A high-resolution imaging method for high-squint SAR based on deep unfolding network

Abstract

The present invention provides a high-resolution imaging algorithm for high-squint SAR (SAR) based on a deep unfolding network: Step 1: Constructing a high-squint SAR echo signal observation model, and determining, based on the RD algorithm, that the imaging matrices required for learning by the imaging network are quadratic range compression, a cubic phase compensation matrix H2, and an azimuth compression matrix H3; Step 2: Constructing a corresponding high-squint SAR imaging network based on the learning parameters H2, H3, and other parameters determined in Step 1, and simultaneously constructing a corresponding high-squint SAR echo dataset. By deeply unfolding the ISTA algorithm into a network form, a more accurate imaging matrix is ​​obtained compared to traditional imaging algorithms, thereby improving imaging accuracy and focusing effects. This imaging method can perform high-resolution two-dimensional imaging of a target without constructing a complex compensation function, effectively suppressing sidelobes, improving imaging accuracy and computational efficiency, and achieving better imaging quality than other imaging algorithms under conditions of increased squint angles, thus meeting SAR imaging requirements under high-squint conditions.

Description

Technical Field

[0001] The present invention relates to signal and information processing and deep learning technology, and in particular to a SAR high-squint high-resolution imaging algorithm based on a deep unfolding network. Background Art

[0002] As an active sensor, Synthetic Aperture Radar (SAR) can perform all-weather, all-day, high-resolution observation of targets and has strong penetration, so it is widely used in military and civilian fields.

[0003] Squint SAR, due to its flexible beam pointing, has the ability to detect oblique forward vision ahead of normal-looking SAR imaging, enabling real-time reconnaissance of enemy targets. Therefore, research on SAR imaging algorithms under high squint angles is of great significance. High squint SAR echo signals exhibit severe range / azimuth coupling and large range migration, making conventional normal-looking SAR imaging methods unsuitable for imaging under high squint conditions. In "Modified Range-Dopplerimaging method for the high squint SAR" (2010 IEEE Radar Conference, 2010, pp. 1450-1453), Shuyan Wang et al. proposed an improved range Doppler (RD) algorithm based on the Keystone transform and rank deficiency, producing more detailed SAR images. In "Modified Range-Doppler Algorithm for High Squint SAR Echo Processing" (IEEE Geoscience and Remote Sensing Letters, vol. 16, no. 3, pp. 422-426), Wenna Fan proposed an improved range-Doppler imaging algorithm for processing high-squint SAR echo signals. This method directly corrects range unit migration in the range-frequency domain. The proposed algorithm uses a more refined fourth-order phase model to implement azimuth compression, and ultimately obtains a focused high-squint SAR image through geometric correction. Yan Wang proposed a nonlinear chirp scaling (NCS) high-squint SAR imaging algorithm in "A New Nonlinear Chirp Scaling Algorithm for High-Squint High-Resolution SARI Imaging" (IEEE Geoscience and Remote Sensing Letters, vol. 14, no. 12, pp. 2225-2229). This method is based on a more refined two-dimensional spectrum, introduces a new chirp scaling factor into the range-Doppler domain to interpolate and correct the residual range offset phase, and designs a new perturbation function to eliminate the dependence of the Doppler phase on the azimuth angle. This method has higher imaging quality than the traditional NCS algorithm.In "An approach for high squint spaceborne SAR imaging based on generalized scale transform" (2020 IET International Radar Conference, 2020, pp. 1161-1165), H. Huang proposed a new high squint spaceborne SAR imaging method based on a generalized scale transform. After range compression of the echo signal, the method first corrects for range walk based on the radar beam center parameters. A reference tilt range is then used for coarse focusing. Finally, Stolt interpolation is performed to compensate for residual phase. Finally, a generalized scale transform is applied to eliminate the effects of azimuth space-variation. After geometric distortion correction, well-focused SAR imaging is achieved.

[0004] However, many current high-squint SAR imaging algorithms have shortcomings in both the time and frequency domains. For time-domain imaging algorithms, such as the back projection (BP) algorithm, while capable of precise imaging, the algorithm requires a point-by-point traversal of the observed scene, thus failing to meet the requirements of real-time SAR imaging in terms of imaging time. Frequency-domain imaging algorithms, including the RD, range migration (RMA), and NCS algorithms, all employ varying degrees of approximation when performing range migration compensation. This makes constructing phase compensation and azimuth compression functions difficult, resulting in high computational complexity. Furthermore, as the squint angle increases, the algorithm's imaging quality gradually degrades. Summary of the Invention

[0005] The present invention aims to overcome the shortcomings of the above imaging methods and proposes a high-resolution imaging method for high-squint SAR based on a deep unfolding network, comprising the following steps:

[0006] Step 1: Construct a high-squint SAR echo signal observation model to determine the imaging matrix that the imaging network needs to learn. First, perform a Taylor series expansion on the instantaneous slant range expression based on the traditional imaging algorithm, perform range motion correction on the echo data in the range frequency domain, and then perform range compression on the echo signal after motion correction to obtain the range-compressed signal. This determines that the matrices that the imaging network needs to learn are quadratic range compression, cubic phase compensation matrix, and azimuth compression matrix.

[0007] Step 2: Based on the learnable parameters determined in step 1, a corresponding imaging network is constructed. The above two matrices are used as learnable parameters. Through network learning, a more accurate imaging matrix is ​​obtained compared with the traditional algorithm, thereby improving imaging accuracy and focusing effect. The imaging method combines the traditional RD imaging algorithm steps and the ISTA solution algorithm to construct an imaging network.

