Self-adaptive sparse foresight super-resolution imaging method based on echo restoration strategy

Abstract

The invention discloses a self-adaptive sparse foresight super-resolution imaging method based on an echo restoration strategy, which comprises the following steps: firstly, establishing a scanning radar super-resolution model, then, based on a regularization theory, using an L1 norm as a constraint term to improve the angular resolution of a sparse target, and then, using a multi-scale representation characteristic of wavelet variation to separate signals and noise in echoes, so as to realize the self-adaptive sparse foresight super-resolution imaging. The problem that an existing L1-IRN method is poor in performance under the low signal-to-noise ratio is solved while the echo signal-to-noise ratio is improved, a new optimization cost function is constructed based on preprocessed echoes, finally, a sparse estimation problem is converted into a maximum posteriori estimation problem based on the Bayesian theory, a self-adaptive iteration weight is obtained, and foresight super-resolution imaging is achieved. The echo repairing strategy of the method can weaken the influence of noise on super-resolution imaging, adaptive sparse foresight super-resolution imaging is realized under the condition of extremely low signal-to-noise ratio, a high-quality imaging result is obtained, meanwhile, the efficiency of a foresight two-dimensional super-resolution imaging algorithm is improved, and high robustness is achieved.

Description

Technical Field

[0001] The invention belongs to the technical field of radar imaging, and in particular relates to an adaptive sparse forward-looking super-resolution imaging method based on an echo repair strategy. Background Art

[0002] Scanning radar has been widely used in the field of forward-looking imaging due to its full-viewing angle, 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 movement of the platform or target to form a larger synthetic aperture, thereby obtaining higher azimuth resolution. However, in the imaging process of SAR and ISAR, due to the small change in Doppler frequency, the azimuth resolution is greatly reduced in ultra-high-resolution forward-looking imaging radars, making it difficult to meet the needs of practical applications.

[0003] In recent years, some new methods have been proposed for scanning radar super-resolution imaging. The literature "Zhang, Yongchao, et al. "Wideband sparse reconstruction for scanning radar." IEEE Transactions on Geoscience and Remote Sensing 56.10 (2018): 6055-6068" uses a constructed broadband dictionary framework and a generalized sparse covariance estimation algorithm to achieve low-complexity sparse imaging, but this method is difficult to obtain good azimuth super-resolution performance under low signal-to-noise ratio. The literature "Wu, Yang, et al." Sparse super-resolution methodbased on truncated singular value decomposition strategy for radar forward-looking imaging." Journal of Applied Remote Sensing 12.3(2018): 035021-035021" introduces the singular value threshold method for preprocessing, improves the pathological characteristics of the deconvolution model and realizes scanning radar super-resolution imaging under low signal-to-noise ratio conditions, but the imaging effect of this method is poor when the signal-to-noise ratio of the echo after pulse compression is lower than 5dB. The literature "Zhang, Qiping, et al." A sparse denoising-based super-resolution method for scanning radar imaging." Remote Sensing 13.14(2021): 2768" integrates the denoising process into the L1-constrained azimuth super-resolution processing optimization function, and realizes azimuth super-resolution under a signal-to-noise ratio of 5dB. However, the above method has multiple hyperparameters that are sensitive to noise, making it difficult to apply in actual scenarios. Summary of the invention

[0004] In order to solve the above technical problems, the present invention provides an adaptive sparse forward-looking super-resolution imaging method based on an echo repair strategy to solve the imaging ambiguity problem of the existing azimuth-elevation super-resolution method at low signal-to-noise ratio.

[0005] The technical solution adopted by the present invention is: an adaptive sparse forward-looking super-resolution imaging method based on echo repair strategy, and the specific steps are as follows:

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

[0007] The real aperture antenna continuously transmits a large bandwidth frequency modulated pulse signal at a pulse repetition frequency PRF set according to the actual situation, and cyclically scans the beam 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 completing a scan, a complete echo matrix can be formed. After performing polar coordinate interpolation projection, a complete scanning radar 2D image can be obtained. Let the distance variable be R and the azimuth variable be θ.

