An adaptive sparse forward-looking super-resolution imaging method based on echo repair strategy

Abstract

The application discloses a kind of based on echo repair strategy's adaptive sparse foresight super-resolution imaging method, first, scanning radar super-resolution model is established, then based on regularization theory, use L1 norm as constraint term to improve the angular resolution of sparse target, then the signal and noise in echo are separated using the multiscale representation characteristics of wavelet variation, the problem that the performance of existing L1-IRN method is poor under low signal-to-noise ratio is solved while improving echo signal-to-noise ratio, and based on preprocessed echo, new optimization cost function is constructed, finally, based on bayesian theory, the sparse estimation problem is converted into maximum posterior estimation problem, adaptive iteration weight is obtained, and foresight super-resolution imaging is realized.The echo repair strategy of the method of the application can weaken the influence of noise on super-resolution imaging, realize adaptive sparse foresight super-resolution imaging under the condition of very low signal-to-noise ratio, obtain high-quality imaging results, improve the efficiency of foresight two-dimensional super-resolution imaging algorithm, and has strong robustness.

Description

Technical Field

[0001] This invention belongs to the field of radar imaging technology, specifically relating to an adaptive sparse forward-looking super-resolution imaging method based on an echo repair strategy. Background Technology

[0002] Scanning radar has been widely used in forward-looking imaging due to its all-view, all-time, all-weather, and rapid revisit capabilities. Existing high-resolution technologies such as Synthetic Aperture Radar (SAR) and Inverse Synthetic Aperture Radar (ISAR) rely on the motion of the platform or target to form a larger synthetic aperture, thereby obtaining higher azimuth resolution. However, during the imaging process of SAR and ISAR, due to the small change in Doppler frequency, the azimuth resolution is significantly reduced in ultra-high-resolution forward-looking imaging radar, making it difficult to meet the requirements of practical applications.

[0003] In recent years, some new methods have been proposed for super-resolution imaging of scanning radar. The paper "Zhang, Yongchao, et al. Wideband sparse reconstruction for scanning radar. IEEE Transactions on Geoscience and Remote Sensing 56.10(2018): 6055-6068" achieves low-complexity sparse imaging based on a constructed wideband dictionary framework and a generalized sparse covariance estimation algorithm. However, this method is difficult to achieve good azimuth super-resolution performance under low signal-to-noise ratio. The paper "Wu, Yang, et al. Sparse super-resolution method based on truncated singular value decomposition strategy for radar forward-looking imaging." Journal of Applied Remote Sensing 12.3 (2018): 035021-035021 improves the ill-conditioned characteristics of the deconvolution model and achieves super-resolution imaging of scanning radar under low signal-to-noise ratio conditions by introducing a singular value thresholding method for preprocessing. However, the imaging effect of this method is poor when the signal-to-noise ratio of the post-pulse compression echo is less than 5dB. The paper "Zhang, Qiping, et al. A sparse denoising-based super-resolution method for scanning radar imaging." Remote Sensing 13.14 (2021): 2768 achieves azimuth super-resolution imaging under a signal-to-noise ratio of 5dB by incorporating the denoising process into the L1-constrained azimuth super-resolution processing optimization function. However, the above methods have several hyperparameters that are sensitive to noise, making them difficult to apply in real-world scenarios. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention provides an adaptive sparse forward-looking super-resolution imaging method based on an echo restoration strategy, which solves the imaging blurring problem of existing azimuth-elevation super-resolution methods at low signal-to-noise ratios.

[0005] The technical solution adopted in this invention is: an adaptive sparse forward-looking super-resolution imaging method based on an echo restoration strategy, the specific steps of which are as follows:

[0006] Step 1: Establish a super-resolution model for scanning radar;

[0007] The real-aperture antenna continuously transmits a wide-bandwidth frequency-modulated pulse signal at a pulse repetition frequency (PRF) set according to the actual situation, while cyclically scanning the beam in the target detection area to acquire a 2D image. During the scanning process, each pulse data is stored in each column of the echo matrix. After completing one scan, a complete echo matrix is ​​formed. After polar coordinate interpolation and projection, a complete 2D image of the scanning radar can be obtained. Let the range variable be R and the azimuth variable be θ.

