GEO sar imaging troposphere error compensation method and device

Abstract

The application relates to a GEO SAR imaging perturbed troposphere error compensation method and device in the technical field of radar image processing, the method constructs a model taking the influence of a perturbed troposphere parameter as input and an image performance index as output, the model considers nonlinearity and can quickly solve the problem by using a linear model; the model establishes the connection between the influence of the perturbed troposphere parameter and block selection, can roughly invert the influence factor by using the constructed model, and provides an initial value for block selection, so that the calculation speed is greatly improved compared with the iteration method. The method can compensate for the phase error of GEO SAR images caused by the perturbed troposphere, and improve the image quality.

Description

Technical Field

[0001] This application relates to the field of radar image processing technology, and in particular to a method and apparatus for compensating for tropospheric errors caused by GEO SAR imaging disturbances. Background Technology

[0002] GEO SAR is a synthetic aperture radar system mounted on geostationary orbit satellites that can achieve imaging within a specific latitude and longitude range. GEO SAR systems possess advantages such as high mapping bandwidth, high resolution, long dwell time, and short revisit time. Research on this system has entered a period of rapid development, with significant application value in areas such as natural disaster monitoring and atmospheric water vapor retrieval. Imaging processing is one of the core technologies of GEO SAR systems, attracting considerable attention from domestic scholars, and its development can be divided into three stages. The first stage addressed the insufficient accuracy of traditional imaging models. The second stage considered the azimuth variation introduced by the Earth's rotation in long synthetic aperture systems. The third stage focuses on the imaging problems of GEO SAR systems under multi-mode, multi-channel, and complex configurations. It can be seen that GEO SAR imaging processing technology has matured, and the correctness of related methods has been widely verified.

[0003] After solving the fundamental challenges of GEO SAR imaging processing, to achieve accurate ground observation, it is also necessary to consider the complex tropospheric propagation delay introduced by GEO SAR. Utilizing the latest advancements in atmospheric science, tropospheric delay is divided into two parts: a deterministic low-order background troposphere and a stochastic high-order disturbed troposphere. W. Sheng proposed a tropospheric delay compensation method based on sub-aperture partitioning. J. Rodon discussed a similar atmospheric phase delay retrieval method that relies on a reference stable point (such as a city or rocky area). The scattering phase of these points is stable, so their phase fluctuations can be directly interpreted as atmospheric phase delay. L. De compensated for each component of the troposphere sequentially in high-resolution SAR. Based on an empirical model and influence analysis of the background tropospheric delay component, a low-order approximation was used to decouple the effects of tropospheric delay from those of geometric spatial variation; thus improving the ideal GEO SAR imaging processing method and compensating for the impact of low-order tropospheric delay. L. De proposed a block autofocus algorithm to compensate for high-order error TTD. The azimuth-decompressed data was divided into different sub-blocks, and a quadratic phase error coefficient was estimated for each sub-block using MDA. Then, the two-dimensional tropospheric delay phase was estimated through interpolation and integration. Finally, the phase estimation error was multiplied by the azimuth-decompressed data to compensate for the tropospheric delay, and azimuth compression was performed again to obtain a precisely focused image.

[0004] However, the methods described above do not detail how to perform block segmentation, relying solely on processing experience. The effectiveness of tropospheric delay compensation depends on the appropriateness of the block selection. Furthermore, ignoring the anomalous frequency modulation estimated in a certain sub-block will amplify errors during subsequent interpolation and integration, degrading image quality. Summary of the Invention

[0005] Therefore, it is necessary to provide a method and apparatus for compensating for tropospheric errors caused by GEO SAR imaging disturbances, in order to address the aforementioned technical problems.

[0006] A method for compensating for tropospheric errors caused by GEO SAR imaging disturbances, the method comprising:

[0007] The obtained GEO SAR image is processed by azimuth Fourier transform, azimuth decompression, and inverse azimuth Fourier transform to obtain azimuth decompressed data.

[0008] The obtained GEO SAR image is divided into several sub-bands along the range direction.

[0009] Based on the tropospheric parameters and entropy affecting the disturbance, a block optimization model is constructed, which is as follows:

[0010]

[0011] Where X is the input of the block optimization model, X=(D,s,l,v,n,c), v is the exponential factor, l is the scale factor, D is the coordinate dimension, s is the standard deviation, n is the number of blocks, c is the block size, H is the intermediate parameter, Y is the entropy, W is the output weight, B is the bias term, g(·) is the nonlinear mapping, and f(·) is the linear mapping.

[0012] The block optimization model is solved using the extreme learning machine method to obtain the optimal number of blocks and the optimal block size when the entropy is minimized.

[0013] The sub-band is divided into several sub-blocks along the azimuth direction based on the optimal number of blocks and the optimal block size.

[0014] The MD algorithm is used to process each sub-block in each sub-band to obtain the frequency modulation error.

[0015] The frequency modulation error is subjected to azimuth interpolation and integration to obtain the estimated azimuth phase value of the disturbed troposphere.

[0016] The estimated azimuth phase of the disturbed troposphere is interpolated in the range direction, and the interpolation result is multiplied with the decompressed azimuth data. Then, the azimuth Fourier transform, refocusing, and inverse Fourier transform are performed to obtain a high-precision GEO SAR image.