[0008] In one embodiment of the present invention, step 1 specifically includes the following steps:

[0009] Step 1) Construct a high squint SAR echo signal observation model, and perform Taylor series expansion on the distance between the radar and the target according to the traditional imaging algorithm to obtain the approximate distance R B (τ; R 。 ), where τ is the slow time variable, R B (τ; R c ) The distance R from the radar to the center of the observation scene c , speed and oblique angle, and calculate the echo delay τ a =2R B (τ; R c ) / c, c is the electromagnetic wave speed; specifically as follows:

[0010] In the positional relationship between the SAR high squint imaging system and the observation scene, the height of the platform is h, the squint angle is θ0, and it is assumed that the platform moves in a uniform straight line with a speed of V r , R0 is the shortest distance between the flight path and the center of the observation scene, R B (t, τ; R0) is the instantaneous slant distance between the platform and the point target, where t is the fast time variable and τ is the slow time variable. The geometric relationship between the SAR platform and the point target is established through the relationship between the instantaneous slant distance and the slow time. The coordinate origin O is set as the starting point of the slow time, and the slow time-slant distance rectangular coordinate system is established. At this time, the beam center ray and the line passing through point P and parallel to the route intersect at point A. Point A is also the starting point of the slow time. t0 is the moment when the beam center passes through. According to the cosine theorem, the instantaneous slant distance between the platform and the point target P is

[0011]

[0012] Where Y n Expressed as the distance between point target P and point A;

[0013] Assume that the radar transmits a linear frequency modulation signal LFM with a modulation frequency of K r , the pulse width is T p , then the baseband echo signal received by the platform is

[0014]

[0015] Where ζ is the radar operating wavelength, rect(·) is its envelope, τ a =2R B (τ, R c ) / c is the echo delay; K r is the modulation frequency of the linear frequency modulation signal;

[0016] R B (τ; R c ) is expanded by Taylor series to obtain

[0017]

[0018] From formula (3), we can see that the linear term is the range movement term, and the high-order term is the range curvature term. When the squint angle is large enough, the value of the high-order term is very small, so the influence of range curvature on the envelope can be ignored. Combining formulas (2) and (3), we can see that the range curvature term and the radar wavelength are at the same order of magnitude, so the influence of range curvature on the echo phase cannot be ignored.

[0019] Step 2) The echo signal S obtained by the platform r (t, τ; R c ) Perform FFT in the range direction to obtain the echo signal in the range frequency domain, construct the movement compensation function and the range compression function H1 to reduce the coupling degree in the range / azimuth direction, and obtain the compressed echo signal S r′ (f r ,τ1;R c ), where t is the fast time variable, f r is the distance-to-frequency domain, equivalent slow time series At this time, the Doppler center frequency of the echo signal after movement correction and range compression is moved to zero frequency, so the center line of the radar transmit beam is located in the zero Doppler plane; the details are as follows:

[0020] Next, the echo signal is transformed into the range frequency domain, the signal envelope in two dimensions is ignored, and range movement correction and range pulse compression are performed on it.

[0021] The movement error is

[0022] ΔR w =V r τsinθ0 (4)

[0023] The constructed distance movement compensation and compression function is

[0024]

[0025] Where, f r is the range frequency domain, f0 is the radar operating frequency;

[0026] The echo signal obtained after the above operation is

[0027]

[0028] Among them, R D (τ1, R c) is the instantaneous slant distance equivalent to the distance movement and compression, and τ1 is the slow time series equivalent to the distance movement and compression, as follows:

[0029]

[0030]

[0031] The above two functions are used as learnable variables to allow the imaging network to learn and train a more accurate compensation matrix;

[0032] Step 3) According to the high squint SAR imaging algorithm, the imaging matrix that the network can learn is determined to be the quadratic range compression matrix H2 and the azimuth matched filter function H3, and the RD imaging process is written as a matrix multiplication form Among them F r 、F a are the Fourier transform matrices of the range and azimuth directions, F r -1 、F a -1 is its inverse transformation matrix, S is the echo matrix under large squint conditions, H1 is the range movement correction and compression function H1(f r , τ), H2 is the matrix form of the quadratic range compression and cubic phase compensation function, and H3 is the matrix form of the azimuth compression function. represents the Hadamard product, Θ is the observed scene scattering coefficient matrix, and M(S) is the operator form of the imaging algorithm; specifically:

[0033] Combining equations (2) and (5), the imaging algorithm process of high squint SAR can be expressed as matrix multiplication form:

[0034]

[0035] The original echo data is obtained by the inverse process of imaging. The inverse process is expressed as

[0036]

[0037] Where * represents the matrix conjugation operation, M -1 This is the reverse process of the imaging process (9).

[0038] In another embodiment of the present invention, step 2 specifically includes the following steps:

[0039] Step 1) Based on the learnable imaging matrix determined in step 1, write out its imaging process. Combined with the idea that the SAR imaging problem can be regarded as an inverse problem, the imaging process is solved by the ISTA algorithm. The specific ISTA solution expression is where λ||Θ|| p is the regularization constraint term, λ is the regularization parameter, Expressed as L2 norm, S r is the real echo of high squint SAR, is the estimated scattering coefficient matrix of the observation scene, ||·|| p is the p-norm; specifically:

[0040] According to the analysis of formula (9) and (10), SAR imaging is regarded as an inverse problem of linear solution. The two-dimensional observation model is obtained by solving the optimization problem

[0041]

[0042] Step 2) Expand the solution process of the ISTA algorithm into a network form and construct the corresponding network sublayers, namely the residual sublayer, the operator update sublayer, and the nonlinear transformation sublayer; the details are as follows:

[0043] In the process of solving Equation (11) using the ISTA algorithm, the ISTA algorithm is divided into three steps: residual calculation, operator update, and soft threshold iteration. Therefore, in the deep expansion network, the corresponding three sub-network layers are also constructed in the first layer of the network, which are specifically described as:

[0044] (1) Residual sublayer: denoted by R, this sublayer is used to calculate the residual of the echo signal. In the kth layer of the imaging network, the scene scattering coefficient output by the k-1th layer is used to calculate the residual of the large squint echo signal S r The specific expression is

[0045]

[0046] in represents the residual of the k-th layer network iteration, is the scattering coefficient of the kth layer, k is the number of network layers, S r is the real echo of high squint SAR, M -1 It is the inverse process of RD imaging algorithm; M in the deep expansion network -1 is a variable. When the imaging matrices H2 and H3 change after the error back propagation, M -1 Changes followed;

[0047] (2) Operator update sublayer: denoted by P. The input of this sublayer is the residual calculated by the residual layer and acts on M. The specific expression is:

[0048]

