,n2 represent the process of performing convolution operation on the high-resolution reference image.

[0030] Optionally, the normalized point spread function is expressed as:

[0031]

[0032] In the formula, h'(n1,n2; m1',m'2) represents the normalized point spread function, and S h This represents the support domain of the point spread function.

[0033] Optionally, the final high-resolution range image reconstruction expression is:

[0034]

[0035] In the formula, r k (m1,m2,l) represents the residual between the original low-resolution image and the estimated low-resolution image, ref k (n1,n2) represents the high-resolution reference image, and δ0(m1,m2,l) represents the threshold. This indicates a constraint.

[0036] Optionally, the constraint condition is:

[0037]

[0038] The present invention has the following technical effects:

[0039] This invention obtains an estimated low-resolution image based on a transformation model and a high-resolution reference image, and then reconstructs a high-resolution image based on the residual of the estimated low-resolution image and the original low-resolution image. This not only solves the problem of edge blurring in the original convex set projection algorithm, but also enhances the image edge structure and improves image quality; it can realize super-resolution reconstruction of the target range image of GM-APD lidar. Attached Figure Description

[0040] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0041] Figure 1 This is the amplitude-frequency response curve of the fractional derivative in the embodiments of the present invention;

[0042] Figure 2 This is a 5×5 fractional-order mask in the embodiments of the present invention;

[0043] Figure 3 This is a schematic diagram of the GM-APD lidar range image reconstruction method based on convex set projection in an embodiment of the present invention.

[0044] Figure 4 This is a comparison chart of simulation results of the evaluation metrics IE, AG, and EI of different algorithms in an embodiment of the present invention at a resolution of 128*128 and a frame count of 100 frames.

[0045] Figure 5 This is a comparison chart of simulation results of the evaluation metrics IE, AG, and EI of different algorithms in an embodiment of the present invention at a resolution of 256*256 and a frame count of 100 frames.

[0046] Figure 6 This is a comparison chart of the experimental results of different algorithms' evaluation metrics IE, AG, and EI when the resolution is 128*128 and the number of frames is 500, according to an embodiment of the present invention.

[0047] Figure 7 This is a comparison chart of the experimental results of the evaluation metrics IE, AG, and EI of different algorithms in an embodiment of the present invention at a resolution of 256*256 and a frame count of 500 frames. Detailed Implementation

[0048] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0049] Example 1

[0050] This embodiment discloses a GM-APD lidar range image reconstruction method based on convex set projection to overcome the problem of low target range image resolution acquired by GM-APD lidar. The method specifically includes the following steps:

[0051] Step S1: Perform bicubic interpolation on the original low-resolution image to obtain a high-resolution reference image;

[0052] Step S2, obtaining the estimated low-resolution image, includes the following steps:

[0053] Step S21: Construct an image degradation model;

[0054] Step S22: Construct a transformation model that estimates the transformation between the low-resolution image and the high-resolution reference image;

[0055] Step S23: Construct a fractional differential mask window using the GL fractional differential operator, then perform a convolution operation on the high-resolution reference image, and finally combine the normalized point spread function to obtain the estimated low-resolution image.

[0056] Step S3: Calculate the residual between the original low-resolution image and the estimated low-resolution image, and correct the high-resolution reference image in combination with the constraints to obtain the final high-resolution range image.

[0057] Furthermore, in step S21, the image degradation model formula is:

[0058] g = h*x + n

[0059] Where g represents a low-resolution image, h is called the degradation function, x represents a high-resolution image, and n represents noise.

[0060] Furthermore, in step S22, the transformation model is represented as:

[0061]

[0062] Where g(m1,m2,l) is the low-resolution image of the l-th frame, f(n1,n2) is the high-resolution image, n(m1,m2,l) is noise, and h(n1,n2;m1',m'2,l) is the point spread function (PSF) of the observed image at point (m1',m'2), which can be represented by the common Gaussian model as follows:

[0063]

[0064] In the above formula, (n1, n2) represent the x and y coordinates of the reconstructed image pixels, (m1', m'2) represent the center coordinates of the PSF template, and S h This indicates the support field of the PSF template.

[0065] Furthermore, in step S23, the fractional derivative of GL is defined as:

[0066]

[0067] in, This is represented as a fractional derivative, where G represents the definition of the fractional derivative in GL, α is the order of the fractional derivative, a and b represent the interval range, R represents the differential step size, and [] represents the floor function. The coefficients are generalized binomial coefficients. This is a gamma function.