[0008] Super-resolution imaging is achieved in the range direction through pulse compression. Considering azimuth processing, for a fixed range cell, the azimuth echo model is represented as the convolution of target scattering and antenna pattern. Additive white Gaussian noise is also considered. The discrete expression for the azimuth echo model is as follows:

[0009] y m =As m +e m (1)

[0010] in, Represents the set of complex numbers. Let N represent the echo vector of the m-th distance cell, and N represent the number of echo azimuth sampling points. T This indicates the transpose operation. This represents the target backscattering coefficient, and K represents the number of azimuth sampling points for the target backscattering coefficient. The guidance matrix is ​​represented by the following expression:

[0011]

[0012] Among them, h l Represents antenna vector The l-th element in the matrix, l = 0, ..., L-1, where L represents the number of sampling points for the antenna pattern, and A is a K-column circular matrix, where each column is generated by shifting h.

[0013] Step 2: Based on Step 1, construct a regularization framework based on L1 norm constraints;

[0014] Using the L1 norm as a sparsity constraint, the cost function J is constructed as follows:

[0015]

[0016] Where ||·||2 represents the L2 norm of the vector, ||·||1 represents the L1 norm of the vector, and λ represents the penalty parameter.

[0017] Define the weighted matrix W = diag(|s|) -1 The weighting matrix can be updated using the scattering result s from the previous iteration. The iterative expression of equation (3) obtained by the IRN method is as follows:

[0018] s (q+1) =(A T A+λW (q) ) -1 A T y m (4)

[0019] Where diag(·) represents the diagonal matrix transformed from the vector, q represents the number of iterations, and W (q) It can be accessed via s (q) get.

[0020] Step 3: Based on Step 2, perform wavelet decomposition on the echo signal, i.e., perform echo restoration processing;

[0021] First, echo restoration is performed. Equation (1) is rewritten as an echo restoration model, as shown in the following expression:

[0022] y m =f m +e m (5)

[0023] Among them, f m This represents an echo signal without noise interference, set e. m The standard N(0,σ) satisfies the independent and identically distributed (IID) 2 ), σ 2 This represents the noise variance.

[0024] The goal of equation (5) is to estimate the vector f. m =As m By minimizing the mean square error, that is, with a small risk Find an estimate Depends on [y1,y2,…,y N ].

[0025] in, Represents the risk function, This represents the echo vector after repair.

[0026] Define an orthogonal discrete wavelet transform matrix. Its wavelet decomposition level is P, and the radar echo signal is complex. The echo y is then analyzed. m The real and imaginary parts are decomposed using wavelet decomposition, as shown in the following expression:

[0027]

[0028] in, and The wavelet coefficient vector represents the real and imaginary parts of the echo, Re(·) and Im(·) represent the operations of taking the real and imaginary parts, respectively, and Q represents the number of sampling points of the echo in the wavelet domain.

[0029] Step 4: Perform wavelet thresholding on the echo signal after wavelet decomposition in Step 3, and adaptively select an appropriate threshold by estimating the noise level.

[0030] The soft threshold rule is set to be used, as shown in the following expression:

[0031]

[0032] Where, η T (w) represents the soft thresholding function, where w is the independent variable, T is the threshold, and the threshold is only related to the input signal length Q and the noise level σ, and satisfies the following conditions: Estimation of noise level σ The expression is as follows:

[0033]

[0034] Where Median(·) represents the median absolute deviation. and

[0035] Step 5: Reconstruct the echo based on the wavelet thresholding process in Step 4;

[0036] Transformation They are orthogonal, and the inverse transformation matrix can be represented as: The echo signal reconstruction expression is as follows:

[0037]

[0038] Where i represents the imaginary unit.