[0017] In one embodiment, each sub-block within each sub-band is processed using the MD algorithm to obtain the frequency modulation error. Following this step, an anomaly detection and correction step is included, comprising:

[0018] The local outlier factor algorithm is used to detect outliers in the frequency modulation of each sub-block.

[0019] The value at the outlier point is replaced by the interpolation of the normal point in the nearby sub-block.

[0020] In one embodiment, a local outlier factor algorithm is used to detect outliers in the frequency modulation of each sub-block, including:

[0021] Calculate a local reachability density for each frequency modulation (FM) data point; the expression for the local reachability density is:

[0022]

[0023] Where Nk(p) represents the k-th distance neighborhood of point p, o is the set of points within the k-th distance of p, |N k (p) represents the number of points in the set. Let LRD be the k-th reachable distance from data point o to data point p. k (·) represents the locally reachable density.

[0024] Based on the local reachability density, the local outlier factor is calculated using the formula for calculating the local outlier factor, resulting in an outlier factor for each frequency modulation (FM) data point. The formula for calculating the local outlier factor is as follows:

[0025]

[0026] Among them, LOF k (·) is a local outlier.

[0027] Based on the outlier factor and the preset threshold, points with a high degree of outlier are identified as outliers in the frequency modulation of each sub-block.

[0028] In one embodiment, the extreme learning machine method is used to solve the block optimization model to obtain the optimal number of blocks and the optimal block size when the entropy is minimized, including:

[0029] The loss function for constructing the block optimization model is as follows:

[0030]

[0031] Where C is the regularization coefficient, H is the intermediate layer output, T is the true value, and W is the output weight.

[0032] The loss function is solved using a ridge regression approach, yielding an estimated value for the output weights:

[0033]

[0034] Among them, W * This is an estimate of the output weights.

[0035] Based on the preset training data, the estimated values ​​of the output weights, and the block optimization model, the coarse values ​​of the exponential factor and the scale factor are retrieved.

[0036] Substitute the estimated values ​​of the output weights, the coarse values ​​of the exponential factor and the scale factor into the block optimization model to solve for the optimal number of blocks and the optimal block size when the entropy is minimized.

[0037] In one embodiment, based on preset training data, estimated values ​​of output weights, and the block optimization model, the coarse values ​​of the exponential factor and the scaling factor are retrieved, including:

[0038] Based on the preset training data, the estimated output weights, and the block optimization model, the parameter inversion formula is used to solve for the rough values ​​of the exponential factor and the scale factor; the parameter inversion formula is:

[0039]

[0040] Where |·| represents the absolute value, (l min ,l max ) and (v min ,v max ) represent the ranges of values ​​for l and v, respectively. These are the coarse values ​​for l and v, respectively.

[0041] A GEO SAR imaging disturbance tropospheric error compensation device, the device comprising:

[0042] The azimuth decompression data determination module is used to perform azimuth Fourier transform, azimuth decompression, and inverse azimuth Fourier transform on the obtained GEO SAR image to obtain azimuth decompressed data.

[0043] The sub-band division module is used to divide the acquired GEO SAR image into several sub-bands along the range direction.

[0044] The block parameter optimization module is used to construct a block optimization model based on the influencing tropospheric parameters and entropy. The block optimization model is solved using the extreme learning machine method to obtain the optimal number of blocks and the optimal block size when the entropy is minimized. The block optimization model is as follows:

[0045]

[0046] Where X is the input of the block optimization model, X=(D,s,l,v,n,c), v is the exponential factor, l is the scale factor, D is the coordinate dimension, s is the standard deviation, n is the number of blocks, c is the block size, H is the intermediate parameter, Y is the entropy, W is the output weight, B is the bias term, g(·) is the nonlinear mapping, and f(·) is the linear mapping.

[0047] The sub-block partitioning module is used to divide the sub-band into several sub-blocks along the azimuth direction according to the optimal number of blocks and the optimal block size.

[0048] The azimuth phase estimation value determination module is used to process each sub-block in each sub-band using the MD algorithm to obtain the frequency modulation error; and to perform azimuth interpolation and integration processing on the frequency modulation error to obtain the azimuth phase estimation value of the disturbed troposphere.

[0049] The image error compensation module is used to interpolate the estimated azimuth phase value of the disturbed troposphere in the range direction, and multiply the interpolation result with the azimuth decompressed data before performing azimuth Fourier transform, refocusing, and inverse Fourier transform to obtain a high-precision GEO SAR image.

[0050] In one embodiment, the block parameter optimization module further includes an outlier detection and correction module, which uses a local outlier factor algorithm to detect outliers in the frequency modulation of each sub-block; and replaces the value at the outlier with the interpolation of the normal point in the nearby sub-block.

[0051] In one embodiment, the anomaly detection and correction module is further configured to calculate a local reachability density for each frequency modulation data point; the expression for the local reachability density is:

[0052]

[0053] Where Nk(p) represents the k-th distance neighborhood of point p, o is the set of points within the k-th distance of p, |N k (p) represents the number of points in the set. Let LRD be the k-th reachable distance from data point o to data point p. k (·) represents the locally reachable density.