[0068] If the duration interval of a univariate signal f(t) is [a, b], and it is divided into equal parts by a unit R = 1, the difference expression for the α-order differential is:

[0069]

[0070] Considering the directionality of the image, it is divided into eight directions: 0°, 45°, 90°, 135°, 180°, 225°, 270°, and 315°. Then, based on the difference expression, the coefficients of the fractional derivative can be obtained:

[0071]

[0072] The formula for the fractional differential mask window is then obtained as follows:

[0073]

[0074] Where α is the order of the fractional-order mask window, -1 < α < 1.

[0075] Using fractional-order differential masking formulas, convolution processing is performed on the high-resolution reference image:

[0076] ref k(n1,n2) = A*ref(n1,n2)

[0077] Finally, the estimated low-resolution image is obtained by combining the normalized point spread function. The point spread function h(n1,n2; m′1,m′2) is normalized as follows:

[0078]

[0079] In the above formula, h'(n1,n2;m′1,m′2) represents the normalized PSF template.

[0080] Furthermore, in step S3, the following constraints are defined:

[0081]

[0082] in,

[0083] r k (m1,m2,l)=g(m1,m2,l)-∑ref k (n1,n2)h'(n1,n2;m′1,m'2)

[0084] r k (m1,m2,l) represents the residual between the original low-resolution image and the estimated low-resolution image, ref k (n1,n2) represents the high-resolution reference image, and δ0(m1,m2,l) represents the threshold.

[0085] The high-resolution reference image is corrected by incorporating constraints; the corrected image is the reconstructed high-resolution image.

[0086]

[0087] Example 2

[0088] This invention provides a method for reconstructing the range image of a GM-APD lidar based on convex set projection, comprising the following steps:

[0089] Step S1: Perform bicubic interpolation on the original low-resolution image to obtain a high-resolution reference image;

[0090] Step S2: Starting with the image degradation model, a transformation model is constructed between the estimated low-resolution image and the high-resolution reference image obtained in step S1. The high-resolution reference image is convolved using the GL fractional differential operator, and the estimated low-resolution image is obtained by combining this with the point spread function. The specific steps are as follows:

[0091] Step S21, the image degradation model is characterized as the relationship between low-resolution and high-resolution images, such as... Figure 1 As shown, the formula for this model can be expressed as:

[0092] g = h*x + n

[0093] Here, g represents the low-resolution image, h is called the degradation function, x represents the high-resolution image, and n represents noise. It can be seen that the image super-resolution process is the inverse operation of the image degradation process.

[0094] Step S22: Construct a transformation model to estimate the transformation between the low-resolution image and the high-resolution reference image:

[0095]

[0096] Where g(m1,m2,l) is the low-resolution image of the l-th frame, f(n1,n2) is the high-resolution image, h(n1,n2;m′1,m′2,l) is the point spread function (PSF) of the observed image at point (m′1,m′2), also known as the degradation function, and n(m1,m2,l) is noise.

[0097] The point spread function (PSF) is represented by a common Gaussian model, and its expression can be given as:

[0098]

[0099] In the above formula, (n1,n2) represent the x and y coordinates of the reconstructed image pixels, (m′1,m′2) represent the center coordinates of the PSF template, and S h This indicates the support field of the PSF template.

[0100] Step S23: Construct a fractional-order differential mask window using the GL fractional-order differential operator, then perform a convolution operation on the high-resolution reference image, and finally combine it with the normalized point spread function to obtain the estimated low-resolution image. The specific steps are as follows:

[0101] First, a fractional differential mask window is constructed using the GL fractional differential operator:

[0102] For a function f(x), its first differential is defined as:

[0103]

[0104] The second-order differential is defined as:

[0105]

[0106] By mathematical induction, the integer n-th order differential operator is defined as:

[0107]

[0108] Generalize the integer n to the real number α∈R + The fractional derivative of GL can be defined as:

[0109]

[0110] in, This is represented as a fractional derivative, where G represents the definition of the fractional derivative in GL, α is the order of the fractional derivative, a and b represent the interval range, R represents the differential step size, and [·] represents the floor operator. The coefficients are generalized binomial coefficients. This is a gamma function.

[0111] If the duration interval of a univariate signal f(t) is [a, b], and it is divided into equal parts by a unit R = 1, then... Therefore, the difference expression for the α-order differential of a one-dimensional signal f(t) is:

[0112]

[0113] For any square-integrable real function f(t) ∈ L 2 (R), whose Fourier transform is:

[0114]

[0115] Among them, D α Let represent the α-order differential operator, w represent the angular frequency, and sgn(·) represent the sign function. Plot the amplitude-frequency response curves for α = 0, α = 0.2, α = 0.4, α = 0.6, α = 0.8, α = 1, α = 1.2, and α = 1.4, respectively, as shown below. Figure 1 As shown, fractional derivatives can enhance the edge information of an image.