[0039] Step 6: Based on the echo reconstructed in Step 5, construct the L1 norm-constrained cost function and transform the sparse estimation problem into a maximum a posteriori estimation problem based on Bayesian theory.

[0040] Based on the repaired echo vector Define a new sparse constraint optimization problem The expression is as follows:

[0041]

[0042] Here, the penalty parameter λ is a constant used to balance the L1 norm sparsity regularization term ||s m ||1. By setting different penalty parameters at different angles, equation (10) can be rewritten as follows:

[0043]

[0044] Among them, s m,i Represents vector s m The i-th element, λ i This represents the penalty parameter in direction i.

[0045] By transforming problem (10) into a maximum a posteriori estimation problem (MAP), within the Bayesian framework, a s m and The maximum a posteriori estimate is expressed as follows:

[0046]

[0047] Where P(·) represents the probability function. The further simplified expression of equation (12) is as follows:

[0048]

[0049] Additive Gaussian noise is still present in the restored echo. And it meets the criteria for independent and identically distributed IID. The expression can then be obtained as follows:

[0050]

[0051] in, P(s) represents the standard deviation of the residual noise after echo restoration. m () is a zero-mean Laplace probability model that satisfies IID, and its specific expression is as follows:

[0052]

[0053] Where, δ i s m,i The standard deviation of . According to the principle of logarithmic operations, equation (13) can be further rewritten as follows:

[0054]

[0055] Will and P(s) m Substituting expressions (14) and (15) into (16) yields the following expression:

[0056]

[0057] Equation (17) can be simplified to the following expression:

[0058]

[0059] Among them, the third term in equation (18) and the fourth item With s m Irrelevant and can be ignored. Multiply the right side of equation (18) by a constant. The expression can then be obtained as follows:

[0060]

[0061] Step 7: Based on Step 6, derive the adaptive iterative weights of the IRN;

[0062] Comparing equations (10) and (19), setting the coefficients of corresponding terms to be equal yields the penalty parameter. Considering numerical stability, the penalty parameter expression is as follows:

[0063]

[0064] in, This represents the noise power estimate during the super-resolution imaging stage, and Let q represent the target scattering estimate in the q-th iteration. s m,i The standard deviation can be estimated by calculation. Each element s in m,i The standard deviation is used for estimation. ε represents a small constant set according to the actual situation.

[0065] Step 8: Based on Step 7, perform adaptive iterative super-resolution imaging processing to achieve forward-looking super-resolution imaging;

[0066] The adaptive iterative estimation expression for target scattering is as follows:

[0067]

[0068] in,[] H This represents the conjugate transpose operation, with the penalty parameter vector λ. (q) =[λ1,λ2,…,λ K It can be calculated using equation (20). During the iteration process, Initialize to I represents a K-dimensional identity matrix, and α represents the noise level after echo restoration, which can be calculated by equation (8).

[0069] The beneficial effects of this invention are as follows: First, a scanning radar super-resolution model is established. Then, based on regularization theory, the L1 norm is used as a constraint term to improve the angular resolution of sparse targets. Next, the multi-scale representation characteristics of wavelet transform are used to separate the signal and noise in the echo, i.e., noise reduction preprocessing is performed on the echo. This improves the echo signal-to-noise ratio while addressing the poor performance of existing L1-IRN methods at low signal-to-noise ratios. Based on the preprocessed echo, a new optimization cost function is constructed. Finally, based on Bayesian theory, the sparse estimation problem is transformed into a maximum a posteriori estimation problem to obtain adaptive iterative weights, achieving forward-looking super-resolution imaging. The echo restoration strategy of this invention can reduce the impact of noise on super-resolution imaging, achieving adaptive sparse forward-looking super-resolution imaging under extremely low signal-to-noise ratio conditions, obtaining high-quality imaging results, while improving the efficiency of the forward-looking two-dimensional super-resolution imaging algorithm, exhibiting strong robustness. Attached Figure Description

[0070] Figure 1 This is a flowchart of an adaptive sparse forward-looking super-resolution imaging method based on an echo restoration strategy according to the present invention.