[0054] Based on the local reachability density, the local outlier factor is calculated using the formula for calculating the local outlier factor, resulting in an outlier factor for each frequency modulation (FM) data point. The formula for calculating the local outlier factor is as follows:

[0055]

[0056] Among them, LOF k (·) is a local outlier.

[0057] Based on the outlier factor and the preset threshold, points with a high degree of outlier are identified as outliers in the frequency modulation of each sub-block.

[0058] In one embodiment, the block parameter optimization module is further configured to construct a loss function for the block optimization model, wherein the loss function is:

[0059]

[0060] Where C is the regularization coefficient, H is the intermediate layer output, T is the true value, and W is the output weight.

[0061] The loss function is solved using a ridge regression approach, yielding an estimated value for the output weights:

[0062]

[0063] Among them, W * This is an estimate of the output weights.

[0064] Based on the preset training data, the estimated values ​​of the output weights, and the block optimization model, the coarse values ​​of the exponential factor and the scale factor are retrieved.

[0065] Substitute the estimated values ​​of the output weights, the coarse values ​​of the exponential factor and the scale factor into the block optimization model to solve for the optimal number of blocks and the optimal block size when the entropy is minimized.

[0066] In one embodiment, the block parameter optimization module is further configured to solve for the coarse values ​​of the exponential factor and the scale factor using a parameter inversion formula based on preset training data, estimated values ​​of output weights, and the block optimization model; the parameter inversion formula is:

[0067]

[0068] Where |·| represents the absolute value, (l min ,l max ) and (v min ,v max ) represent the ranges of values ​​for l and v, respectively. These are the coarse values ​​for l and v, respectively.

[0069] The aforementioned method and apparatus for compensating for tropospheric errors in GEO SAR imaging constructs a model that takes the influencing tropospheric parameters as input and image performance indicators as output. This model considers both nonlinearity and can utilize linear models to quickly solve the problem. The model establishes the relationship between the influencing tropospheric parameters and block selection, and can roughly deduce the influencing factors using the constructed model, providing initial values ​​for block selection. Compared with simple iterative methods, this significantly improves the computational speed. This method can compensate for the phase errors caused by tropospheric disturbances in GEO SAR images, thus improving image quality. Attached Figure Description

[0070] Figure 1 This is a flowchart illustrating a method for compensating for tropospheric errors caused by GEO SAR imaging disturbances in one embodiment.

[0071] Figure 2 This is the processing flow of the GEO SAR imaging disturbance tropospheric error compensation method in another embodiment;

[0072] Figure 3 Here is an image result from another embodiment, where (a) is the original image and (b) is the affected image;

[0073] Figure 4 In another embodiment, several image results are shown: (a) using the iterative method, (b) using known parameters, (c) using unknown parameters, and (d) using the inversion initial value for iteration.

[0074] Figure 5 In another embodiment, the original and estimated phases of different sub-bands are shown, where (a) and (b) are the original and estimated phases of two different sub-bands, respectively.

[0075] Figure 6 The image shown in another embodiment is the second estimated phase and the image after two complete compensations, where (a) is the original phase and the estimated phase in the second compensation, and (b) is the image after the second compensation;

[0076] Figure 7 In another embodiment, outlier detection results are ignored;

[0077] Figure 8 This is a structural block diagram of a GEO SAR imaging disturbance tropospheric error compensation device in one embodiment. Detailed Implementation

[0078] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0079] In one embodiment, such as Figure 1 , Figure 2 As shown, a method for compensating for tropospheric errors caused by GEO SAR imaging disturbances is provided. This method includes the following steps:

[0080] Step 100: After performing azimuth Fourier transform, azimuth decompression, and inverse azimuth Fourier transform on the obtained GEO SAR image, azimuth decompressed data is obtained.

[0081] Specifically, the obtained GEO SAR image is a GEO SAR image after background tropospheric delay compensation.

[0082] The two-dimensional variation of the impact of tropospheric disturbances was estimated using the MD algorithm.

[0083] Step 102: Divide the obtained GEO SAR image into several sub-bands along the range direction.

[0084] Step 104: Based on the tropospheric parameters and entropy affecting the disturbance, construct a block optimization model. The block optimization model is as follows:

[0085]

[0086] Where X is the input of the block optimization model, X=(D,s,l,v,n,c), v is the exponential factor, l is the scale factor, D is the coordinate dimension, s is the standard deviation, n is the number of blocks, c is the block size, H is the intermediate parameter, Y is the entropy, W is the output weight, B is the bias term, g(·) is the nonlinear mapping, and f(·) is the linear mapping.

[0087] Specifically, it's important to note that the choice of the number and size of the blocks determines the accuracy and efficiency of the final phase prediction. Drawing inspiration from Extreme Learning Machines, a mathematical model is established that is primarily nonlinear while also considering the ease of solving linear models. First, a model is established with the influencing tropospheric parameters and block selection as inputs, and an index measuring image quality as the output. A nonlinear transformation is performed on the input data to obtain intermediate variables. Then, a linear weighted model is established between the output and the intermediate variables. This approach ensures both nonlinearity and the ability to quickly solve the problem using a linear model, improving timeliness.