[0049] in, is the residual between the scene scattering coefficient matrices, is the residual between the true echo signal and the estimated echo signal calculated by the residual sublayer, P (k) is the operator after update, is the scene scattering coefficient estimated at the kth layer β is the iteration step size and is a learnable parameter;

[0050] (3) Nonlinear transformation sublayer: denoted by F, this subnetwork layer is used to reflect the nonlinear mapping ability of the imaging network, and the P obtained by the operator update layer is (k) Perform nonlinear transformation to obtain the nonlinear mapping capability of high squint SAR echo signal to scene scattering coefficient, and output the scene scattering coefficient of the next layer at the same time The specific expression is

[0051]

[0052] F(P (k) ;λ,T)=soft(P (k) ;λ,T) (16)

[0053] Among them, F(·) is the nonlinear transformation function of the imaging network, which is set as the soft threshold function soft(·), soft(P (k) ; λ, T) is the soft threshold function related to the regularization parameter λ. In the constructed imaging network, it is directly used as the activation function of the nonlinear transformation layer, and T is the iteration threshold. The learnable parameters of this network layer can be the iteration threshold T and the regularization parameter λ.

[0054] In summary, the constructed high squint SAR LRD imaging network has a single-layer topology consisting of three sub-network layers: a residual layer, an operator update layer, and a nonlinear transformation layer. The learnable parameter set is Ω = {H2, H3, β, T, λ}. During network training, in order to reduce the scale of network learning parameters, the imaging matrices H2 and H3 only change after one round of back-propagation training, while the iterative parameters β, T, and λ are variable in each layer.

[0055] Step 3) Construct an echo training sample set. This method uses an ideal random point scattering model and a high-squint SAR observation model to generate high-squint SAR echoes. System environmental noise is added to generate a large number of echo data samples without changing the SAR imaging model. The details are as follows:

[0056] The ideal random point scattering model is used to generate high squint SAR echoes according to the echo signal model of formula (2). The system environmental noise is added to generate a large number of echo data samples without changing the SAR imaging model. The number of echo samples is set to N, and the real echo sample set S isn ={S1, S2, S3, ..., S N}, where n=1, 2, ..., N is the echo sample sequence number;

[0057] Step 4) Use the mean square error (MSE) as the loss function to implement unsupervised training of the high squint SAR imaging network. The network is optimized using the Adam optimization algorithm based on stochastic gradient descent. During the final imaging, the imaging matrices H2 and H3 learned by the network, the iteration step size, the regularization parameter, and the iteration threshold are input as fixed values ​​into the imaging network. The imaging process is then transformed into a feedforward operation of the network, which can directly output the imaging results. The details are as follows:

[0058] Directly use the estimated scene scattering coefficient obtained from the last layer of the network to act on M -1 , get the estimated value of SAR echo and compare it with the real echo; the expression of the echo estimate is shown in formula (17), and the loss function is set to the mean square error function MSE, and the specific expression is shown in formula (18)

[0059]

[0060]

[0061] in, represents the nth estimated high squint SAR echo, n is the sequence number of the echo sample, and its range is n = 1, 2, ..., N. Equation (17) obtains the estimated nth high squint SAR echo; Loss(Ω) is the loss function of the learnable parameter set Ω; here Ω = arg min(Loss(Ω)) is to obtain a more accurate learnable parameter set after the network converges.

[0062] In another embodiment of the present invention, in step 2), the specific expression of the soft threshold function soft(·) is the sign function sign(·)

[0063] F(P (k) ;λ,T)=soft(P (k) ;λ,T)=sign(P (k) )·(P (k) |-T) (16-1)

[0064] In formula (16-1), the sign function first performs a sign calculation on the first bracketed term, and then multiplies the sign calculation result by the second bracketed term.

[0065] This method combines high-squint SAR imaging with deep learning. Using the RD imaging steps, it constructs an RD learning imaging network structure based on a deep unfolding network. High-squint SAR imaging is treated as a linear inversion problem and, combined with traditional imaging steps, the SAR problem is unfolded into a network. Deep iteration of the network is used to determine the scattering coefficient of the target scene, which is then used to generate a high-squint SAR image. This method, provided that the network parameters converge, can accurately image high-squint SAR echo signals. The imaging quality is significantly superior to that of traditional high-squint imaging algorithms, while the imaging time is comparable to that of the improved RD imaging method, meeting the requirements for SAR imaging under high-squint conditions.

[0066] The beneficial effects of the present invention are: on the one hand, it overcomes the shortcomings of the existing SAR imaging algorithm, such as the need to construct a relatively complex compensation function, and the low imaging accuracy and efficiency. On the other hand, since the deep learning method is adopted for imaging, the design of the compensation function is avoided by learning, and an imaging matrix that is more accurate than the traditional algorithm is obtained, and the imaging quality is significantly improved. The proposed SAR high-squint range Doppler high-resolution imaging algorithm based on the deep unfolding network can quickly obtain an accurate SAR image by only inputting the high-squint SAR echo signal after all parameters in the imaging network are fixed. The imaging method has low complexity. After simulation verification, the proposed method can perform high-resolution two-dimensional imaging of point targets and real scene targets, effectively suppress sidelobes, improve imaging accuracy and computational efficiency, and the imaging quality is better than other imaging algorithms under the condition of increasing the squint angle, meeting the SAR imaging requirements under high-squint conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Figure 1 is a flow chart of the method of the present invention;

[0068] Figure 2(a) is a schematic diagram of high squint SAR imaging, and Figure 2(b) is a diagram of the geometric relationship between the radar and the target;

[0069] Figure 3(a) is a diagram of the high squint SAR imaging network structure, and Figure 3(b) is a schematic diagram of the structure of a single-layer network;

[0070] Figure 4 Schematic diagram of the unsupervised training structure of the imaging network;

[0071] Figure 5 Error curves for different network layers;

[0072] Figure 6(a) is a simulated scattering point model diagram, Figure 6(b) is a diagram showing the imaging results of the improved RD algorithm under the conditions of a signal-to-noise ratio of 15dB and 45°, Figure 6(c) is a diagram showing the imaging results of the L2 ISTA algorithm under the conditions of a signal-to-noise ratio of 15dB and 45°, and Figure 6(d) is a diagram showing the imaging results of the proposed method under the conditions of a signal-to-noise ratio of 15dB and 45°;