[0071] Figure 2 This is a geometric model diagram of forward-looking super-resolution imaging in an embodiment of the present invention.

[0072] Figure 3 This is a comparison chart of the original scene, echo, and point target imaging results of the existing L1 method and the method of the present invention at a signal-to-noise ratio of 0dB in an embodiment of the present invention.

[0073] Figure 4 This is a comparison diagram of the original scene, echo, and surface target imaging results of the existing L1 method and the method of the present invention at a signal-to-noise ratio of 5dB in an embodiment of the present invention.

[0074] Figure 5 This is a comparison chart of the measured original scene, echo, existing L1 method, and the measured results of the method of the present invention on a motion platform in the embodiments of the present invention. Detailed Implementation

[0075] All steps and conclusions of this invention have been verified to be correct on the Matlab 2019b simulation platform. To enable those skilled in the art to understand the invention, the method of this invention will be further described below with reference to the accompanying drawings and embodiments.

[0076] like Figure 1 The flowchart of the adaptive sparse forward-looking super-resolution imaging method based on an echo restoration strategy of the present invention is shown below. The specific steps are as follows:

[0077] Step 1: Establish a super-resolution model for scanning radar;

[0078] In this embodiment, the forward-looking super-resolution imaging geometric model is as follows: Figure 2 As shown in the figure, the working principle of a forward-looking scanning radar is as follows: a solid aperture antenna continuously transmits a wide-bandwidth frequency-modulated pulse signal at a pulse repetition frequency (PRF) of 2kHz, while simultaneously cyclically scanning the beam in the target detection area to acquire a 2D image. During the scanning process, each pulse data is stored in each column of the echo matrix. After one scan is completed, a complete echo matrix is ​​formed (e.g., ...). Figure 2 (As shown in the lower left). After polar coordinate interpolation and projection, a complete 2D image of the scanning radar can be obtained. Let the range variable be R and the azimuth variable be θ.

[0079] In range-direction super-resolution imaging achieved through pulse compression, considering azimuth processing, for a fixed range cell, the azimuth echo model is represented as the convolution of target scattering and antenna pattern (e.g., ...). Figure 2 (As shown on the right). Consider additive white Gaussian noise. The discrete expression for the azimuth echo model is as follows:

[0080] y m =As m +e m (1)

[0081] in, Represents the set of complex numbers. Let N represent the echo vector of the m-th distance cell, and N = 256 represent the number of echo azimuth sampling points. T This indicates the transpose operation. K represents the target backscattering coefficient, and K = 256 represents the number of azimuth sampling points for the target backscattering coefficient. The steering matrix is ​​mathematically a Topplitz matrix constructed by cyclically shifting the azimuth antenna pattern function, and its specific expression is as follows:

[0082]

[0083] Among them, h l Represents antenna vector The l-th element in the matrix, l = 0, ..., L-1, where L represents the number of sampling points for the antenna pattern, and A is a K-column circular matrix, where each column is generated by shifting h.

[0084] Step 2: Based on Step 1, construct a regularization framework based on L1 norm constraints;

[0085] Based on the linear model of Equation (1), reconstructing the target using the least squares method is the simplest approach. However, due to the low-pass filtering characteristics (illness) of the antenna pattern matrix A, high-frequency noise is severely amplified. Therefore, various regularization methods can be introduced to mitigate this illness. Considering that the target scene observed by scanning radar is typically sparsely distributed, the L1 norm is used as a sparsity constraint to construct the cost function J, expressed as follows:

[0086]

[0087] Where ||·||2 represents the L2 norm of the vector, ||·||1 represents the L1 norm of the vector, and λ represents the penalty parameter.