[0088] The perturbation troposphere is described by the power spectral density derived from the Matérn covariance function. Drawing inspiration from the Extreme Learning Machine (ELM) concept, a database is constructed that takes as input the parameters influencing the perturbation troposphere, including the exponential factor v, scale factor l, coordinate dimension D, and standard deviation s, and as input the number and size of the blocks, and outputs metrics for image performance (contrast and entropy). By incorporating the ELM concept, the problem can be solved quickly using a linear model while considering nonlinearity. The input data is represented by a vector X. A nonlinear transformation is performed on X to obtain the intermediate variable H. Then, H and the output Y are used to establish a linear weighted model. The model expression is shown in equation (1).

[0089] According to the general approximation theorem, the Extreme Learning Machine (ELM) approaches an arbitrary continuous objective function infinitely. The feature mapping can be any nonlinear continuous function, and the core of the algorithm is to solve for the output weights that minimize the loss function. Preferably, the trigonometric function g(A,b,X)=cos(A·X+b) is chosen as the nonlinear mapping, where A and b represent the nonlinear mapping parameters.

[0090] The established model can quickly obtain optimized blocks when the coarse values ​​of the TTD parameters are known, and can also reverse these parameters to obtain block selection as initial values ​​and find the optimal blocks through iteration. The TTD parameters include: exponential factor, scale factor, coordinate dimension, standard deviation, number of blocks, and block size.

[0091] Based on this model, coarse values ​​of the exponent and scaling factor can be estimated, and then reasonable block selection can be derived, providing initial values ​​for iteration when high accuracy is required.

[0092] Step 106: Use the Extreme Learning Machine method to solve the block optimization model to obtain the optimal number of blocks and the optimal block size when the entropy is minimized.

[0093] Step 108: Divide the sub-band into several sub-blocks along the azimuth direction according to the optimal number of blocks and the optimal block size.

[0094] Step 110: Process each sub-block in each sub-band using the MD algorithm to obtain the frequency modulation error.

[0095] Step 112: Perform azimuth interpolation and integration on the frequency modulation error to obtain the estimated azimuth phase value of the disturbed troposphere.

[0096] Specifically, the image is divided into sub-blocks along the distance and azimuth directions, and the corresponding quadratic phase coefficients are estimated. By combining the phase coefficients, the second derivative of the phase is constructed, and the phase is further estimated by upsampling and integration.

[0097] Step 114: Interpolate the azimuth phase estimate of the disturbed troposphere in the range direction, multiply the interpolation result with the azimuth decompressed data, and then perform azimuth Fourier transform, refocusing, and inverse Fourier transform to obtain a high-precision GEO SAR image.

[0098] In the aforementioned GEO SAR imaging tropospheric error compensation method, a model is constructed that takes the influencing tropospheric parameters as input and image performance indicators as output. This model considers both nonlinearity and can utilize linear models to quickly solve the problem. The model establishes the relationship between the influencing tropospheric parameters and block selection, and can roughly deduce the influencing factors using the constructed model, providing initial values ​​for block selection. Compared with simply using iterative methods, this significantly improves the computational speed. This method can compensate for the phase error caused by tropospheric disturbances in GEO SAR images, thus improving image quality.

[0099] In one embodiment, step 110 is followed by an outlier detection and correction step, which includes: using a local outlier factor algorithm to detect outliers in the frequency modulation of each sub-block; and replacing the value at the outlier with the interpolation of the normal point in the nearby sub-block.

[0100] Specifically, when the estimated frequency modulation of a sub-block is abnormal, it is filtered and corrected to improve the image focus depth.

[0101] The image is divided into multiple sub-blocks, and the frequency error within each sub-block is estimated as the result of the sub-block center position. Subsequent interpolation and integration yield the secondary phase error. Therefore, the rationality of the sub-block selection directly affects the estimation of the tropospheric delay phase caused by disturbances. Furthermore, the optimal block selection is not fixed each time, as it is influenced by the scale factor, a parameter of the tropospheric delay. When the scattering points within the terrain covered by a sub-block are uniformly distributed, even if the scene is affected by tropospheric delay, the offset estimated by the MD algorithm is almost zero, resulting in anomalies. Moreover, the presence of several strong scattering points within the same sub-block also easily leads to abnormal estimation results. Therefore, it is necessary to address the issues of block optimization and anomaly correction to improve image quality. The proposed block optimization, anomaly detection, and correction algorithm is based on the block autofocus algorithm.

[0102] Since the estimated frequency modulation frequency within adjacent sub-blocks is correlated (and the changes are not particularly drastic), we use a local outlier detection method to determine outliers by defining the distance by a threshold, and then interpolate the normal results near the outliers to replace the outliers.

[0103] In one embodiment, a local outlier factor algorithm is used to detect outliers in the frequency modulation (FM) data in each sub-block, including: calculating a local reachability density for each FM data point; the expression for the local reachability density is:

[0104]

[0105] Where Nk(p) represents the k-th distance neighborhood of point p, o is the set of points within the k-th distance of p, |N k (p) represents the number of points in the set. Let LRD be the k-th reachable distance from data point o to data point p. k (·) represents the locally reachable density.