[0116] Although the original POCS algorithm can reconstruct high-resolution range images by combining a large amount of prior information, such as Figure 2 As shown, due to the insufficient information contained in low-resolution range images, it may be impossible to accurately recover the details of the image, resulting in blurred image edges and ultimately making it difficult to obtain high-quality range images. Fractional derivatives have an enhancing effect on image edges. Therefore, this paper combines POCS with GL fractional derivatives and processes high-resolution reference images by constructing fractional derivative masks to achieve high-frequency image enhancement and improve image texture details.

[0117] Considering the directionality of the image, it is divided into eight directions: 0°, 45°, 90°, 135°, 180°, 225°, 270°, and 315°. Then, based on the difference expression for the fractional derivative of GL, the coefficients of the fractional derivative can be obtained:

[0118]

[0119] Image processing typically uses a 5×5 fractional-order mask, such as... Figure 2 As shown. Therefore, the formula for the fractional-order differential mask window is:

[0120]

[0121] Where α is the order of the fractional-order mask window, -1 < α < 1.

[0122] Then, convolution processing is performed on the high-resolution reference image:

[0123] ref k (n1,n2) = A*ref(n1,n2)

[0124] Where ref n1,n2 represent the original high-resolution reference images.

[0125] Finally, the estimated low-resolution image is obtained by combining the normalized point spread function:

[0126] The point spread function h(n1,n2; m′1,m′2) requires further normalization:

[0127]

[0128] In the above formula, h'(n1,n2;m′1,m′2) represents the normalized PSF template.

[0129] Step S3:

[0130] First, calculate the residual between the original low-resolution image and the estimated low-resolution image, defining the following set of closed convex constraints:

[0131]

[0132] in,

[0133] r k (m1,m2,l)=g(m1,m2,l)-∑ref k (n1,n2)·h'(n1,n2;m′1,m'2)

[0134] r k (m1,m2,l) represents the residual, ref k(n1,n2) represents the high-resolution reference image, and δ0(m1,m2,l) represents the threshold.

[0135] Then, the high-resolution reference image is corrected based on constraints, and the corrected image is the reconstructed high-resolution image. The principle diagram of the GM-APD lidar range image reconstruction method using convex set projection is shown below. Figure 3 As shown.

[0136]

[0137] To verify the reconstruction effect of the proposed algorithm, this invention uses the Monte Carlo method to simulate the range image of GM-APD lidar.

[0138] Simulation analysis parameter settings: The laser single-pulse output energy is set to 1.25*10^-12 J, the laser wavelength to 1064 nm, the laser pulse width to 5 ns, the detector array to 64*64, the detector time resolution to 1 ns, the round-trip atmospheric attenuation coefficient to 0.8*0.8, the target diffuse reflectance to 0.3, the receiver transmittance to 90%, the transmitter transmittance to 80%, the gating gate width to 200 bins, and the target position within the gating gate to 60 bins. Under the conditions of 100 frames and resolutions of 128*128 and 256*256, inverse range interpolation, Kriging interpolation, POCS, and the algorithm proposed in this invention are used to process the simulated range image. Information entropy, average gradient, and edge intensity are used to evaluate the simulation results.

[0139] Simulation Analysis Experiment 1: Under the condition of 100 frames, the resolution of the range image is increased by 2 times by using inverse range interpolation, Kriging interpolation, POCS and improved algorithms respectively, that is, from 64*64 to 128*128.

[0140] Simulation results from different algorithms show that at a resolution of 128*128, the non-edge regions of the distance images processed by inverse distance interpolation, kriging interpolation, and POCS algorithms are consistent with the original distance images, and the detailed information is fully preserved, but the outlines of the edge regions are relatively blurry. The distance images processed by the improved algorithm not only fully preserve the detailed information of the car, but also better maintain the edge structure of the car, making its edge outline clearer.

[0141] Simulation Analysis Experiment 2: To investigate the quality of the reconstructed range image, this paper evaluates the quality of the reconstructed range image using three metrics—information entropy, average gradient, and edge intensity—within a frame count of 100 frames. The comparison results of each evaluation metric at a resolution of 128*128 are shown below. Figure 4 As shown.

[0142] As can be seen, under the condition of 100 frames, the improved POCS algorithm improves the information entropy, average gradient, and edge strength of the distance image after processing compared with inverse distance interpolation, Kriging interpolation, and the POCS algorithm. Moreover, the improved POCS algorithm uses a GL fractional-order mask window to perform convolution operation on the high-resolution reference image, which enhances the contour features of the image and increases the texture details of the image. At a resolution of 128*128, the improved POCS algorithm improves the information entropy by 4.418%, the average gradient by 7.370%, and the edge strength by 8.949% compared with the original POCS algorithm.