[0073] Figure 7(a) is the range profile of the RD algorithm, Figure 7(b) is the range profile of the L2 ISTA algorithm, Figure 7(c) is the range profile of the proposed imaging algorithm, and Figure 7(d) is the azimuth profile of RD, L2 ISTA, and the proposed inventive method;

[0074] Figure 8(a) shows the results of RD, L2 ISTA, and the proposed method for sea surface ship targets under the conditions of a signal-to-noise ratio of 15dB and 45°. Figure 8(b) shows the results of RD, L2 ISTA, and the proposed method for sea surface ship targets under the conditions of a signal-to-noise ratio of 15dB and 70°. DETAILED DESCRIPTION

[0075] The present invention is achieved through the following steps: constructing a high squint mode SAR echo observation model, obtaining the instantaneous slant range based on the geometric relationship between the point target and the platform, performing range movement compensation on the obtained echo signal in the range frequency domain to reduce the degree of coupling between the range and azimuth, and determining the learnable imaging matrices H2 and H3 using the traditional SAR high squint mode SAR imaging algorithm "High squint mode SAR imaging using modified RD algorithm" (2013 IEEE China Summit and International Conference on Signal and Information Processing, 2013, pp.589-592), where H2 is a quadratic range compression and cubic phase compensation matrix, and H3 is an azimuth compression matrix. The imaging algorithm is written in the form of matrix multiplication, and taking the ISTA algorithm as an example, the steps of ISTA solving the scattering scene coefficient are deeply expanded into a network form, thereby obtaining the nonlinear fitting ability of the high squint SAR echo signal to the scene scattering coefficient. After the network is trained and the parameters are fixed, an echo signal is input to output a high squint SAR image through a single feedforward operation of the network. The overall process of the present invention is as follows: Figure 1 Specific instructions are as follows:

[0076] Step 1: Construct a high-squint SAR echo signal observation model to determine the imaging matrix that the imaging network needs to learn. First, based on the traditional imaging algorithm, a Taylor series expansion is performed on the instantaneous slant range expression. The echo data is corrected for range motion in the range frequency domain. The echo signal after motion correction is then range-compressed to obtain the range-compressed signal. This determines that the matrices that the imaging network needs to learn are quadratic range compression, cubic phase compensation matrix, and azimuth compression matrix.

[0077] Step 1 specifically includes the following steps:

[0078] Step 1) Construct a high squint SAR echo signal observation model, and perform Taylor series expansion on the distance between the radar and the target according to the traditional imaging algorithm to obtain the approximate distance R B (τ; R c ), where τ is the slow time variable, R B (τ; R c ) The distance R from the radar to the center of the observation scene c , speed and oblique angle, and calculate the echo delay τ a =2R B (τ; R c ) / c, c is the electromagnetic wave speed;

[0079] Figure 2(a) shows the positional relationship between the SAR high squint imaging system and the observation scene, where the height of the platform is h, the squint angle is θ0, and the platform is assumed to move in a uniform straight line with a speed of V. r , R0 is the shortest distance between the flight path and the center of the observation scene, R B (t, τ; R0) is the instantaneous slant distance between the platform and the point target, where t is the fast time variable and τ is the slow time variable. The relationship between the instantaneous slant distance and the slow time can be used to establish the geometric relationship between the SAR platform and the point target as shown in Figure 2(b). Let the coordinate origin O be the starting point of the slow time, and establish a rectangular coordinate system of slow time-slant distance. At this time, the beam center ray and the line passing through point P and parallel to the route intersect at point A, which is also the starting point of the slow time. t0 is the moment when the beam center passes through. According to the cosine theorem, the instantaneous slant distance between the platform and the point target P can be obtained as

[0080]

[0081] Where Y n Expressed as the distance between point target P and point A.

[0082] Assume that the radar transmits a linear frequency modulation signal (LFM) with a modulation frequency of K. r , the pulse width is T p, then the baseband echo signal received by the platform is

[0083]

[0084] Where ζ is the radar operating wavelength, rect(·) is its envelope, τ a =2R B (τ, R c ) / c is the echo delay. K r is the modulation frequency of the linear frequency modulation signal.

[0085] Traditional RD imaging algorithms perform a second-order approximation of equation (1), ignoring the errors caused by higher-order terms. Range migration correction is performed directly in the range-Doppler domain, resulting in imaging through range compression and azimuth compression. This algorithm does not consider the characteristics of high-squint echo signals and therefore does not meet the imaging requirements under high-squint viewing angle conditions.

[0086] Next, R B (τ; R c ) is expanded by Taylor series to obtain

[0087]

[0088] From Equation (3), we can see that the linear term is the range movement term, and the higher-order term is the range curvature term. When the squint angle is large enough, the value of the higher-order term is very small, so the effect of range curvature on the envelope can be ignored. Combining Equations (2) and (3), we can see that the range curvature term and the radar wavelength are on the same order of magnitude, so the effect of range curvature on the echo phase cannot be ignored.

[0089] Step 2) The echo signal S obtained by the platform r (t, τ; R c ) Perform FFT in the range direction to obtain the echo signal in the range frequency domain, construct the movement compensation function and the range compression function H1 to reduce the coupling degree in the range / azimuth direction, and obtain the compressed echo signal S r′ (f r ,τ1;R c ), where t is the fast time variable, f r is the distance-to-frequency domain, equivalent slow time series At this time, the Doppler center frequency of the echo signal after movement correction and distance compression is moved to zero frequency, so the center line of the radar transmitting beam is located in the zero Doppler plane.

[0090] Next, the echo signal is transformed into the range frequency domain, the signal envelope in two dimensions is ignored, and range movement correction and range pulse compression are performed on it.

[0091] The movement error is

[0092] ΔRw =V r τsinθ0 (4)

[0093] The constructed distance movement compensation and compression function is:

[0094]

[0095] Where, f r is the range frequency domain, and f0 is the radar operating frequency.