[0106] Based on the local reachability density, the local outlier factor is calculated using the formula for calculating the local outlier factor, resulting in an outlier factor for each frequency modulation (FM) data point. The formula for calculating the local outlier factor is as follows:

[0107]

[0108] Among them, LOF k (·) is a local outlier.

[0109] Based on the outlier factor and a preset threshold, points with a high degree of outlier are identified as outliers in the frequency modulation of each sub-block.

[0110] Specifically, the estimated frequency modulation error between adjacent sub-blocks after block selection optimization should be correlated, and anomalies occur when the frequency modulation changes drastically. After subsequent interpolation and integration, this error will be amplified and affect the compensation effect. We use the local outlier factor algorithm to detect outliers and replace the value at that location with the interpolation of nearby normal points. The basic idea of ​​this algorithm is to first calculate a local reachability density for each data point based on the density around the data point, and then further calculate an outlier factor for each data point through the local reachability density. The outlier factor represents the degree of outlier of a data point. The larger the factor value, the higher the degree of outlier; otherwise, the lower the degree of outlier. Finally, the points with a high degree of outlier are output by comparing the factor with the set threshold. The calculation formulas for local reachability density and local outlier factor are shown in equations (2) and (3).

[0111] LOF k (p) is the N of point p. k (p) The ratio of the average local reachability density of all points in the neighborhood to the local reachability density of point p. A ratio greater than 1 indicates that the density of point p is less than the density of its surrounding points, making point p more likely to be an outlier; otherwise, p is a normal point. This algorithm has no requirements regarding data distribution and is highly robust. After selecting the abnormal frequency modulation, the correct value for that sub-block can be obtained by interpolating the frequency modulation of nearby sub-blocks.

[0112] In one embodiment, step 106 includes: constructing a loss function for the block optimization model, the loss function being:

[0113]

[0114] Where C is the regularization coefficient, H is the intermediate layer output, T is the true value, and W is the output weight.

[0115] The loss function is solved using a ridge regression approach, yielding an estimated value for the output weights:

[0116]

[0117] Among them, W * This is the estimated value of the output weights.

[0118] Based on the preset training data, the estimated values ​​of the output weights, and the block optimization model, the coarse values ​​of the exponential factor and the scale factor are inverted; the estimated values ​​of the output weights, the coarse values ​​of the exponential factor and the scale factor are substituted into the block optimization model to solve for the optimal number of blocks and the optimal block size when the entropy is minimized.

[0119] Specifically, the process of constructing the loss function of the block optimization model is as follows: first, an L2 loss function is constructed, and in order to prevent overfitting, an L2 regularization term is introduced. The expression of the loss function of the block optimization model is shown in Equation (4).

[0120] In one embodiment, the rough values ​​of the exponential factor and the scale factor are retrieved based on preset training data, estimated output weights, and a block optimization model. This includes: solving the problem using a parameter inversion formula based on the preset training data, estimated output weights, and the block optimization model to obtain the rough values ​​of the exponential factor and the scale factor; the parameter inversion formula is:

[0121]

[0122] Where |·| represents the absolute value, (l min ,l max ) and (v min ,v max ) represent the ranges of values ​​for l and v, respectively. These are the coarse values ​​for l and v, respectively.

[0123] Specifically, since D is known and s does not affect the block selection, we can set three different sets of n and c and substitute them into the Block-MDA compensation program to obtain the output y. i (Contrast or entropy). Then, the output is substituted into the derived model to retrieve the rough values ​​of l and v, as shown in equation (6). Because trigonometric functions are non-convex, differentiation is not possible; only a loop can be used to find the solution that best approximates the true values ​​of l and v. and Then, the found solution is fed into the model to find the optimal block selection solution when the contrast (entropy) is maximized (minimum). and As shown in equation (7). This application selects entropy as the output.

[0124]

[0125] Where |·| represents absolute value. (l min ,l max ) and (v min ,v max ) represents the range of values ​​for l and v.

[0126] In a verification embodiment, to verify the effectiveness of our proposed method, Sentinel-1 data was selected for experimentation. A portion of the region was zero-padding, with azimuth and range pixels set to 14460 and 5616 respectively. Figure 3 As shown in (a), the GEO SAR perturbation troposphere was generated using the Matérn covariance function model and injected into the selected focusing region, as shown in (a). Figure 3 As shown in (b), among the parameters affecting the generation of the disturbed troposphere, D = 3, s = 2π, and l = 3 × 10⁻⁶. 4 v = 5 / 6. Table 1 lists the parameters of the GEO SAR system. We choose contrast and entropy as the metrics for image performance. For a complex image R containing M×N (azimuth and range) pixels, the contrast C and entropy S are defined as:

[0127]

[0128]

[0129] Where (m,n) represents the position of the pixel in the azimuth and range directions, R(m,n) represents the pixel value, and R max Let J(m,n) represent the maximum amplitude of a pixel within the image, J(m,n) represent the normalized amplitude of the pixel, σ(·) represent the standard deviation, and E(·) represent the mean. ρ(m,n) and P represent the proportion of each pixel's power in the total image power and the total pixel power, respectively.