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

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

[0010] in, represents a complex set, represents the echo vector of the mth distance unit, N represents the number of echo azimuth sampling points, [] T Represents a transpose operation. represents the target backscatter coefficient, and K represents the number of azimuth sampling points of the target backscatter coefficient. represents the steering matrix, and its specific expression is as follows:

[0011]

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

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

[0014] Using the L1 norm as the sparse constraint, construct the cost function J, which is expressed as follows:

[0015]

[0016] Among them, ||·||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 weight matrix W = diag(|s| -1 ), the weighting matrix can be updated by the scattering result s of the previous iteration, and the iterative expression of equation (3) solved 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) Available through (q) get.

[0020] Step 3: Based on step 2, perform wavelet decomposition on the echo signal, that is, perform echo repair processing;

[0021] First, perform echo repair processing and rewrite equation (1) into an echo repair model, which is expressed as follows:

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

[0023] Among them, f m Indicates the echo signal without noise influence, set e m Satisfy the independent and identically distributed IID standard N(0,σ 2 ), σ 2 represents the noise variance.

[0024] The goal of formula (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, represents the restored echo vector.

[0026] Set an orthogonal discrete wavelet transform matrix The number of wavelet decomposition layers is P, and the radar echo signal is complex. m The real and imaginary parts of are decomposed by wavelet, and the expression is as follows:

[0027]

[0028] in, and Re(·) and Im(·) represent the real and imaginary part of the echo, respectively. Q represents the number of sampling points of the echo in the wavelet domain.

[0029] Step 4: Perform wavelet threshold processing on the echo signal after wavelet decomposition in step 3, and adaptively select a suitable threshold by estimating the noise level;

[0030] Set the soft threshold rule to use, the expression is as follows:

[0031]

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

[0033]

[0034] Where Median(·) represents the median absolute deviation. The real and complex wavelet coefficients after threshold processing are and

[0035] Step 5: Reconstruct the echo based on the wavelet threshold processing in step 4;

[0036] Transform is orthogonal, the inverse transformation matrix can be expressed as Then the echo signal reconstruction expression is as follows:

[0037]

[0038] Here, i represents the imaginary unit.

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

[0040] According to the restored echo vector Set up a new sparse constrained optimization problem The expression is as follows:

[0041]

[0042] Among them, 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 of i Represents the penalty parameter in direction i.

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

[0046]

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

[0048]

[0049] Additive Gaussian noise still exists in the echo after repair And it meets the independent and identically distributed IID standard Then the expression is as follows:

[0050]

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

[0052]

[0053] Among them, δ i Indicates m,i The standard deviation of . According to the principle of logarithmic operation, formula (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] Formula (17) can be simplified to the following expression:

[0058]

[0059] Among them, the third term in formula (18) and the fourth item With s m is irrelevant and can be ignored. Multiply the right side of equation (18) by the constant Then the expression is as follows:

[0060]

[0061] Step 7: Based on step 6, derive the adaptive iteration weight of IRN;

[0062] Comparing equations (10) and (19), making the coefficients of the corresponding items equal, we can get the penalty parameter Considering numerical stability, the penalty parameter expression is as follows:

[0063]

[0064] in, represents the noise power estimate of the super-resolution imaging stage, and represents the target scattering estimate at the qth iteration. Indicates m,i The standard deviation can be estimated by calculating Each element s in m,i ε is a small constant set according to the actual situation.

[0065] Step 8: Based on step 7, adaptively iterate super-resolution imaging processing to achieve forward-looking super-resolution imaging;

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

[0067]

[0068] in,[] H represents the conjugate transpose operation, the penalty parameter vector λ (q) =[λ1,λ2,…,λ K ] can be calculated by formula (20). In the iterative process, Initialize to I represents the K-dimensional unit matrix, α represents the noise level after echo restoration, which can be calculated by formula (8).

