Real-aperture scanning radar forward-looking super-resolution imaging method based on non-convex sparsity and generalized total variation joint constraint

Abstract

The present application belongs to the field of radar signal processing and radar imaging technology, and proposes a real-aperture scanning radar forward-looking super-resolution imaging method based on non-convex sparse and generalized total variation joint constraint: the system parameters of the real-aperture scanning radar forward-looking imaging are initialized, and the radar forward-looking scanning echo data are obtained; the radar forward-looking scanning echo data are sequentially subjected to range direction pulse compression and range migration correction; the range direction echo data of the target are extracted, and a range direction convolution observation model is established; a non-convex sparse constraint and generalized total variation joint regularization optimization problem is constructed; the non-convex sparse constraint and generalized total variation joint regularization optimization problem is solved, the target scattering coefficient estimation result is obtained, and the radar forward-looking super-resolution imaging result is output. The present application can simultaneously consider the super-resolution recovery ability of point-like scattering targets and the structure maintaining ability of extended targets, and improves the stability and reconstruction precision of the real-aperture scanning radar forward-looking super-resolution imaging.

Description

Technical Field

[0001] This invention relates to the field of radar signal processing and radar imaging technology, and particularly to a real aperture scanning radar forward-looking super-resolution imaging method based on joint constraints of non-convex sparsity and generalized total variation. Background Technology

[0002] Real aperture scanning radar (LAS) forward-looking imaging is widely used in airborne detection, ground surveillance, target recognition, and complex scene perception. Unlike side-looking synthetic aperture radar (SAR), forward-looking imaging geometry provides weak target Doppler information, making it difficult for traditional SAR methods to directly achieve high azimuth resolution. Furthermore, the azimuth resolution of LAS is limited by antenna aperture size and beamwidth, resulting in significant azimuth echo broadening, which fails to meet high-resolution imaging requirements. Therefore, improving the angular resolution of LAS through signal processing methods without increasing hardware aperture or system complexity is a crucial research challenge in radar forward-looking imaging.

[0003] From an imaging model perspective, the azimuth echo of a real-aperture scanning radar can typically be approximated as a convolution relationship between the target scattering coefficient distribution and the antenna pattern. Due to the wide main lobe and side lobes of the antenna pattern, and the strong correlation between the system responses of adjacent azimuth cells, the resulting convolution measurement matrix often exhibits significant ill-conditioning. Directly employing least-squares or pseudo-inverse methods for target scattering coefficient inversion can easily lead to problems such as noise amplification, spurious peak enhancement, main lobe broadening, and unstable reconstruction results. Therefore, existing research typically transforms the radar forward-looking super-resolution imaging problem into a regularized deconvolution problem, introducing prior constraints to improve inversion stability and imaging resolution. The paper "Tuo X, Mao D, Zhang Y, Zhang Y, Huang Y, Yang J. Radar Forward-Looking Super-Resolution Imaging Using a Two-Step Regularization Strategy[J]. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 2023, 16" proposes a two-step regularization strategy for radar forward-looking super-resolution imaging. This strategy transforms the forward-looking imaging problem into a regularized deconvolution problem and improves target reconstruction through staged constraints. While this method can address the insufficient resolution of traditional forward-looking imaging, the two-step processing still requires designing regularization parameters for different scenarios, and there is still room for improvement in its ability to uniformly model point scattering and extended target structures. The paper "Tan K, Zhou S, Lu X, Yang J, Su W, Gu H. RealAperture Radar Super-Resolution Imaging for Sea Surface Monitoring Based on a Hybrid Model[J]. Sensors, 2023, 23(23): 9609" proposes a real-aperture radar super-resolution imaging method for sea surface monitoring scenarios. This method incorporates factors such as sea clutter and noise into the modeling framework to improve the imaging capability of real-aperture radar in complex sea surface scenarios. The method demonstrates that super-resolution technology can effectively improve the azimuth resolution of real-aperture scanning radar; however, target scattering structure, edge contour preservation, and recovery of locally continuously changing regions in complex scenarios remain important factors affecting imaging quality.The paper “Chartrand R. Exact Reconstruction of Sparse Signals via Nonconvex Minimization[J]. IEEE Signal Processing Letters, 2007, 14(10): 707-710” studies the sparse signal reconstruction problem based on nonconvex minimization, and points out that compared with the traditional L1 norm, the L1 norm is used. q Non-convex sparse constraints of the form (q<1) can achieve accurate reconstruction of sparse signals with fewer observations under certain conditions. This type of non-convex sparse constraint has a stronger compression effect on small-amplitude components and a relatively weaker penalty on large-amplitude components, making it suitable for improving the sparse recovery capability of radar point-scattering targets and adjacent narrow-peak targets. However, relying solely on sparse constraints is insufficient to effectively maintain the continuous contour and regional structure of extended targets. The literature “Rudin LI, Osher S, Fatemi E. Nonlinear TotalVariation Based Noise Removal Algorithms[J]. Physica D: Nonlinear Phenomena,1992, 60(1-4): 259-268” proposes a classic total variational regularization method, which achieves noise suppression and edge preservation by constraining the image gradient. Total variational regularization is widely used in image restoration and super-resolution reconstruction, and can preserve target edge information to a certain extent. However, traditional total variational methods are inherently more suitable for piecewise constant signals. For continuously varying regions commonly found in radar extended targets, they are prone to a staircase effect, causing the target's internal structure to be reconstructed as an unnatural piecewise constant shape. The literature "Bredies K, Kunisch K, Pock T. Total Generalized Variation[J].SIAM Journal on Imaging Sciences, 2010, 3(3): 492-526." proposes a generalized total variational regularization method, which introduces higher-order derivative information on the basis of the first-order gradient constraint of traditional total variation. This method can better describe the smooth variation structure inside the region while maintaining the edge abrupt change characteristics, thereby reducing the staircase effect of traditional total variational methods. This method provides an effective approach to preserving the structure of radar extended targets, but if the generalized total variational constraint is used alone, the sparse recovery capability for point-scattering targets and adjacent narrow-peak targets is still limited.