[0130] Table 1 GEO SAR System Parameters

[0131] Parameter [Unit] value Parameter [Unit] value Ground speed [m / s] 300 Carrier frequency [GHz] 1.25 Azimuth bandwidth [Hz] 60 Integration time [s] 175 Pulse repetition frequency [Hz] 100 Distance bandwidth [MHz] 80 Range sampling frequency [MHz] 100 Pulse width [μs] 1

[0132] Table 2. Metrics for measuring image focusing performance

[0133] image Contrast entropy Original image 1652.36 5.66 Contaminated images 1529.53 6.25 Iterative method 1639.37 5.77 Known parameters 1635.87 5.81 Unknown parameters 1637.52 5.81 Using inversion initial value iteration 1639.33 5.77

[0134] Then, we iteratively changed the number and size of the blocks during the compensation process to find suitable values, stopping the loop when the contrast (entropy) was at its maximum (minimum). After 22 iterations, the optimal block size was selected as 30×500 (number and size). The result after compensation is as follows. Figure 4 As shown in (a), Table 2 lists the metrics for evaluating image focusing performance. To verify the accuracy of the model, assuming we know the parameters affecting the disturbed troposphere, we selected a block size of 47×550 based on the model, and similarly obtained the compensated image and metrics as shown in (a). Figure 4 (b) and Table 2. Because the feature mapping parameters A and b in the Extreme Learning Machine are random, the optimal solution differs each time. Therefore, based on the model, we can quickly obtain 10 sets of solutions, select the three sets with the best fitting effect, and input them into the compensation process. Finally, we select the set with the best performance as the optimal solution. However, in many cases, the parameters affecting the disturbed troposphere are unknown. According to the above analysis, we can first invert the coarse values ​​of l and v, and then input them into the model to find the optimal block selection when the index is optimal. The inverted values ​​of l and v are 33181 and 0.8333, respectively, which are close to the true values. After inputting them into the model, the optimal block selection is 40×650. The compensated image and index are shown below. Figure 4 (c) and Table 2.

[0135] contrast Figure 3 and Figure 4 It can be seen that the image is severely defocused due to the influence of the disturbed troposphere. After block selection optimization compensation, the image focusing performance is improved. Table 2 shows that the proposed optimization algorithm, after compensation, performs basically the same as the iterative method, and can quickly obtain a locally optimal solution for block selection without iteration. When the parameters are unknown, some areas of the compensated image are still defocused, such as... Figure 4 The region marked in (c) can be used as the initial value for iteration to improve image quality. After 6 iterations, the image quality is further improved, and the calculation speed is faster than that of full iteration. The compensated image and indicators are shown in [link to image]. Figure 4 (d) and Table 2. Since the MD algorithm can only compensate for second-order phase errors, it cannot compensate for the rapidly changing components in the perturbed troposphere, resulting in differences from the original image, such as... Figure 5 As shown.

[0136] It can be seen Figure 5 In (a), the phase can be basically fitted, while Figure 5 In (b), the drastically changing parts show poor fitting results, and the range integral amplifies the error, resulting in slightly worse focusing performance in the compensated image compared to the original. To further improve image quality, we can optimize the range block selection and perform two complete compensations. The compensated images and metrics are shown in [link to image description]. Figure 6 And Table 2.

[0137] The optimized distance-oriented block size is 29×300. Figure 6 It can be seen that Figure 5 Based on the first residual phase in (b), a second estimation was performed, and the image quality was slightly improved again.

[0138] Anomaly detection and correction have been performed in the compensation process described above. To verify the necessity of this step, the results of ignoring this step are given below. The block size is selected as 40×650.

[0139] Figure 7 There was obvious defocusing and Figure 4 In comparison (c) (the marked area in the figure), the calculated contrast and entropy are 1609.54 and 5.96, respectively. This demonstrates the importance of correcting outliers. It is important to note that the LOF algorithm requires the input data to be at least two-dimensional; in addition to the frequency tuning, the other dimension needs to be supplemented with a sequence of the same length.

[0140] It should be understood that, although Figure 1 The steps in the flowchart are shown sequentially as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified in this document, there is no strict order in which these steps are executed, and they can be performed in other orders. Figure 1 At least some of the steps in the process may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily executed at the same time, but may be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but may be executed in turn or alternately with other steps or at least some of the sub-steps or stages of other steps.

[0141] In one embodiment, such as Figure 8 As shown, a GEO SAR imaging disturbance tropospheric error compensation device is provided, comprising: an azimuth decompression data determination module, a sub-band division module, a block parameter optimization module, a sub-block division module, an azimuth phase estimation value determination module, and an image error compensation module, wherein:

[0142] The azimuth decompression data determination module is used to perform azimuth Fourier transform, azimuth decompression, and inverse azimuth Fourier transform on the obtained GEO SAR image to obtain azimuth decompressed data.

[0143] The sub-band division module is used to divide the acquired GEO SAR image into several sub-bands along the range direction.

[0144] The block parameter optimization module is used to construct a block optimization model based on the tropospheric parameters and entropy that affect the disturbance. The block optimization model is solved by the extreme learning machine method to obtain the optimal number of blocks and the optimal block size when the entropy is minimized. The block optimization model is shown in Equation (1).

[0145] The sub-block partitioning module is used to divide the sub-band into several sub-blocks along the azimuth direction according to the optimal number of blocks and the optimal block size.