[0143] Simulation Analysis Experiment 3: Under the condition of 100 frames, the resolution of the range image was increased by 4 times by using inverse range interpolation, Kriging interpolation, POCS and improved algorithms, that is, from 64*64 to 256*256.

[0144] Simulation results from different algorithms show that at a resolution of 256*256, the detailed information of the range image processed by inverse distance interpolation, kriging interpolation, and POCS algorithm is completely preserved, but the outline of the edge region is still relatively blurry. The edge outline of the improved algorithm is clearer than other algorithms, and is almost consistent with the original range image effect.

[0145] Simulation Analysis Experiment 4: To investigate the quality of the reconstructed range image, this paper evaluates the quality of the reconstructed range image using three metrics—information entropy, average gradient, and edge intensity—within a frame count of 100 frames. The comparison results of each evaluation metric at a resolution of 256*256 are shown below. Figure 5 As shown.

[0146] As can be seen, under the condition of 100 frames, the improved POCS algorithm improves the information entropy, average gradient, and edge strength of the distance image compared to inverse distance interpolation, Kriging interpolation, and the overall POCS algorithm metrics. Furthermore, the improved POCS algorithm produces images with clearer contour structures. At a resolution of 256*256, the improved POCS algorithm increases information entropy by 9.398%, average gradient by 9.507%, and edge strength by 6.383% compared to the original POCS algorithm.

[0147] The above analysis verifies the superiority of the algorithm proposed in this invention through simulation data. The following will verify it through experiments. The experiment builds a 64*64 array GM-APD lidar system, which mainly includes a transmitting system, a receiving system, a control system, a data processing system, a display device, and a target.

[0148] Experimental equipment: 1064nm fiber laser, 64×64 array GM-APD lidar, with the laser output repetition rate set at 10kHz, pulse width at 5ns, single pulse energy at 120μJ, and field of view at the moment of transmission and reception of 0.8°×0.8°.

[0149] Imaging experiment verification: In order to verify the effectiveness of the algorithm proposed in this invention, an imaging experiment was conducted on a residential building 3124m away from the system.

[0150] Experimental Verification 1: With a statistical frame count of 500 frames, the resolution of the range image was increased by 2 times using inverse distance interpolation, Kriging interpolation, POCS, and an improved algorithm, respectively, from 64*64 to 128*128.

[0151] Experimental results from different algorithms show that the distance images reconstructed by inverse distance interpolation, kriging interpolation, and POCS lose the detailed information of the original distance image. The boundary lines of pixel values ​​at different distances on the right side of the building are not clear enough, and the edge contours are relatively blurry. The outline of the window can be roughly seen. However, the distance image reconstructed by the improved algorithm can clearly show the edge contour of the window and has richer detailed information.

[0152] Experimental Verification 2: Under the condition of 500 frames, this paper uses three indicators—information entropy, average gradient, and edge intensity—to evaluate the quality of the reconstructed distance images by different algorithms. The comparison results of each evaluation indicator at a resolution of 128*128 are as follows. Figure 6 As shown.

[0153] As can be seen, under the condition of 500 frames, the improved POCS algorithm improves the information entropy, average gradient and edge strength of the distance image after processing, compared with inverse distance interpolation, Kriging interpolation and POCS algorithm. The improved algorithm improves the information entropy by 29.007%, the average gradient by 24.936% and the edge strength by 20.089% compared with the original POCS algorithm.

[0154] Experiment 3: To verify the effectiveness of the proposed algorithm, this paper explores the processing results of inverse distance interpolation, Kriging interpolation, POCS, and the improved algorithm under the condition of 500 frames and a resolution of 256*256.

[0155] Experimental results from different algorithms show that the edge contours of the distance images reconstructed by inverse distance interpolation, kriging interpolation, and POCS are still relatively blurry, while the distance images reconstructed by the improved algorithm can clearly show the edge contours of buildings and windows.

[0156] Experiment 4: Under the condition of 500 frames, this paper uses three indicators—information entropy, average gradient, and edge intensity—to evaluate the quality of the reconstructed range image after different algorithms. The comparison results of each evaluation indicator at a resolution of 256*256 are as follows. Figure 7 As shown.