[0069] Beneficial effects of the present invention: The method of the present invention first establishes a scanning radar super-resolution model, and then based on the regularization theory, uses the L1 norm as a constraint term to improve the angular resolution of sparse targets, and then uses the multi-scale representation characteristics of wavelet changes to separate the signal and noise in the echo, that is, the echo is pre-processed for noise reduction, while improving the echo signal-to-noise ratio, solving the problem of poor performance of the existing L1-IRN method under low signal-to-noise ratio, and constructing a new optimization cost function based on the pre-processed echo, and finally based on the Bayesian theory, the sparse estimation problem is converted into a maximum a posteriori estimation problem, and adaptive iterative weights are obtained to achieve forward-looking super-resolution imaging. The echo repair strategy of the method of the present invention can reduce the impact of noise on super-resolution imaging, realize adaptive sparse forward-looking super-resolution imaging under extremely low signal-to-noise ratio conditions, obtain high-quality imaging results, and at the same time improve the efficiency of the forward-looking two-dimensional super-resolution imaging algorithm, with strong robustness. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1 The present invention is a flowchart of an adaptive sparse forward-looking super-resolution imaging method based on an echo repair strategy.

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

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

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

[0074] Figure 5 It is a comparison chart of the measured results of the original scene, echo, existing L1 method and the method of the present invention under a moving platform in an embodiment of the present invention. DETAILED DESCRIPTION

[0075] All steps and conclusions of the present invention are verified to be correct on the Matlab2019b simulation platform. In order for relevant personnel in this field to understand the content of the invention, the method of the present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0076] like Figure 1 As shown in the flowchart of the adaptive sparse forward-looking super-resolution imaging method based on the echo repair strategy of the present invention, the specific steps are as follows:

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

[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 the forward-looking scanning radar can be seen from the figure. The real aperture antenna continuously transmits a large-bandwidth frequency-modulated pulse signal at a pulse repetition frequency PRF = 2kHz, and cyclically scans the beam 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 completing a scan, a complete echo matrix (such as Figure 2 (shown in the lower left). After polar coordinate interpolation projection, a complete scanning radar 2D image can be obtained. Let the distance variable be R and the azimuth variable be θ.

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

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

[0081] in, represents a complex set, represents the echo vector of the mth range unit, N=256 represents the number of echo azimuth sampling points, [] T Represents a transpose operation. Represents the target backscatter coefficient, and K=256 represents the number of azimuth sampling points of the target backscatter coefficient. represents the steering matrix, which is mathematically a Toeplitz matrix constructed by cyclic shift of the azimuth antenna pattern function. The specific expression is as follows:

[0082]

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

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

[0085] Based on the linear model of formula (1), the simplest method is to reconstruct the target by the least squares method. However, due to the low-pass filtering characteristics (ill-conditioned) of the antenna pattern matrix A, high-frequency noise will be severely amplified. To this end, various regularization methods can be introduced to alleviate the ill-conditioned. Considering that the target scene observed by the scanning radar is usually sparsely distributed, the L1 norm is used as the sparse constraint to construct the cost function J, which is expressed as follows:

[0086]

[0087] Among them, ||·||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, a series of weighted L2 constrained optimization problems are solved by iterative reweighting (IRN) to approximate the original L1 norm problem. Define the weight matrix W = diag(|s| -1 ), the weighting matrix can be updated by the scattering result s of the previous iteration. The iterative expression for solving equation (3) 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) Available through (q) get.

[0091] Step 3: Based on step 2, perform wavelet decomposition on the echo signal, that is, perform echo repair processing;

[0092] Directly using the existing angular super-resolution method under the condition of high noise variance cannot effectively image. Therefore, echo repair processing is required first. Then, equation (1) is rewritten as an echo repair model, and the expression is as follows:

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

[0094] Among them, f m Indicates the echo signal without noise influence, set e m Satisfy the independent and identically distributed IID standard N(0,σ 2 ), σ 2 represents the noise variance.