[0088] Due to the non-differentiability of the L1 norm, the original L1 norm problem is approximated by solving a series of weighted L2-constrained optimization problems through iterative reweighting (IRN). The weighting matrix is ​​defined as W = diag(|s|). -1 The weighting matrix can be updated using the scattering result s from the previous iteration. The iterative expression for equation (3) obtained by the IRN method is as follows:

[0089] s (q+1) =(A T A+λW (q) ) -1 A T y m (4)

[0090] Where diag(·) represents the diagonal matrix transformed from the vector, q represents the number of iterations, and W (q) It can be accessed via s (q) get.

[0091] Step 3: Based on Step 2, perform wavelet decomposition on the echo signal, i.e., perform echo restoration processing;

[0092] Under conditions of high noise variance, existing angular super-resolution methods cannot effectively image data. Therefore, echo restoration processing is required first. Equation (1) is rewritten as an echo restoration model, as shown below:

[0093] y m =f m +e m (5)

[0094] Among them, f m This represents an echo signal without noise interference, set e. m The standard N(0,σ) satisfies the independent and identically distributed (IID) 2 ), σ 2 This represents the noise variance.

[0095] The goal of equation (5) is to estimate the vector f. m =As m By minimizing the mean square error, that is, with a small risk Find an estimate Depends on [y1,y2,…,y N ].

[0096] in, Represents the risk function, This represents the echo vector after repair.

[0097] Define an orthogonal discrete wavelet transform matrix. Its wavelet decomposition level is P, and the radar echo signal is complex. The echo y is then analyzed. m The real and imaginary parts are decomposed using wavelet decomposition, as shown in the following expression:

[0098]

[0099] in, and The wavelet coefficient vector represents the real and imaginary parts of the echo, Re(·) and Im(·) represent the operations of taking the real and imaginary parts, respectively, and Q represents the number of sampling points of the echo in the wavelet domain.

[0100] Step 4: Perform wavelet thresholding on the echo signal after wavelet decomposition in Step 3, and adaptively select an appropriate threshold by estimating the noise level.

[0101] The wavelet thresholding process removes noise by thresholding only the wavelet coefficients of the high-frequency components, while keeping the low-frequency coefficients unchanged.

[0102] The soft threshold rule is set to be used, as shown in the following expression:

[0103]

[0104] Where, η T (w) represents the soft thresholding function, where w is the independent variable, T is the threshold, and the threshold is only related to the input signal length Q and the noise level σ, and satisfies the following conditions: Estimation of noise level σ The expression is as follows:

[0105]

[0106] Where Median(·) represents the median absolute deviation, and 0.6745 is an empirical constant. The real and complex wavelet coefficients after thresholding are respectively... and

[0107] Step 5: Reconstruct the echo based on the wavelet thresholding process in Step 4;

[0108] Due to the transformation They are orthogonal, and the inverse transformation matrix can be simply represented as: The echo signal reconstruction expression is as follows:

[0109]

[0110] Where i represents the imaginary unit.

[0111] Through steps three through five, y m Strong noise in the signal is largely removed, and the echo signal-to-noise ratio is improved.

[0112] Step 6: Based on the echo reconstructed in Step 5, construct the L1 norm-constrained cost function and transform the sparse estimation problem into a maximum a posteriori estimation problem based on Bayesian theory.

[0113] Based on the repaired echo vector Define a new sparse constraint optimization problem The expression is as follows:

[0114]

[0115] Here, the penalty parameter λ is a constant used to balance the L1 norm sparsity regularization term ||s m ||1. By setting different penalty parameters at different angles, equation (10) can be rewritten as follows:

[0116]

[0117] Among them, s m,i Represents vector s m The i-th element, λ i This represents the penalty parameter in direction i.