[0004] In summary, existing real-aperture scanning radar forward-looking super-resolution imaging methods still have the following shortcomings: First, direct inversion methods are sensitive to noise, easily leading to unstable reconstruction results; second, traditional L1 sparse regularization methods are prone to amplitude contraction of strong scattering components, affecting the accuracy of target scattering intensity estimation; third, traditional total variational regularization methods are prone to step effects in continuously varying regions, making it difficult to accurately recover the internal structure of extended targets; fourth, a single regularization constraint cannot simultaneously consider the super-resolution recovery capability of point targets and the structure preservation capability of extended targets. Therefore, it is necessary to propose a real-aperture scanning radar forward-looking super-resolution imaging method based on joint constraints of non-convex sparse and generalized total variational constraints, simultaneously introducing sparse priors and structure priors within a unified optimization framework, thereby improving the resolution, structure preservation capability, and reconstruction stability of radar forward-looking imaging. Summary of the Invention

[0005] The purpose of this invention is to provide a forward-looking super-resolution imaging method for real aperture scanning radar based on joint constraints of non-convex sparsity and generalized total variation. This method can solve the problems in existing forward-looking super-resolution imaging methods for real aperture scanning radar, such as the difficulty of maintaining the continuous structure of extended targets by a single sparsity constraint, the tendency of a single total variation constraint to produce a staircase effect, and the insufficient ability to recover the sparsity of point scattering targets. Furthermore, it can improve the ability to maintain the structure of extended targets while improving the resolution of point scattering targets.

[0006] The technical solution adopted by this invention to solve its technical problem is as follows:

[0007] A forward-looking super-resolution imaging method for real aperture scanning radar based on joint constraints of non-convex sparsity and generalized total variation includes the following steps:

[0008] The parameters of the real aperture scanning radar forward-looking imaging system are initialized, and radar forward-looking scan echo data are acquired.

[0009] The radar forward-looking scan echo data are sequentially subjected to range pulse compression and range migration correction.