[0096] At this time, after the movement correction and distance compression, the Doppler center frequency of the echo signal moves to zero frequency, so the center line of the radar transmit beam is located in the zero Doppler plane. The echo signal obtained after the above operation is

[0097]

[0098] Among them, R D (τ1, R c ) is the instantaneous slant distance equivalent to the distance movement and compression, and τ1 is the slow time series equivalent to the distance movement and compression, as follows:

[0099]

[0100]

[0101] After compression, the coupling between range and azimuth is significantly reduced, but residual range migration and the influence of range curvature on the phase still exist. The improved RD algorithm addresses these issues by constructing quadratic range compression, cubic phase compensation functions, and azimuth pulse compression functions in the two-dimensional frequency domain. These functions employ varying degrees of approximation, resulting in a significant decrease in imaging quality with increasing oblique viewing angles. Therefore, these two functions can be used as learnable variables to train the imaging network to a more accurate compensation matrix.

[0102] Step 3) According to the high squint SAR imaging algorithm, the imaging matrix that the network can learn is determined to be the quadratic range compression matrix H2 and the azimuth matched filter function H3, and the RD imaging process is written as a matrix multiplication form Among them F r 、F a are the Fourier transform matrices of the range and azimuth directions, F r -1 、F a -1 is its inverse transformation matrix, S is the echo matrix under large squint conditions, H1 is the range movement correction and compression function H1(f r, τ), H2 is the matrix form of the quadratic range compression and cubic phase compensation function, and H3 is the matrix form of the azimuth compression function. represents the Hadamard product, Θ is the scattering coefficient matrix of the observed scene, and M(S) is the operator form of the imaging algorithm.

[0103] In order to better describe the relationship between learnable parameters and imaging results, the imaging algorithm process of high squint SAR is written into matrix multiplication form by combining equations (2) and (5):

[0104]

[0105] The above imaging algorithm is a reversible process, that is, the original echo data can be obtained by using the inverse process of the imaging. The inverse process is expressed as

[0106]

[0107] Where * represents the matrix conjugation operation, M -1 This is the reverse process of the imaging process (9).

[0108] Step 2: Based on the learnable parameters determined in Step 1, a corresponding imaging network is constructed. Using the two matrices mentioned above as learnable parameters, network learning yields a more accurate imaging matrix than traditional algorithms, thereby improving imaging accuracy and focusing. This imaging method combines the steps of a traditional RD imaging algorithm with the ISTA solution algorithm to construct an imaging network.

[0109] Step 2 specifically includes the following steps:

[0110] Step 1) Based on the learnable imaging matrix determined in step 1, write out its imaging process. Combined with the idea that the SAR imaging problem can be regarded as an inverse problem, the imaging process is solved by the ISTA algorithm. The specific ISTA solution expression is where λ||Θ|| p is the regularization constraint term, λ is the regularization parameter, Expressed as L2 norm, S r is the real echo of high squint SAR, is the estimated scattering coefficient matrix of the observation scene, ||·|| p is the p-norm.

[0111] According to the analysis of equations (9) and (10), SAR imaging can be regarded as an inverse problem with linear solution. The two-dimensional observation model can be obtained by solving the optimization problem

[0112]

[0113] Step 2) The solution process of the ISTA algorithm is deeply expanded into a network form, and the corresponding network sublayers are constructed, namely the residual sublayer, the operator update sublayer, and the nonlinear transformation sublayer;

[0114] Taking the ISTA algorithm to solve equation (11) as an example, the ISTA algorithm is mainly divided into three steps: residual calculation, operator update, and soft threshold iteration. Therefore, in the deep expansion network, the corresponding three sub-network layers are also constructed in the / th layer of the network, which are specifically described as:

[0115] (1) Residual sublayer: denoted by R, this sublayer is used to calculate the residual of the echo signal. In the kth layer of the imaging network, the scene scattering coefficient output by the k-1th layer is used to calculate the residual of the large squint echo signal S r The specific expression is

[0116]

[0117] in represents the residual of the k-th layer network iteration, is the scattering coefficient of the kth layer, k is the number of network layers, S r is the real echo of high squint SAR, M -1 It is the inverse process of the RD imaging algorithm. It should be noted that the M -1 is a variable. When the imaging matrices H2 and H3 change after the error back propagation, M -1 It changes accordingly, while the traditional ISTA is directly determined by the echo signal form.

[0118] (2) Operator update sublayer: denoted by P. The input of this sublayer is the residual calculated by the residual layer and acts on M. The specific expression is:

[0119]

[0120]

[0121] in, is the residual between the scene scattering coefficient matrices, is the residual between the true echo signal and the estimated echo signal calculated by the residual sublayer (which can be calculated by the above formula (12) ), P (k) is the operator after update, is the scene scattering coefficient estimated at the kth layer ( is the output of each layer of the network), β is the iteration step size. In each iteration of traditional ISTA, the value of β is fixed, but it is a learnable parameter in the imaging network.

[0122] (3) Nonlinear transformation sublayer: denoted by F, this subnetwork layer is used to reflect the nonlinear mapping ability of the imaging network, and the P obtained by the operator update layer is (k) Perform nonlinear transformation to obtain the nonlinear mapping capability of high squint SAR echo signal to scene scattering coefficient, and output the scene scattering coefficient of the next layer at the same time The specific expression is

[0123]

[0124] F(P (k) ;λ,T)=soft(P (k) ;λ,T)=sign(P (k) )·(|P (k) |-T) (16)

[0125] Where F(.) is the nonlinear transformation function of the imaging network, which is usually set to the soft threshold function soft(·) (see "Two-step Iterative Shrinkage Thresholding Algorithms for Image Restoration", IEEE Transactions on Image Processing, 2007, 16(12): 2992-3004.), soft(P (k) ;λ,T) is the soft threshold function related to the regularization parameter λ. The specific expression of the soft threshold function is generally the sign function sign(·). In the constructed imaging network, it is directly used as the activation function of the nonlinear transformation layer. T is the iteration threshold. In formula (16), the sign function first calculates the sign of the first bracketed term and then multiplies the sign calculation result with the second bracketed term. The parameters that can be learned in this network layer can be the iteration threshold T and the regularization parameter λ.

[0126] In summary, the constructed single-layer topology of the high-squint SAR LRD imaging network consists of three sub-network layers: a residual layer, an operator update layer, and a nonlinear transformation layer. The learnable parameter set is Ω = {H2, H3, β, T, λ}. It should be noted that during network training, to reduce the size of the network learning parameters, the imaging matrices H2 and H3 only change after one round of backpropagation training, while the iterative parameters β, T, and λ are variable within each layer.