[0118] By transforming problem (10) into a maximum a posteriori estimation problem (MAP), within the Bayesian framework, a s m and The maximum a posteriori estimate is expressed as follows:

[0119]

[0120] Where P(·) represents the probability function. The further simplified expression of equation (12) is as follows:

[0121]

[0122] Additive Gaussian noise is still present in the restored echo. And it meets the criteria for independent and identically distributed IID. The expression can then be obtained as follows:

[0123]

[0124] in, P(s) represents the standard deviation of the residual noise after echo restoration. m () is a zero-mean Laplace probability model that satisfies IID, and its specific expression is as follows:

[0125]

[0126] Where, δ i s m,i The standard deviation of . According to the principle of logarithmic operations, equation (13) can be further rewritten as follows:

[0127]

[0128] Will and P(s) m Substituting expressions (14) and (15) into (16) yields the following expression:

[0129]

[0130] Equation (17) can be simplified to the following expression:

[0131]

[0132] Among them, the third term in equation (18) and the fourth item With s m It is irrelevant and therefore can be ignored. Because If is a constant, then multiply the right side of equation (18) by the constant. It will not affect s m The estimation yields the following expression:

[0133]

[0134] Step 7: Based on Step 6, derive the adaptive iterative weights of the IRN;

[0135] Comparing equations (10) and (19), setting the coefficients of corresponding terms to be equal yields the penalty parameter. Considering numerical stability, the penalty parameter expression is as follows:

[0136]

[0137] in, This represents the noise power estimate during the super-resolution imaging stage, and Let q represent the target scattering estimate in the q-th iteration. s m,i The standard deviation can be estimated by calculation. Each element s in m,i The standard deviation is used for estimation. ε represents a small constant set according to the actual situation.

[0138] Step 8: Based on Step 7, perform adaptive iterative super-resolution imaging processing to achieve forward-looking super-resolution imaging;

[0139] The adaptive iterative estimation expression for target scattering is as follows:

[0140]

[0141] in,[] H This represents the conjugate transpose operation, with the penalty parameter vector λ. (q) =[λ1,λ2,…,λ K It can be calculated using equation (20). During the iteration process, Initialize to I represents a K-dimensional identity matrix, and α represents the noise level after echo restoration, which can be calculated by equation (8).

[0142] This embodiment also further conducted simulation verification, including: scanning radar point target simulation, scanning radar surface target simulation, and scanning radar actual measurement.

[0143] like Figure 3 As shown, a radar point target simulation is performed, and the radar system parameters are set according to Table 1.

[0144] Table 1

[0145] parameter numerical values carrier frequency 10.5GHz Transmit signal bandwidth 20MHz Scan range -10°～10° Scan speed 90° / s Azimuth beamwidth 2° Pulse repetition frequency 2kHz

[0146] The simulation results of the point target show that Figure 3 (a) is the original scene of the point target with a signal-to-noise ratio of 0dB. Figure 3 (b) shows the echo at a signal-to-noise ratio (SNR) of 0 dB. It can be seen that the echo is significantly blurred when the SNR is very low. Figure 3 (c) shows the imaging results of the existing L1 method. At a signal-to-noise ratio (SNR) of 0 dB, it can be seen that the existing model has many false targets and cannot display the target results at all. Figure 3 (d) shows the imaging results of the method of the present invention. It can be seen that when the signal-to-noise ratio (SNR) is 0 dB, the target can be reconstructed with good effect under the condition of better suppression of sidelobes.

[0147] like Figure 4As shown, a radar surface target simulation is performed, and the radar system parameters are set according to Table 2.

[0148] Table 2

[0149] parameter numerical values carrier frequency 10.5GHz Transmit signal bandwidth 20MHz Transmit signal duration 2us Scan range -10°～10° Scan speed 90° / s Azimuth beamwidth 3° Pulse repetition frequency 2kHz effective range 3000m Platform speed 30m / s

[0150] The simulation results of the surface target show that Figure 4 (a) is the original scene of the target at a signal-to-noise ratio of 5dB. Figure 4 (b) The echo at a signal-to-noise ratio (SNR) of 5 dB is blurred to varying degrees due to the wide antenna beam. Figure 4 (c) shows the imaging results of the existing L1 method. At a signal-to-noise ratio (SNR) of 5dB, the ship targets are effectively separated due to the large distance between the ships. However, the improvement in their azimuth resolution is limited, and there is obvious background noise. Figure 4 (d) shows the imaging results of the method of the present invention. It can be seen that when the signal-to-noise ratio (SNR) is 5 dB, the method of the present invention not only improves the azimuth resolution but also effectively suppresses background noise. In addition, the method of the present invention reconstructs the amplitude of ship targets uniformly, resulting in the best visual effect of the image.