[0010] For the migration-corrected echo data, azimuth echo data is extracted within the range cell where the target is located, and an azimuth convolution observation model is established;

[0011] Based on the azimuth-oriented convolutional observation model, a joint regularization optimization problem of non-convex sparse constraints and generalized total variation is constructed.

[0012] The joint regularization optimization problem of non-convex sparse constraints and generalized total variation is solved to obtain the target scattering coefficient estimation results;

[0013] The radar forward-looking super-resolution imaging results are output based on the target coefficient estimation results.

[0014] In some embodiments, initializing the parameters of the real aperture scanning radar forward-looking imaging system includes:

[0015] Establish a forward-looking imaging geometric model of the moving platform radar. Assume that the radar platform is at a height of H above the ground, the platform moves along the positive Y-axis at a constant speed v, and the antenna beam scans in the azimuth direction at an angular velocity ω.

[0016] Let the initial slant distance of the target point at the initial time be R0, the initial spatial azimuth angle between the target and the Y-axis be θ0, and the slow time be t;

[0017] Based on the geometric relationship between the motion platform and the target point, the distance history of the target point at slow time t is obtained:

[0018] ;

[0019] Performing a Taylor expansion on the distance history around t=0 yields an approximate expression for the distance history:

[0020] ;

[0021] in, This represents a third-order or higher-order term with respect to slow time t.

[0022] In some embodiments, the distance-oriented pulse compression includes:

[0023] Let τ represent the range-long time and t represent the azimuth-slow time, then the linear frequency modulated signal transmitted by the radar can be expressed as:

[0024] ;

[0025] Among them, f c For carrier frequency, K r T is the frequency modulation slope. p Where is the pulse width, and rect(·) is the rectangular window function;

[0026] The received echo signal is quadrature demodulated to obtain the baseband echo signal. A matched filter is then constructed based on the baseband form of the transmitted signal, as shown below:

[0027] ;

[0028] The baseband echo signal is transformed to the range frequency domain, multiplied by the frequency domain response of the matched filter, and then subjected to an inverse Fourier transform to obtain the range-compressed echo signal, the approximate expression of which is:

[0029] ;

[0030] Where u(R0,θ0) represents the target scattering coefficient, ha (·) represents the antenna pattern, B represents the signal bandwidth, c represents the electromagnetic wave propagation speed, λ represents the carrier wavelength, and R(t) represents the instantaneous slant range of the target.

[0031] After range pulse compression, the target echo is compressed in the range direction to a position centered on the target's instantaneous slant range R(t).

[0032] In some embodiments, the distance migration correction includes:

[0033] Based on the target point's distance history, the target's distance migration relative to the initial time within slow time t is defined as:

[0034] ;

[0035] Under the condition that the distance between the radar platform and the target is much greater than the platform displacement during the beam dwell time and the scanning azimuth angle is small, ignoring the higher-order terms in the range history, we obtain an approximate expression for the range migration:

[0036] ;

[0037] When the range migration amount is greater than the range resolution unit, it is determined that the target echo has experienced range migration, wherein the range migration criterion is:

[0038] ;

[0039] Based on the time-shift property of Fourier transform, a distance migration correction phase compensation factor is constructed:

[0040] ;

[0041] Will Substituting, we get:

[0042] ;

[0043] The range-compressed echo signal is transformed to the range frequency domain, multiplied by the range migration correction phase compensation factor, and then subjected to an inverse Fourier transform to obtain the range migration-corrected echo signal.

[0044] ;

[0045] In the formula, f τ Indicates distance frequency;

[0046] After range migration correction, the echo energy of the same target at different slow times is aligned to the initial reference range cell.