[0095] The goal of formula (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, represents the restored echo vector.

[0097] Set an orthogonal discrete wavelet transform matrix The number of wavelet decomposition layers is P, and the radar echo signal is complex. m The real and imaginary parts of are decomposed by wavelet, and the expression is as follows:

[0098]

[0099] in, and Re(·) and Im(·) represent the real and imaginary part of the echo, respectively. Q represents the number of sampling points of the echo in the wavelet domain.

[0100] Step 4: Perform wavelet threshold processing on the echo signal after wavelet decomposition in step 3, and adaptively select a suitable threshold by estimating the noise level;

[0101] Since 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] Set the soft threshold rule to use, the expression is as follows:

[0103]

[0104] Among them, η T (w) represents the soft threshold processing function, w represents the independent variable, T represents the threshold, and the threshold is only related to the input signal length Q and the noise level σ, and satisfies 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 threshold processing are and

[0107] Step 5: Reconstruct the echo based on the wavelet threshold processing in step 4;

[0108] Due to the transformation is orthogonal, the inverse transformation matrix can be simply expressed as Then the echo signal reconstruction expression is as follows:

[0109]

[0110] Here, i represents the imaginary unit.

[0111] Through steps three to five, y m The strong noise in the image is removed to a great extent, and the echo signal-to-noise ratio is improved.

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

[0113] According to the restored echo vector Set up a new sparse constrained optimization problem The expression is as follows:

[0114]

[0115] Among them, 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 of i Represents the penalty parameter in direction i.

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

[0119]

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

[0121]

[0122] Additive Gaussian noise still exists in the echo after repair And it meets the independent and identically distributed IID standard Then the expression is as follows:

[0123]

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

[0125]

[0126] Among them, δ i Indicates m,i The standard deviation of . According to the principle of logarithmic operation, formula (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] Formula (17) can be simplified to the following expression:

[0131]

[0132] Among them, the third term in formula (18) and the fourth item With s m is irrelevant and can be ignored. is a constant, then multiply the right side of equation (18) by the constant Will not affect m The estimate of , then the expression is as follows:

[0133]

[0134] Step 7: Based on step 6, derive the adaptive iteration weight of IRN;

[0135] Comparing equations (10) and (19), making the coefficients of the corresponding items equal, we can get the penalty parameter Considering numerical stability, the penalty parameter expression is as follows:

[0136]

[0137] in, represents the noise power estimate of the super-resolution imaging stage, and represents the target scattering estimate at the qth iteration. Indicates m,i The standard deviation can be estimated by calculating Each element s in m,i ε is a small constant set according to the actual situation.

[0138] Step 8: Based on step 7, adaptively iterate super-resolution imaging processing to achieve forward-looking super-resolution imaging;

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

[0140]

[0141] in,[] H represents the conjugate transpose operation, the penalty parameter vector λ (q) =[λ1,λ2,…,λ K ] can be calculated by formula (20). In the iterative process, Initialize to I represents the K-dimensional unit matrix, α represents the noise level after echo restoration, which can be calculated by formula (8).

[0142] This embodiment further performs 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 scanning radar point target simulation is performed and the radar system parameters are set according to Table 1.

[0144] Table 1

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

[0146] It can be seen from the point target simulation results that Figure 3 (a) is the original scene of a point target with a signal-to-noise ratio of 0 dB. Figure 3 (b) is the echo when the signal-to-noise ratio (SNR) is 0 dB. It can be seen that the echo is significantly blurred when the signal-to-noise ratio is very low. Figure 3 (c) is the imaging result of the existing L1 method. When the signal-to-noise ratio (SNR) is 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) is the imaging result of the method of the present invention. It can be seen that when the signal-to-noise ratio SNR=0 dB, the target can be reconstructed with good effect under the condition of better suppression of side lobes.