[0127] Step 3) Construct an echo training sample set. The present invention uses an ideal random point scattering model and generates high-squint SAR echoes based on the observation model of high-squint SAR. System environmental noise is added to generate a large number of echo data samples without changing the SAR imaging model.

[0128] In terms of echo sample generation, since sample generation is a pre-processing before training and testing and can be completed offline, the accuracy of sample generation is more important than time cost and computational burden. At the same time, since completely accurate real scattering information is difficult to obtain, it is difficult to establish an effective sample set based on actual measurement data. In order to obtain a more accurate echo sample set, the present invention adopts an ideal random point scattering model and generates a large squint SAR echo according to the echo signal model of formula (2), adds system environmental noise, and generates a large number of echo data samples without changing the SAR imaging model. Set the number of echo samples to N, and the real echo sample set S n ={S1, S2, S3, ..., S N}, where n=1, 2, ..., N is the echo sample sequence number.

[0129] Step 4) The mean square error (MSE) is used as the loss function to implement unsupervised training of the high-squint SAR imaging network. The network is optimized using the Adam optimization algorithm based on stochastic gradient descent. During the final imaging, the imaging matrices H2 and H3 learned by the network, as well as the iteration step size, regularization parameter, and iteration threshold are input as fixed values ​​into the imaging network. The imaging process is then transformed into a feedforward operation of the network, which can directly output the imaging results.

[0130] After the echo sample set is constructed, unsupervised learning is realized by designing a loss function. When the network is back-propagated, the difference between the network output and the actual scene scattering coefficient cannot be directly measured because of the unsupervised learning. Instead, the estimated scene scattering coefficient obtained by the last layer of the network is directly used to act on M. -1 , get the estimated value of SAR echo and compare it with the real echo. The expression of the echo estimate is shown in formula (17), and the loss function is set to mean square error function (MSE), and the specific expression is shown in formula (18)

[0131]

[0132]

[0133] in, =(Ω) / (Ω) represents the nth estimated high-squint SAR echo, where n is the sequence number of the echo sample, ranging from n = 1, 2, ..., N. Equation (17) yields the estimated nth high-squint SAR echo. Loss(Ω) is the loss function of the learnable parameter set Ω (the learnable parameter set Ω is obtained in step (2) in step 2). Here, Ω = arg min(Loss(Ω)) is used to obtain a more accurate learnable parameter set after the network converges.

[0134] Example: Simulation experiment of SAR high-squint high-resolution imaging algorithm based on deep learning

[0135] Simulation experiment: In order to verify the effectiveness of the method of the present invention, a two-dimensional imaging simulation is performed with point targets and real scene targets as models. The transmitted signal is a linear frequency modulation signal. The corresponding radar parameters and network parameters are shown in Table 1.

[0136] Table 1 Radar parameters and network parameters

[0137]

[0138] Simulation 1: First, the imaging performance of point targets in a noisy environment is verified. The imaging mode is a strip mode, and the observation scene contains several target scattering points. In terms of generating training samples and test samples, 1000 echo samples are generated by adding random additive Gaussian white noise. The signal-to-noise ratio range is -15dB to 30dB, and 80% of the samples are randomly selected as training samples and 20% as test samples. In the training stage, for the initialization of network parameters, the imaging matrices H2 and H3 are initialized according to formula (9), and Θ0 is further obtained. The iterative parameters are initialized to λ0 = 0.8, β0 = 0.8, T0 = 0.5, and the initialization parameter set Ω0 is obtained. The learning rate is set to η = 0.001, the batch size is set to 8, the number of training epochs for the entire sample set is set to 1000, and the training sample N train =700. In the testing phase, the test sample is N test = 100, and the final imaging result is averaged over the test sample set. During final imaging, the imaging matrices H2 and H3 learned by the network, along with the iteration step size, regularization parameter, and iteration threshold, are input into the imaging network as fixed values. This transforms the imaging process into a network feedforward operation, directly outputting the imaging result. Assuming the radar operates in the X-band (0.03 m) and the point target is 30 m away in both range and azimuth, Figure 6 shows the point target imaging results of the proposed algorithm at a 45° slant viewing angle and a 15 dB signal-to-noise ratio.

[0139] Simulation 2: To verify the effectiveness of the proposed method, we analyze the imaging performance of the proposed method by taking cross-sections in both the range and azimuth directions of the central point target in Simulation 1. Figure 7 and Table 2 compare the imaging performance of different algorithms, demonstrating that the proposed method significantly improves imaging performance compared to other algorithms.

[0140] Table 2 Comparison of imaging quality evaluation index results

[0141]

[0142] Simulation 3: To further verify the imaging performance and quality of the proposed method, a simulation of a surface ship target captured by Radarsat-1 is performed. Figure 8 compares the results of the three algorithms under different squint angles for the measured scene. It can be seen that all three algorithms are able to image the target area, but the proposed method achieves higher reconstruction accuracy and better background noise suppression than the other two algorithms. Table 3 compares the image entropy of the surface ship target SAR image obtained by the three algorithms, further verifying the effectiveness of the proposed method in improving SAR imaging performance under high squint conditions.

[0143] Table 3 Comparison of SAR image entropy of sea surface ship targets

[0144]

[0145] The proposed high-resolution imaging algorithm for high-squint SAR (SAR) based on deep unrolled network learning eliminates the need to construct complex compensation functions or pulse compression functions. Instead, it iteratively obtains the function using a deep network. This method places low demands on radar performance, thereby reducing imaging costs. This method can achieve rapid and accurate imaging for the same model of spaceborne SAR or airborne SAR performing a specific mission, provided its radar imaging parameters are essentially fixed. Simulation results for point and scene targets demonstrate that the proposed method effectively suppresses sidelobes, improves imaging accuracy and computational efficiency, and meets the imaging requirements of SAR at high squint angles.