[0047] In some embodiments, the step of extracting azimuth echo data within the target's range cell from the migration-corrected echo data and establishing an azimuth convolutional observation model includes:

[0048] Within a fixed range cell, the azimuth echo can be approximated as a convolution relationship between the target scattering coefficient distribution and the antenna pattern:

[0049] ;

[0050] In the formula, y(θ) represents the azimuth echo signal, x(θ) represents the target scattering coefficient distribution, h(θ) represents the antenna pattern function, n(θ) represents additive noise, and * represents convolution operation;

[0051] Discretizing the azimuth convolution relationship yields the discrete azimuth convolution observation model:

[0052] y = Hx + n;

[0053] Where H represents the convolutional measurement matrix, and y, x, and n represent the discretized azimuth echo observation vector, target scattering coefficient vector, and noise vector, respectively. Specifically, y, x, and n are expressed as follows:

[0054] ;

[0055] ;

[0056] ;

[0057] The convolution measurement matrix H is composed of antenna pattern sampling vectors, which are expressed as follows:

[0058] ;

[0059] In the formula, L represents the number of sampling points corresponding to the coverage area of ​​the antenna main lobe, N represents the azimuth discrete dimension of the scene to be reconstructed, and M represents the sampling dimension of the observed echo, and satisfies:

[0060] M = N + L - 1;

[0061] Based on the beam scanning imaging relationship, we have:

[0062] ;

[0063] ;

[0064] In the formula, Ω represents the angular domain range covered by the antenna scan, and θ b ω represents the antenna beamwidth, ω represents the scanning speed, and PRF represents the pulse repetition frequency.

[0065] In some embodiments, the construction of a joint regularized optimization problem based on the azimuth-oriented convolutional observation model, involving non-convex sparse constraints and generalized total variation, includes:

[0066] Based on the aforementioned discrete azimuth convolutional observation model, the radar forward-looking super-resolution imaging inversion problem is expressed as a regularized optimization problem, which is as follows:

[0067] ;

[0068] in, For data fidelity items, λ is the regularization term, and λ is the regularization parameter;

[0069] Introducing non-convex L q The sparse constraint is used as the first regularization term, and the non-convex L q Sparse constraints are represented as:

[0070] ;

[0071] In the formula, x i Let represent the i-th element in the target scattering coefficient vector x, and q be a non-convex sparse control parameter;

[0072] Introducing a generalized total variation constraint as the second regularization term, the generalized total variation constraint is expressed as:

[0073] ;

[0074] In the formula, D represents the discrete difference operator, v represents the auxiliary variable, and α1 and α0 are used to adjust the first-order structural constraint and the higher-order smoothing constraint, respectively.

[0075] The data fidelity item, non-convex L q A weighted combination of sparse constraints and generalized total variational constraints yields a joint regularized optimization problem of nonconvex sparse and generalized total variational constraints, which is expressed as:

[0076] ;

[0077] In the formula, λ1 is the regularization parameter of the non-convex sparse constraint, and λ2 is the regularization parameter of the generalized total variation constraint.

[0078] In some embodiments, an alternating iterative optimization method with variable splitting is used to solve the joint regularization optimization problem of non-convex sparse constraints and generalized total variation to obtain the target scattering coefficient estimation results;

[0079] The method employs an alternating iterative optimization approach with variable splitting to solve the joint regularized optimization problem involving non-convex sparse constraints and generalized total variation, obtaining the target scattering coefficient estimation results, including:

[0080] The non-convex sparse constraint and generalized total variational joint regularized optimization problem is equivalently split, and auxiliary variables z1, z2, and z3 corresponding to the structural constraints and sparse constraints are introduced, and z1 = Dx - v, z2 = Dv, and z3 = x are set.

[0081] The original problem is transformed into the following constrained optimization problem:

[0082] ;

[0083] By constructing an equivalent optimization function with a penalty term and alternately updating the main variable, auxiliary variable, and Lagrange multiplier, the iterative solution of the joint regularization optimization problem is achieved.

[0084] In some embodiments, the equivalent optimization function with a penalty term is expressed as:

[0085] ;

[0086] In the formula, u1, u2, u3 are scaled Lagrange multipliers, and ρ1, ρ2, ρ3 are penalty parameters.