[0151] like Figure 5 As shown, perform actual scanning radar measurements and set the radar system parameters according to Table 3.

[0152] Table 3

[0153] parameter numerical values carrier frequency X-band Scan range -30°～30° Scan speed 72° / s Azimuth beamwidth 5.1° Pulse repetition frequency 200Hz Platform speed 47m / s Platform Height 300m Pitch angle 30°

[0154] The actual measurement results show that Figure 5 (a) is the original scene as measured. Figure 5 (b) shows the measured echo, where the real beam image resolution is very low and the river between the islands and the lake shore appears unclear. Figure 5 (c) shows the imaging results of the existing L1 method, which can be seen to improve the azimuth resolution to some extent. However, due to the low echo signal-to-noise ratio, their imaging results are affected by noise. The boundaries between islands and lake water are unclear, and there are a large number of false targets in the lake water. Figure 5 (d) shows the imaging result of the method of the present invention. Because the method of the present invention can effectively suppress noise through the echo repair strategy and adaptively select appropriate regularization parameters according to the echo signals of different distance cells, the imaging method of the present invention achieves high imaging quality, which enhances the practicality of the target recognition method of the present invention.

[0155] In summary, the echo restoration strategy of the present invention can reduce the impact of noise on super-resolution imaging, achieve adaptive sparse forward-looking super-resolution imaging under extremely low signal-to-noise ratio conditions, obtain high-quality imaging results, and improve the efficiency of forward-looking two-dimensional super-resolution imaging algorithm, thus exhibiting strong robustness.

[0156] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.