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

[0148] Table 2

[0149] parameter Numeric 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 Range 3000m Platform speed 30m / s

[0150] It can be seen from the surface target simulation results that Figure 4 (a) is the original scene of the target with a signal-to-noise ratio below 5dB. Figure 4 (b) is the echo at SNR=5dB. Due to the wider antenna beam, several ships are blurred to varying degrees. Figure 4 (c) is the imaging result of the existing L1 method. When the signal-to-noise ratio (SNR) is 5 dB, the ship targets are effectively separated due to the large distance between the ships, but their azimuth resolution is limited and there is obvious background noise. Figure 4 (d) is the imaging result of the method of the present invention. It can be seen that when the signal-to-noise ratio SNR=5dB, the method of the present invention not only improves the azimuth resolution, but also suppresses the background noise very well. In addition, the amplitude of the ship target is uniformly reconstructed by the method of the present invention, and the visual effect of the image is the best.

[0151] like Figure 5 As shown, conduct scanning radar measurement and set radar system parameters according to Table 3.

[0152] Table 3

[0153] parameter Numeric 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] It can be seen from the test results that Figure 5 (a) is the original scene measured. Figure 5 (b) is the measured echo. It can be seen that the resolution of the real beam image is very low, and the river channel between the island and the lakeshore does not look clear. Figure 5 (c) is the imaging result of the existing L1 method. It can be seen that it improves the azimuth resolution to a certain extent. However, due to the low signal-to-noise ratio of the echo, their imaging results are affected by noise. The boundary between the island and the lake is not clear, and there are a large number of false targets in the lake. Figure 5 (d) is 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 units, which enables the imaging method of the present invention to obtain very high imaging quality, which enhances the practicability of the target recognition of the method of the present invention.

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

[0156] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific variations and combinations that do not deviate from the essence of the present invention based on the technical revelations disclosed by the present invention, and these variations and combinations are still within the protection scope of the present invention.