[0157] As can be seen, under the condition of 500 frames, the improved POCS algorithm improves the information entropy, average gradient, and edge strength of the distance image compared to inverse distance interpolation, Kriging interpolation, and the POCS algorithm itself. This is because the improved POCS algorithm introduces a GL fractional differential operator, which enhances the image edge structure, enriches the image texture information, and solves the problem of blurred image edges. At a resolution of 256*256, the improved POCS algorithm improves the information entropy by 24.190%, the average gradient by 10.812%, and the edge strength by 21.006% compared to the original POCS algorithm.

[0158] This invention combines the GL fractional differential operator with a high-resolution reference image to correct the high-resolution reference image, improve the POCS algorithm, and construct a GM-APD lidar range image reconstruction method based on convex set projection. In this algorithm, the invention combines the classic convex set projection algorithm with the GL fractional operator. By constructing a fractional differential mask, the high-resolution reference image is processed, which not only solves the edge blurring problem of the original POCS algorithm but also enhances the image edge structure and improves image texture details.

[0159] This method was applied to the range image acquired by the GM-APD lidar, and both simulation and experimental results show that it has achieved the expected results. Monte Carlo simulation and experimental results demonstrate that the proposed super-resolution reconstruction algorithm improves the information entropy by at least 29.007%, the average gradient by at least 24.936%, and the edge intensity by at least 20.089% compared to the original convex set projection algorithm. It can achieve super-resolution reconstruction of the target range image of the GM-APD lidar.

[0160] Currently, most existing algorithms that combine GL fractional differential operators are applied to two-dimensional images, with limited research on GM-APD lidar range images.

[0161] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for reconstructing the range image of a GM-APD lidar based on convex set projection, characterized in that, include: Interpolation is performed on the original low-resolution image to obtain a high-resolution reference image; A transformation model is constructed based on the image degradation model, and an estimated low-resolution image is obtained based on the transformation model and the high-resolution reference image. The calculation formula for the transformation model is as follows: In the formula, Indicates the first Frame low-resolution image, Represents a high-resolution reference image. Indicates noise. Indicates the observed image at point The point spread function at that location, Represents the x and y coordinates of pixels in the reconstructed image. Represents the center coordinates of the point spread function; The process of obtaining an estimated low-resolution image based on the transformation model and the high-resolution reference image includes: constructing a fractional differential mask window based on the GL fractional differential operator; convolving the high-resolution reference image with the fractional differential mask window to obtain a convolved high-resolution reference image; and obtaining an estimated low-resolution image based on the convolved high-resolution reference image and a normalized point spread function. The process of constructing a fractional differential mask window based on the GL fractional differential operator includes: defining the formula for the GL fractional differential; dividing the image into several directions, and obtaining the coefficients of the GL fractional differential based on the several directions and the difference expression; and obtaining the fractional differential mask window based on the coefficients of the GL fractional differential. The formula for the fractional derivative of GL is as follows: In the formula, It is represented as a fractional differential, where G represents the definition of the fractional differential in GL. For fractional derivatives, and Indicates the range of intervals. Indicates the differential step size. This represents the floor operator. The coefficients are generalized binomial coefficients. It is a gamma function; , represents the differential step size, and x represents the high-resolution image; Define constraints; calculate the residual between the original low-resolution image and the estimated low-resolution image; and correct the high-resolution reference image based on the residual and the constraints to obtain the final high-resolution range image.

2. The GM-APD lidar range image reconstruction method based on convex set projection according to claim 1, characterized in that, A high-resolution reference image is obtained by calculating the original low-resolution image using a bicubic interpolation method.

3. The GM-APD lidar range image reconstruction method based on convex set projection according to claim 1, characterized in that, The formula for the fractional-order differential mask window is: In the formula, Let be the order of the fractional-order mask window. A represents a fractional-order differential mask window.

4. The GM-APD lidar range image reconstruction method based on convex set projection according to claim 1, characterized in that, The formula for convolving the high-resolution reference image using the fractional-order differential mask window is as follows: In the formula, This represents the high-resolution reference image after convolution. This represents the original high-resolution reference image.

5. The GM-APD lidar range image reconstruction method based on convex set projection according to claim 1, characterized in that, The normalized point spread function is expressed as: In the formula, This represents the normalized point spread function. This represents the support domain of the point spread function.

6. The GM-APD lidar range image reconstruction method based on convex set projection according to claim 1, characterized in that, The final image reconstruction expression for the high-resolution range image is: In the formula, This represents the residual between the original low-resolution image and the estimated low-resolution image. Represents a high-resolution reference image. Indicates the threshold. This indicates a constraint.

7. The GM-APD lidar range image reconstruction method based on convex set projection according to claim 6, characterized in that, The constraints are as follows: 。

Images