[0087] In some embodiments, the alternating update of the main variable, auxiliary variable, and Lagrange multiplier refers to:

[0088] In the (k+1)th iteration, with the other variables fixed, the update formula for the main variable x is:

[0089] ;

[0090] The update formula for the auxiliary variable v is:

[0091] ;

[0092] For the auxiliary variables z1 and z2 related to the generalized total variation, their subproblems are updated using a threshold shrinkage method, where the threshold shrinkage function is defined as:

[0093] ;

[0094] Therefore, the update formulas for z1 and z2 are as follows:

[0095] ;

[0096] For non-convex L q The sparsely correlated auxiliary variable z3 is updated using a non-convex sparse thresholding method for its subproblems:

[0097] ;

[0098] In the formula, Represents a non-convex sparse thresholding function;

[0099] After updating the main variables and auxiliary variables, the Lagrange multipliers are updated, as shown below:

[0100] ;

[0101] ;

[0102] .

[0103] In some embodiments, after each iteration, it is determined whether the iteration termination condition has been met;

[0104] The iteration termination condition refers to the relative error between two consecutive target scattering coefficient estimation results, which is expressed as:

[0105] ;

[0106] When the above iteration termination condition is met, or the number of iterations reaches the preset maximum number of iterations, the iteration stops, and the current iteration result is used as the final estimated value of the target scattering coefficient, which is expressed as:

[0107] .

[0108] The beneficial effects of this invention are as follows: Based on the azimuth convolutional observation model of forward-looking imaging in a real-aperture scanning radar, this invention simultaneously introduces non-convex sparsity constraints and generalized total variational constraints to construct a joint regularized optimization problem. This allows for the simultaneous consideration of the sparse recovery capability of point-scattering targets and the structure preservation capability of extended targets within the same inversion framework. Specifically, the non-convex sparsity constraints reduce the amplitude contraction of strong scattering components caused by traditional sparsity constraints, thereby improving the super-resolution recovery capability of point targets and adjacent narrow-peak targets. The generalized total variational constraints preserve the edge contours and continuously changing structures of extended targets, thus mitigating the step effect easily generated by traditional total variational constraints. Therefore, this invention can improve the stability, noise resistance, and reconstruction accuracy of forward-looking super-resolution imaging in real-aperture scanning radar, obtaining clearer, more continuous imaging results with better structure preservation. Attached Figure Description

[0109] Figure 1 This is a flowchart of the real aperture scanning radar forward-looking super-resolution imaging method based on the joint constraints of non-convex sparsity and generalized total variation in Embodiment 1 of the present invention.

[0110] Figure 2 This is a schematic diagram of the forward-looking imaging geometric model of the motion platform radar in Embodiment 1 of the present invention;

[0111] Figure 3This is a schematic diagram of the simulated original target scene in Embodiment 2 of the present invention;

[0112] Figure 4 This is a schematic diagram of the real beam echo after range pulse compression and range migration correction in Embodiment 2 of the present invention;

[0113] Figure 5 This is a schematic diagram showing the result of two-dimensional extended target super-resolution imaging using the L2 regularization method in Embodiment 2 of the present invention;

[0114] Figure 6 This is a schematic diagram illustrating the results of two-dimensional extended target super-resolution imaging using the TV regularization method in Embodiment 2 of the present invention.

[0115] Figure 7 This is a schematic diagram of the results of two-dimensional extended target super-resolution imaging using the L1-TV regularization method in Embodiment 2 of the present invention;

[0116] Figure 8 This is a schematic diagram of the results of two-dimensional extended target super-resolution imaging using the L2-TV regularization method in Embodiment 2 of the present invention;

[0117] Figure 9 L is used in Embodiment 2 of the present invention q -A schematic diagram of the results of two-dimensional extended target super-resolution imaging using the TV regularization method;

[0118] Figure 10 This is a schematic diagram showing the result of two-dimensional extended target super-resolution imaging using the method proposed in Example 1 in Embodiment 2 of the present invention;

[0119] Figure 11 This is a schematic diagram showing the comparison results of the MSE of a two-dimensional target under different signal-to-noise ratios in Embodiment 2 of the present invention;

[0120] Figure 12 This is a schematic diagram showing the SSIM comparison results of two-dimensional targets under different signal-to-noise ratios in Embodiment 2 of the present invention. Detailed Implementation

[0121] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0122] Example 1

[0123] This embodiment provides a forward-looking super-resolution imaging method for real aperture scanning radar based on joint constraints of non-convex sparsity and generalized total variation. See the flowchart below. Figure 1 The method may include the following steps:

[0124] S1. Initialize the parameters of the real aperture scanning radar forward-looking imaging system and acquire radar forward-looking scan echo data;

[0125] S2. Perform range pulse compression and range migration correction sequentially on the radar forward-looking scan echo data;

[0126] S3. Extract azimuth echo data from the target range cell after migration correction and establish an azimuth convolution observation model.