[0146] The azimuth phase estimation module is used to process each sub-block in each sub-band using the MD algorithm to obtain the frequency modulation error; the frequency modulation error is then processed by azimuth interpolation and integration to obtain the azimuth phase estimation value of the disturbed troposphere.

[0147] The image error compensation module is used to interpolate the azimuth phase estimate of the disturbed troposphere in the range direction, and then multiply the interpolation result with the azimuth decompressed data before performing azimuth Fourier transform, refocusing, and inverse Fourier transform to obtain a high-precision GEO SAR image.

[0148] In one embodiment, the block parameter optimization module further includes an outlier detection and correction module, which uses a local outlier factor algorithm to detect outliers in the frequency modulation of each sub-block; and replaces the value at the outlier with the interpolation of the normal point in the nearby sub-block.

[0149] In one embodiment, the anomaly detection and correction module is also used to calculate a local reachability density for each frequency modulation data point; the expression for the local reachability density is shown in equation (2).

[0150] Based on the local reachability density, the local outlier factor is calculated using the formula for calculating the local outlier factor, and an outlier factor is obtained for each frequency modulation data point; the formula for calculating the local outlier factor is shown in Equation (3).

[0151] Based on the outlier factor and a preset threshold, points with a high degree of outlier are identified as outliers in the frequency modulation of each sub-block.

[0152] In one embodiment, the block parameter optimization module is also used to construct the loss function of the block optimization model, as shown in equation (4).

[0153] The loss function is solved by ridge regression, and the estimated value of the output weight is shown in equation (5).

[0154] Based on the preset training data, the estimated values ​​of the output weights, and the block optimization model, the coarse values ​​of the exponential factor and the scale factor are retrieved.

[0155] Substitute the estimated values ​​of the output weights, the coarse values ​​of the exponential factor and the scale factor into the block optimization model to solve for the optimal number of blocks and the optimal block size when the entropy is minimized.

[0156] In one embodiment, the block parameter optimization module is further configured to solve for the coarse values ​​of the exponential factor and the scale factor using a parameter inversion formula based on preset training data, estimated values ​​of output weights, and the block optimization model; the parameter inversion formula is shown in equation (6).

[0157] Specific limitations regarding the GEO SAR imaging disturbance tropospheric error compensation device can be found in the limitations of the GEO SAR imaging disturbance tropospheric error compensation method described above, and will not be repeated here. Each module in the aforementioned GEO SAR imaging disturbance tropospheric error compensation device can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in hardware or independently of the processor in a computer device, or stored in software in the memory of a computer device, so that the processor can call and execute the corresponding operations of each module.

[0158] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above 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.

[0159] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

Claims

1. A method for compensating for tropospheric errors in GEO SAR imaging disturbances, characterized in that, The method includes: After performing azimuth Fourier transform, azimuth decompression, and inverse azimuth Fourier transform on the obtained GEO SAR image, azimuth decompressed data is obtained. The obtained GEO SAR image is divided into several sub-bands along the range direction; Based on the tropospheric parameters and entropy affecting the disturbance, a block optimization model is constructed, which is as follows: Where X is the input of the block optimization model, X=(D,s,l,v,n,c), v is the exponential factor, l is the scale factor, D is the coordinate dimension, s is the standard deviation, n is the number of blocks, c is the block size, H is the intermediate parameter, Y is the entropy, W is the output weight, B is the bias term, g(·) is the nonlinear mapping, and f(·) is the linear mapping; The block optimization model is solved using the extreme learning machine method to obtain the optimal number of blocks and the optimal block size when the entropy is minimized. The sub-band is divided into several sub-blocks along the azimuth direction according to the optimal number of blocks and the optimal block size; The MD algorithm is used to process each sub-block in each sub-band to obtain the frequency modulation error; The frequency modulation error is subjected to azimuth interpolation and integration to obtain the estimated azimuth phase value of the disturbed troposphere. The estimated azimuth phase of the disturbed troposphere is interpolated in the range direction, and the interpolation result is multiplied with the decompressed azimuth data. Then, the azimuth Fourier transform, refocusing, and inverse Fourier transform are performed to obtain a high-precision GEOSAR image.

2. The method of claim 1, wherein, The MD algorithm is applied to each sub-block within each sub-band to obtain the frequency modulation error. Following this step, an anomaly detection and correction step is included, which comprises: The local outlier factor algorithm is used to detect outliers in the frequency modulation of each sub-block; The value at the outlier point is replaced by the interpolation of the normal point in the nearby sub-block.

3. The method according to claim 2, characterized in that, The local outlier factor algorithm is used to detect outliers in the frequency modulation of each sub-block, including: Calculate a local reachability density for each frequency modulation (FM) data point; the expression for the local reachability density is: where N k (p) denotes the kth distance neighborhood of point p, o is the set of points within the kth distance of p, |N k (p) | denotes the number of points in the set; is the kth reach distance of data point o to data point p, LRD k (·) is the local reach density; Based on the local reachability density, the local outlier factor is calculated using the formula for calculating the local outlier factor, resulting in an outlier factor for each frequency modulation (FM) data point. The formula for calculating the local outlier factor is as follows: where LOF k (·) is the local outlier factor; Based on the outlier factor and the preset threshold, points with a high degree of outlier are identified as outliers in the frequency modulation of each sub-block.