Claims

1. A high-resolution imaging method for high-squint SAR based on a deep unfolding network, characterized in that: The following steps are involved: Step 1: Construct a high-squint SAR echo signal observation model to determine the imaging matrix that the imaging network needs to learn. First, perform a Taylor series expansion on the instantaneous slant range expression based on the traditional imaging algorithm, perform range motion correction on the echo data in the range frequency domain, and then perform range compression on the echo signal after motion correction to obtain a range-compressed signal. This determines that the matrices that the imaging network needs to learn are quadratic range compression, cubic phase compensation matrix, and azimuth compression matrix. This includes the following steps: Step 1) Construct a high squint SAR echo signal observation model, and perform Taylor series expansion on the distance between the radar and the target according to the traditional imaging algorithm to obtain the approximate distance R B (τ; R c ), where τ is the slow time variable, R B (τ; R c ) The distance R from the radar to the center of the observation scene c , speed and oblique angle, and calculate the echo delay τ a =2R B (τ; R c ) / c, c is the electromagnetic wave speed; Step 2) The echo signal S obtained by the platform r (t, τ; R c ) Perform FFT in the range direction to obtain the echo signal in the range frequency domain, construct the movement compensation function and the range compression function H1 to reduce the coupling degree in the range / azimuth direction, and obtain the compressed echo signal S r′ (f r ,τ1;R c ), where t is the fast time variable, f r is the distance-to-frequency domain, equivalent slow time series At this time, the Doppler center frequency of the echo signal after movement correction and range compression is moved to zero frequency, so the center line of the radar transmit beam is located in the zero Doppler plane; Step 3) According to the high squint SAR imaging algorithm, the imaging matrix that the network can learn is determined to be the quadratic range compression matrix H2 and the azimuth matched filter function H3, and the RD imaging process is written as a matrix multiplication form Among them F r 、F a are the Fourier transform matrices of range and azimuth, respectively. is its inverse transformation matrix, S is the echo matrix under large squint conditions, H1 is the range movement correction and compression function H1(f r , τ), H2 is the matrix form of the quadratic range compression and cubic phase compensation function, and H3 is the matrix form of the azimuth compression function. represents the Hadamard product, Θ is the scattering coefficient matrix of the observed scene, and M(S) is the operator form of the imaging algorithm; Step 2: Based on the learnable parameters determined in step 1, a corresponding imaging network is constructed. The above two matrices are used as learnable parameters. Through network learning, an imaging matrix that is more accurate than the traditional algorithm is obtained, thereby improving imaging accuracy and focusing effect. The imaging method combines the traditional RD imaging algorithm steps and the ISTA solution algorithm to construct an imaging network.

2. The method for high-resolution SAR imaging based on a deep unfolding network according to claim 1, wherein: Step 1 specifically includes the following steps: Step 1) Construct a high squint SAR echo signal observation model, and perform Taylor series expansion on the distance between the radar and the target according to the traditional imaging algorithm to obtain the approximate distance R B (τ; R c ), where τ is the slow time variable, R B (τ; R c ) The distance R from the radar to the center of the observation scene c , speed and oblique angle, and calculate the echo delay τ a =2R B (τ; R c ) / c, c is the electromagnetic wave speed; specifically as follows: In the positional relationship between the SAR high squint imaging system and the observation scene, the height of the platform is h, the squint angle is θ0, and it is assumed that the platform moves in a uniform straight line with a speed of V r , R0 is the shortest distance between the flight path and the center of the observation scene, R B (t, τ; R0) is the instantaneous slant distance between the platform and the point target, where t is the fast time variable and τ is the slow time variable. The geometric relationship between the SAR platform and the point target is established through the relationship between the instantaneous slant distance and the slow time. The coordinate origin O is set as the starting point of the slow time, and the slow time-slant distance rectangular coordinate system is established. At this time, the beam center ray and the line passing through point P and parallel to the route intersect at point A. Point A is also the starting point of the slow time. t0 is the moment when the beam center passes through. According to the cosine theorem, the instantaneous slant distance between the platform and the point target P is Where Y n Expressed as the distance between point target P and point A; Assume that the radar transmits a linear frequency modulation signal LFM with a modulation frequency of K r , the pulse width is T p , then the baseband echo signal received by the platform is Where ζ is the radar operating wavelength, rect(·) is its envelope, τ a =2R B (τ, R c ) / c is the echo delay; K r is the modulation frequency of the linear frequency modulation signal; R B (τ; R c ) is expanded by Taylor series to obtain From formula (3), we can see that the linear term is the range movement term, and the high-order term is the range curvature term. When the squint angle is large enough, the value of the high-order term is very small, so the influence of range curvature on the envelope can be ignored. Combining formulas (2) and (3), we can see that the range curvature term and the radar wavelength are at the same order of magnitude, so the influence of range curvature on the echo phase cannot be ignored. Step 2) The echo signal S obtained by the platform r (t, τ; R c ) Perform FFT in the range direction to obtain the echo signal in the range frequency domain, construct the movement compensation function and the range compression function H1 to reduce the coupling degree in the range / azimuth direction, and obtain the compressed echo signal S r′ (f r ,τ1;R c ), where t is the fast time variable, f r is the distance-to-frequency domain, equivalent slow time series At this time, the Doppler center frequency of the echo signal after movement correction and range compression is moved to zero frequency, so the center line of the radar transmit beam is located in the zero Doppler plane; the details are as follows: Next, the echo signal is transformed into the range frequency domain, the signal envelope in two dimensions is ignored, and range movement correction and range pulse compression are performed on it. The movement error is ΔR w =V r τsinθ0 (4) The constructed distance movement compensation and compression function is Where, f r is the range frequency domain, f0 is the radar operating frequency; The echo signal obtained after the above operation is Among them, R D (τ1, R c ) is the instantaneous slant distance equivalent to the distance movement and compression, and τ1 is the slow time series equivalent to the distance movement and compression, as follows: The above two functions are used as learnable variables to allow the imaging network to learn and train a more accurate compensation matrix; Step 3) According to the high squint SAR imaging algorithm, the imaging matrix that the network can learn is determined to be the quadratic range compression matrix H2 and the azimuth matched filter function H3, and the RD imaging process is written as a matrix multiplication form Among them F r 、F a are the Fourier transform matrices of range and azimuth, respectively. is its inverse transformation matrix, S is the echo matrix under large squint conditions, H1 is the range movement correction and compression function H1(f r , τ), H2 is the matrix form of the quadratic range compression and cubic phase compensation function, and H3 is the matrix form of the azimuth compression function. represents the Hadamard product, Θ is the observed scene scattering coefficient matrix, and M(S) is the operator form of the imaging algorithm; specifically: Combining equations (2) and (5), the imaging algorithm process of high squint SAR can be expressed as matrix multiplication form: The original echo data is obtained by the inverse process of imaging. The inverse process is expressed as Where * represents the matrix conjugation operation, M -1 This is the reverse process of the imaging process (9).