[0127] S4. Based on the azimuth-oriented convolutional observation model, construct a joint regularization optimization problem of non-convex sparse constraints and generalized total variation.

[0128] S5. Solve the joint regularization optimization problem of non-convex sparse constraints and generalized total variation to obtain the target scattering coefficient estimation results;

[0129] S6. Output the radar forward-looking super-resolution imaging results based on the target coefficient estimation results.

[0130] In specific applications, the initialization of the parameters of the real aperture scanning radar forward-looking imaging system includes:

[0131] See Figure 2 Establish a forward-looking imaging geometric model of the moving platform radar. Assume that the height of the radar platform above the ground is H, the platform moves along the positive Y-axis at a constant speed v, and the antenna beam scans in the azimuth direction at an angular velocity ω.

[0132] Let the initial slant distance of the target point at the initial time be R0, the initial spatial azimuth angle between the target and the Y-axis be θ0, and the slow time be t;

[0133] Based on the geometric relationship between the motion platform and the target point, the distance history of the target point at slow time t is obtained:

[0134] ;

[0135] Performing a Taylor expansion on the distance history around t=0 yields an approximate expression for the distance history:

[0136] ;

[0137] in, This represents a third-order or higher-order term with respect to slow time t.

[0138] The aforementioned distance history is used to describe the pattern of target slant range change with slow time during platform movement, and serves as the basis for subsequent range processing and azimuth modeling.

[0139] After initializing the parameters of the real aperture scanning radar forward-looking imaging system, range pulse compression and range migration correction can be performed sequentially on the radar forward-looking scan echo data.

[0140] For range pulse compression, it can include: Let τ represent the fast time in the range direction and t represent the slow time in the azimuth direction, then the linear frequency modulated signal transmitted by the radar can be expressed as:

[0141] ;

[0142] Among them, f c For carrier frequency, K r T is the frequency modulation slope. p Where is the pulse width, and rect(·) is the rectangular window function;

[0143] The received echo signal is quadrature demodulated to obtain the baseband echo signal. A matched filter is then constructed based on the baseband form of the transmitted signal, as shown below:

[0144] ;

[0145] The baseband echo signal is transformed to the range frequency domain, multiplied by the frequency domain response of the matched filter, and then subjected to an inverse Fourier transform to obtain the range-compressed echo signal, the approximate expression of which is:

[0146] ;

[0147] Where u(R0,θ0) represents the target scattering coefficient, h a (·) represents the antenna pattern, B represents the signal bandwidth, c represents the electromagnetic wave propagation speed, λ represents the carrier wavelength, and R(t) represents the instantaneous slant range of the target.

[0148] After range pulse compression, the target echo is compressed in the range direction to a position centered on the target's instantaneous slant range R(t).

[0149] Because platform motion causes the instantaneous slant range R(t) of the target to change with slow time t, after range pulse compression, the echo peak of the same target may be distributed in different range cells, thus causing range migration. Therefore, the range migration correction includes: defining the range migration of the target relative to the initial time within slow time t as based on the target point distance history:

[0150] ;

[0151] Under the condition that the distance between the radar platform and the target is much greater than the platform displacement during the beam dwell time and the scanning azimuth angle is small, ignoring the higher-order terms in the range history, we obtain an approximate expression for the range migration:

[0152] ;

[0153] When the range migration amount is greater than the range resolution unit, it is determined that the target echo has experienced range migration, wherein the range migration criterion is:

[0154] ;

[0155] Based on the time-shift property of Fourier transform, a distance migration correction phase compensation factor is constructed:

[0156] ;

[0157] Will Substituting, we get:

[0158] ;

[0159] The range-compressed echo signal is transformed to the range frequency domain, multiplied by the range migration correction phase compensation factor, and then subjected to an inverse Fourier transform to obtain the range migration-corrected echo signal.