Claims

1. An adaptive sparse forward-looking super-resolution imaging method based on echo repair strategy, the specific steps are as follows: Step 1: Establish a scanning radar super-resolution model; The real aperture antenna continuously transmits a large bandwidth frequency modulated pulse signal at a pulse repetition frequency PRF set according to the actual situation, and cyclically scans the beam 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 completing a scan, a complete echo matrix can be formed; after performing polar coordinate interpolation projection, a complete scanning radar 2D image can be obtained; let the distance variable be R and the azimuth variable be θ; Super-resolution imaging is achieved in the range direction through pulse compression. Considering azimuth processing, for a fixed distance unit, the azimuth echo model is represented as the convolution of target scattering and antenna pattern; considering additive Gaussian white noise The discrete expression of the azimuth echo model is as follows: the m =As m +e m (1) in, represents a complex set, represents the echo vector of the mth range unit, N represents the number of echo azimuth sampling points, [ ] T Represents a transpose operation; represents the target backscatter coefficient, K represents the number of sampling points of the target backscatter coefficient; represents the steering matrix, and its specific expression is as follows: Among them, h l Represents the antenna vector The lth element in , l = 0, ..., L-1, L represents the number of antenna pattern sampling points, and A is a circulant matrix with K columns, each column is generated by h shifts; Step 2: Based on step 1, construct a regularization framework based on L1 norm constraint; Using the L1 norm as the sparse constraint, construct the cost function J, which is expressed as follows: Among them, ||·||2 represents the L2 norm of the vector, ||·||1 represents the L1 norm of the vector, and λ represents the penalty parameter; Define the weight matrix W = diag(|s| -1 ), the weighting matrix can be updated by the scattering result s of the previous iteration, and the iterative expression of equation (3) solved by the IRN method is as follows: and (q+1) =(The T A+λW (q) ) -1 THE T y m (4) Where diag(·) represents the diagonal matrix transformed from the vector, q represents the number of iterations, and W (q) Available through (q) get; Step 3: Based on step 2, perform wavelet decomposition on the echo signal, that is, perform echo repair processing; First, perform echo repair processing and rewrite equation (1) into an echo repair model, which is expressed as follows: y m =f m +e m (5) Among them, f m Indicates the echo signal without noise influence, set e m Satisfy the independent and identically distributed IID standard N(0,σ 2 ), σ 2 represents the noise variance; The goal of formula (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 ]; in, represents the risk function, represents the restored echo vector; Set an orthogonal discrete wavelet transform matrix The number of wavelet decomposition layers is P, and the radar echo signal is complex. m The real and imaginary parts of are decomposed by wavelet, and the expression is as follows: in and Re(·) and Im(·) represent the wavelet coefficient vector of the real and imaginary parts of the echo, respectively. Q represents the number of sampling points of the echo in the wavelet domain. Step 4: Perform wavelet threshold processing on the echo signal after wavelet decomposition in step 3, and adaptively select a suitable threshold by estimating the noise level; Set the soft threshold rule to use, the expression is as follows: Among them, η T (w) represents the soft threshold processing function, w represents the independent variable, T represents the threshold, and the threshold is only related to the input signal length Q and the noise level σ, and satisfies Estimation of noise level σ The expression is as follows: Where Median(·) represents the median absolute deviation; the real and complex wavelet coefficients after threshold processing are and Step 5: Reconstruct the echo based on the wavelet threshold processing in step 4; The transformation w is orthogonal, and the inverse transformation matrix can be expressed as Then the echo signal reconstruction expression is as follows: Wherein, i represents the imaginary unit; Step 6: Based on the echo reconstructed in step 5, construct a cost function constrained by L1 norm and transform the sparse estimation problem into a maximum a posteriori estimation problem based on Bayesian theory; According to the restored echo vector Set up a new sparse constrained optimization problem The expression is as follows: Among them, the penalty parameter λ is a constant used to balance the L1 norm sparsity regularization term ||s m ||1; setting different penalty parameters at different angles, then equation (10) can be rewritten as follows: Among them, s m,i Represents vector s m The i-th element of i represents the penalty parameter in direction i; By transforming the problem (10) into a maximum a posteriori estimation problem MAP; in the Bayesian framework, an s m and The maximum a posteriori estimate expression is as follows: Where P(·) represents the probability function; then the further simplified expression of formula (12) is as follows: Additive Gaussian noise still exists in the echo after repair And it meets the independent and identically distributed IID standard Then the expression is as follows: in, represents the standard deviation of the residual noise after echo repair; P(s m ) is a zero-mean Laplace probability model that satisfies IID. The specific expression is as follows: Among them, δ i Indicates m,i The standard deviation of; According to the principle of logarithmic operation, formula (13) can be further rewritten as follows: Will and P(s m Substituting expressions (14) and (15) into (16) yields the following expression: Formula (17) can be simplified to the following expression: Among them, the third term in formula (18) and the fourth item With s m is irrelevant and can be ignored; multiply the right side of equation (18) by the constant Then the expression is as follows: Step 7: Based on step 6, derive the adaptive iteration weight of IRN; Comparing equations (10) and (19), making the coefficients of the corresponding items equal, we can get the penalty parameter Considering numerical stability, the penalty parameter expression is as follows: in, represents the noise power estimate of the super-resolution imaging stage, and represents the target scattering estimate at the qth iteration; Indicates m,i The standard deviation can be estimated by calculating Each element s in m,i The standard deviation is used to estimate; ε represents a small constant set according to the actual situation; Step 8: Based on step 7, adaptively iterate super-resolution imaging processing to achieve forward-looking super-resolution imaging; The adaptive iterative estimation expression of target scattering is as follows: in,[ ] H represents the conjugate transpose operation, the penalty parameter vector λ (q) =[λ1,λ2,…,λ K ] can be calculated by formula (20); in the iterative process, Initialize to I represents the K-dimensional unit matrix, α represents the noise level after echo restoration, which can be calculated by formula (8).

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