4. The method of claim 1, wherein, The block optimization model is solved using the Extreme Learning Machine method to obtain the optimal number of blocks and the optimal block size when the entropy is minimized, including: The loss function for constructing the block optimization model is as follows: Where C is the regularization coefficient, H is the intermediate layer output, T is the true value, and W is the output weight; The loss function is solved using a ridge regression approach, yielding an estimated value for the output weights: where W * is an estimate of the output weight; Based on the preset training data, the estimated values ​​of the output weights, and the block optimization model, the coarse values ​​of the exponential factor and the scale factor are retrieved. Substitute the estimated values ​​of the output weights, the coarse values ​​of the exponential factor and the scale factor into the block optimization model to solve for the optimal number of blocks and the optimal block size when the entropy is minimized.

5. The method of claim 4, wherein, Based on the preset training data, the estimated values ​​of the output weights, and the block optimization model, the coarse values ​​of the exponential factor and the scaling factor are retrieved, including: Based on the preset training data, the estimated output weights, and the block optimization model, the parameter inversion formula is used to solve for the rough values ​​of the exponential factor and the scale factor; the parameter inversion formula is: where |·| denotes the absolute value, (l min ,l max ) and (v min ,v max ) are the value intervals of l and v, respectively, are the coarse values of l and v, respectively.

6. A device for compensating for tropospheric errors in GEO SAR imaging disturbances, characterized in that, The device includes: The azimuth decompression data determination module is used to process the obtained GEO SAR image by performing azimuth Fourier transform, azimuth decompression, and inverse azimuth Fourier transform to obtain azimuth decompressed data. The sub-band division module is used to divide the acquired GEO SAR image into several sub-bands along the range direction; The block parameter optimization module is used to construct a block optimization model based on the influencing tropospheric parameters and entropy. The block optimization model is solved using the extreme learning machine method to obtain the optimal number of blocks and the optimal block size when the entropy is minimized. The block optimization model is as follows: Where X is the input of the block optimization model, X=(D,s,l,v,n,c), v is the exponential factor, l is the scale factor, D is the coordinate dimension, s is the standard deviation, n is the number of blocks, c is the block size, H is the intermediate parameter, Y is the entropy, W is the output weight, B is the bias term, g(·) is the nonlinear mapping, and f(·) is the linear mapping; The sub-block partitioning module is used to divide the sub-band into several sub-blocks along the azimuth direction according to the optimal number of blocks and the optimal block size; The azimuth phase estimation value determination module is used to process each sub-block in each sub-band using the MD algorithm to obtain the frequency modulation error; and to perform azimuth interpolation and integration processing on the frequency modulation error to obtain the disturbance tropospheric azimuth phase estimation value. The image error compensation module is used to interpolate the estimated azimuth phase value of the disturbed troposphere in the range direction, and multiply the interpolation result with the azimuth decompressed data before performing azimuth Fourier transform, refocusing, and inverse Fourier transform to obtain a high-precision GEO SAR image.

7. The apparatus of claim 6, wherein, The block parameter optimization module also includes an anomaly detection and correction module; The outlier detection and correction module is used to detect outliers in the frequency modulation of each sub-block using a local outlier factor algorithm; and to replace the value at the outlier with the interpolation value of the normal point in the nearby sub-block.

8. The apparatus of claim 7, wherein, The anomaly detection and correction module is also used to calculate a local reachability density for each frequency modulation data point; the expression for the local reachability density is: Where, N k (p) represents the k-th distance neighborhood of point p, o is the set of points within the k-th distance of p, |N k (p)| represents the number of points in the set; Let LRD be the k-th reachable distance from data point o to data point p. k (·) represents the locally reachable density; Based on the local reachability density, the local outlier factor is calculated using the formula for calculating the local outlier factor, resulting in an outlier factor for each frequency modulation (FM) data point. The formula for calculating the local outlier factor is as follows: where LOF k (·) is the local outlier factor; Based on the outlier factor and the preset threshold, points with a high degree of outlier are identified as outliers in the frequency modulation of each sub-block.

9. The apparatus of claim 6, wherein, The block parameter optimization module is also used to construct the loss function of the block optimization model, wherein the loss function is: Where C is the regularization coefficient, H is the intermediate layer output, T is the true value, and W is the output weight; The loss function is solved using a ridge regression approach, yielding an estimated value for the output weights: where W * is an estimate of the output weight; Based on the preset training data, the estimated values ​​of the output weights, and the block optimization model, the coarse values ​​of the exponential factor and the scale factor are retrieved. Substitute the estimated values ​​of the output weights, the coarse values ​​of the exponential factor and the scale factor into the block optimization model to solve for the optimal number of blocks and the optimal block size when the entropy is minimized.

10. The apparatus of claim 9, wherein, The block parameter optimization module is further used to solve for the coarse values ​​of the exponential factor and the scale factor using a parameter inversion formula based on preset training data, estimated values ​​of output weights, and the block optimization model; the parameter inversion formula is: where |·| denotes the absolute value, (l min ,l max ) and (v min ,v max ) are the value intervals of l and v, respectively, are the coarse values of l and v, respectively.

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