3. The high-resolution imaging method for high-squint SAR based on a deep unfolding network according to claim 2, wherein: Step 2 specifically includes the following steps: Step 1) Based on the learnable imaging matrix determined in step 1, write out its imaging process. Combined with the idea that the SAR imaging problem can be regarded as an inverse problem, the imaging process is solved by the ISTA algorithm. The specific ISTA solution expression is where λ||Θ|| p is the regularization constraint term, λ is the regularization parameter, Expressed as L2 norm, S r is the real echo of high squint SAR, is the estimated scattering coefficient matrix of the observation scene, ||·|| p is the p-norm; specifically: According to the analysis of formula (9) and (10), SAR imaging is regarded as an inverse problem of linear solution, and the two-dimensional observation model is obtained by solving the optimization problem Step 2) Expand the solution process of the ISTA algorithm into a network form and construct the corresponding network sublayers, namely the residual sublayer, the operator update sublayer, and the nonlinear transformation sublayer; the details are as follows: In the process of solving Equation (11) using the ISTA algorithm, the ISTA algorithm is divided into three steps: residual calculation, operator update, and soft threshold iteration. Therefore, in the deep expansion network, the corresponding three sub-network layers are also constructed in the / th layer of the network, which are specifically described as: (1) Residual sublayer: denoted by R, this sublayer is used to calculate the residual of the echo signal. In the kth layer of the imaging network, the scene scattering coefficient output by the k-1th layer is used to calculate the residual of the large squint echo signal S r The specific expression is in represents the residual of the k-th layer network iteration, is the scattering coefficient of the kth layer, k is the number of network layers, S r is the real echo of high squint SAR, M -1 It is the inverse process of RD imaging algorithm; M in the deep expansion network -1 is a variable. When the imaging matrices H2 and H3 change after the error back propagation, M -1 Changes followed; (2) Operator update sublayer: denoted by P. The input of this sublayer is the residual calculated by the residual layer and acts on M. The specific expression is: in, is the residual between the scene scattering coefficient matrices, is the residual between the true echo signal and the estimated echo signal calculated by the residual sublayer, P (k) is the operator after update, is the scene scattering coefficient estimated at the kth layer β is the iteration step size and is a learnable parameter; (3) Nonlinear transformation sublayer: denoted by F, this subnetwork layer is used to reflect the nonlinear mapping ability of the imaging network, and the P obtained by the operator update layer is (k) Perform nonlinear transformation to obtain the nonlinear mapping capability of high squint SAR echo signal to scene scattering coefficient, and output the scene scattering coefficient of the next layer at the same time The specific expression is F(P (k) ;λ,T)=soft(P (k) ;λ,T) (16) Among them, F(.) is the nonlinear transformation function of the imaging network, which is set as the soft threshold function soft(·), soft(P (k) ; λ, T) is the soft threshold function related to the regularization parameter λ. In the constructed imaging network, it is directly used as the activation function of the nonlinear transformation layer, and T is the iteration threshold. The learnable parameters of this network layer can be the iteration threshold T and the regularization parameter λ. In summary, the constructed high squint SAR LRD imaging network has a single-layer topology consisting of three sub-network layers: a residual layer, an operator update layer, and a nonlinear transformation layer. The learnable parameter set is Ω = {H2, H3, β, T, λ}. During network training, to reduce the scale of network learning parameters, the imaging matrices H2 and H3 only change after one round of back-propagation training, while the iterative parameters β, T, and λ are variable in each layer. Step 3) Construct an echo training sample set. This method uses an ideal random point scattering model and a high-squint SAR observation model to generate high-squint SAR echoes. System environmental noise is added to generate a large number of echo data samples without changing the SAR imaging model. The details are as follows: The ideal random point scattering model is used to generate high squint SAR echoes according to the echo signal model of formula (2). The system environmental noise is added to generate a large number of echo data samples without changing the SAR imaging model. The number of echo samples is set to N, and the real echo sample set S is n ={S1, S2, S3, ..., S N }, where n=1, 2, ..., N is the echo sample sequence number; Step 4) Use the mean square error (MSE) as the loss function to implement unsupervised training of the high squint SAR imaging network. The network is optimized using the Adam optimization algorithm based on stochastic gradient descent. During the final imaging, the imaging matrices H2 and H3 learned by the network, the iteration step size, the regularization parameter, and the iteration threshold are input as fixed values ​​into the imaging network. The imaging process is then transformed into a feedforward operation of the network, which can directly output the imaging results. The details are as follows: Directly use the estimated scene scattering coefficient obtained from the last layer of the network to act on M -1 , get the estimated value of SAR echo and compare it with the real echo; the expression of the echo estimate is shown in formula (17), and the loss function is set to the mean square error function MSE, and the specific expression is shown in formula (18) in, represents the nth estimated high squint SAR echo, n is the sequence number of the echo sample, and its range is n = 1, 2, ..., N. Equation (17) obtains the estimated nth high squint SAR echo; Loss(Ω) is the loss function of the learnable parameter set Ω; here Ω = arg min(Loss(Ω)) is to obtain a more accurate learnable parameter set after the network converges.

4. The method for high-resolution SAR imaging based on a deep unfolding network according to claim 3, wherein: In step 2), the specific expression of the soft threshold function soft(·) is the sign function sign(·) F(P (k) ;λ,T)=soft(P (k) ;λ,T)=sign(P (k) )·(|P (k) |-T) (16-1) In formula (16-1), the sign function first performs a sign calculation on the first bracketed term, and then multiplies the sign calculation result by the second bracketed term.

Images