Claims

1. An adaptive sparse forward-looking super-resolution imaging method based on echo repair strategy, the specific steps are as follows: Step one, establish a scanning radar super-resolution model; The real aperture antenna continuously emits a large bandwidth of frequency-modulated pulse signals with a pulse repetition frequency (PRF) set according to actual conditions, while the beam is cyclically scanned in the target detection area to obtain a 2D image; during the scanning process, each pulse data is stored in each column of the echo matrix; After a scan is completed, a complete echo matrix can be formed; after polar coordinate interpolation projection is performed, a complete scanning radar 2D image can be obtained; let the distance variable be , and the azimuth variable be ; In range direction, super-resolution imaging is achieved by pulse compression. Considering azimuth processing, for a fixed range cell, the azimuth echo model is expressed as the convolution of target scattering and antenna pattern. Considering additive white Gaussian noise The discrete expression of the azimuth echo model is as follows: （1）； Wherein, denotes a complex set, denotes the echo vector of the mth range cell, and N denotes the number of azimuth sampling points of the echo, denotes a transpose operation; denotes the target backscattering coefficient, and K denotes the number of azimuth sampling points of the target backscattering coefficient; denotes a steering matrix, and the specific expression is as follows: （2）； wherein denotes the antenna vector , the l-th element in , denotes the number of antenna pattern sampling points, and A is a K-columned circulant matrix, each column of which is generated by shifting Step two, based on step one, construct a regularization framework based on norm-constrained regularizer Using The norm as a sparse constraint, construct cost function , the expression as follows: （3）； wherein denotes the norm of a vector denotes the norm of a vector denotes the norm of a vector denotes the norm of a vector denotes a penalty parameter; Definition of the weighting matrix The weighting matrix can be updated by the scattering results of the last iteration The iterative expression of solving equation (3) by the IRN method is as follows: （4）； wherein denotes a diagonal matrix transformed from the vector, q denotes the number of iterations, may be obtained by ; Step three, based on step two, wavelet decomposition of echo signal, that is, echo repair processing; First, echo repair processing, formula (1) is rewritten as an echo repair model, the expression is as follows: （5）； wherein, represents the echo signal without the influence of noise, is set satisfies the standard of independent and identically distributed (IID) , represents the noise variance; The objective of equation (5) is to estimate the vector i.e. with a small risk of finding an estimate that depends on ; wherein, represents a risk function, represents the repaired echo vector; Setting an orthogonal discrete wavelet transform matrix , and the radar echo signal is a complex number, the real part and the imaginary part of the echo are respectively decomposed by wavelet, and the expression is as follows: （6）； wherein and denote the real and imaginary part of the echo, respectively, and denote the real and imaginary part taking operations, respectively, and Q denotes the number of samples of the echo in the wavelet domain. Step four, wavelet threshold processing of echo signal after wavelet decomposition in step three, and the appropriate threshold is adaptively selected by estimating the noise level; Set to use soft threshold rule, the expression is as follows: （7）； wherein, represents a soft threshold processing function, w represents an argument, T represents a threshold, the threshold is only related to the number of wavelet domain sampling points of the echo and the noise level , and satisfies , the noise level estimate The expression is as follows: （8）； wherein denotes the median absolute deviation; the thresholded real and complex wavelet coefficients are and ; Step five, based on wavelet threshold processing in step four, reconstruct the echo; Transform are orthogonal, the inverse transform matrix can be represented as ; then the echo signal reconstruction expression is as follows: （9）； wherein represents the imaginary unit; Step six, construct a cost function based on the echoes reconstructed in step five the norm-constrained cost function and transform the sparse estimation problem into a maximum a posteriori estimation problem based on the Bayes theory; According to the repaired echo vector , a new sparse constraint optimization problem is set , expressed as follows: （10）； wherein the penalty parameter is a constant for balancing the norm sparsity regularizer ; setting different penalty parameters at each angle, expression (10) is rewritten as follows: （11）； wherein denotes the vector the i-th element of denotes the penalty parameter in direction i; By transforming the problem (10) into a maximum a posteriori estimation problem, MAP; in the Bayesian framework, a and Maximum a posteriori estimation expression is as follows: （12）； wherein wherein p denotes a probability function; then the expression of equation (12) is further simplified as follows: （13）； The set echo after repair still exists in additive Gaussian noise and meet the standard of independent and identically distributed IID The expression can be obtained as follows: （14）； wherein, denotes the standard deviation of the residual noise after echo repair; is a zero-mean Laplacian probability model satisfying IID, and the specific expression is as follows: （15）； wherein represents the standard deviation of the values of the parameter; according to the logarithm operation principle, equation (13) can be further modified, and the expression is as follows: （16）； Will and Substituting expressions (14) and (15) into (16) yields the following expression: （17）； Formula (17) can be simplified as follows: （18）； where the third term in equation (18) and the fourth term are independent of and can be ignored; multiplying the right side of equation (18) by the constant yields the expression （19）； Step seven, based on step six, the adaptive iterative weight of IRN is derived; Comparing equation (10) and (19), the penalty parameter can be obtained by equating the coefficients of the corresponding terms ; considering numerical stability, the penalty parameter expression is as follows: （20）； wherein, denotes the noise power estimate of the super-resolution imaging stage, and , denotes the target scatter estimate of the qth iteration; denotes an estimate of the standard deviation, which can be estimated by computing the standard deviation of each element of the vector ; denotes a small constant set according to the actual situation; Step eight, based on step seven, adaptive iterative super-resolution imaging processing is carried out to realize forward-looking super-resolution imaging; The adaptive iterative estimation expression of target scattering is as follows: （21）； wherein denotes a conjugate transpose operation, a penalty parameter vector may be computed by equation (20); during the iteration process, is initialized to , denotes a K-dimensional identity matrix, denotes the noise level after echo repair, which can be computed by equation (8).

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