[0160] ;

[0161] In the formula, f τ Indicates distance frequency.

[0162] After range migration correction, the echo energy of the same target at different slow times is aligned to the initial reference range cell, which can provide a basis for subsequent extraction of azimuth data within a fixed range cell.

[0163] After range pulse compression and range migration correction are completed, azimuth echo data is extracted within the reference range cell where the target is located. Since the azimuth echo is mainly formed by the target scattering distribution modulated by the antenna pattern, the azimuth echo within a fixed range cell can be approximated as the convolution relationship between the target scattering coefficient distribution and the antenna pattern:

[0164] ;

[0165] In the formula, y(θ) represents the azimuth echo signal, x(θ) represents the target scattering coefficient distribution, h(θ) represents the antenna pattern function, n(θ) represents additive noise, and * represents convolution operation;

[0166] Discretizing the azimuth convolution relationship yields a discrete azimuth convolution observation model:

[0167] y = Hx + n;

[0168] Where H represents the convolutional measurement matrix, and y, x, and n represent the discretized azimuth echo observation vector, target scattering coefficient vector, and noise vector, respectively. Specifically, y, x, and n are expressed as follows:

[0169] ;

[0170] ;

[0171] ;

[0172] The convolution measurement matrix H is composed of antenna pattern sampling vectors, which are expressed as follows:

[0173] ;

[0174] In the formula, L represents the number of sampling points corresponding to the coverage area of ​​the antenna main lobe, N represents the azimuth discrete dimension of the scene to be reconstructed, and M represents the sampling dimension of the observed echo, and satisfies:

[0175] M = N + L - 1;

[0176] Based on the beam scanning imaging relationship, we have:

[0177] ;

[0178] ;

[0179] In the formula, Ω represents the angular domain range covered by the antenna scan, and θ b ω represents the antenna beamwidth, ω represents the scanning speed, and PRF represents the pulse repetition frequency.

[0180] It should be noted that, since antenna patterns typically have a certain main lobe width, there is a strong correlation between adjacent columns of the convolutional measurement matrix H. Directly inverting the above observation model can easily lead to noise amplification and unstable reconstruction results. Therefore, this embodiment further introduces regularization constraints based on the observation model.

[0181] Based on the discrete azimuth convolutional observation model established above, the forward-looking super-resolution imaging problem of real aperture scanning radar can be reduced to an ill-conditioned inverse problem of retrieving the target scattering coefficient vector x from the observed echo vector y. To improve the inversion stability, in this embodiment, regularization constraints can be introduced on the basis of the data fidelity term. Therefore, in this embodiment, the construction of the joint regularization optimization problem of non-convex sparse constraints and generalized total variation based on the azimuth convolutional observation model includes:

[0182] Based on the aforementioned discrete azimuth convolutional observation model, the radar forward-looking super-resolution imaging inversion problem is expressed as a regularized optimization problem, which is as follows:

[0183] ;

[0184] in, For data fidelity items, λ is the regularization term, and λ is the regularization parameter;

[0185] Introducing non-convex L q The sparse constraint is used as the first regularization term, and the non-convex L q Sparse constraints are represented as:

[0186] ;

[0187] In the formula, x i Let represent the i-th element in the target scattering coefficient vector x, and q be a non-convex sparse control parameter;

[0188] Introducing a generalized total variation constraint as the second regularization term, the generalized total variation constraint is expressed as:

[0189] ;

[0190] In the formula, D represents the discrete difference operator, v represents the auxiliary variable, and α1 and α0 are used to adjust the first-order structural constraint and the higher-order smoothing constraint, respectively.

[0191] The data fidelity item, non-convex L q A weighted combination of sparse constraints and generalized total variational constraints yields a joint regularized optimization problem of nonconvex sparse and generalized total variational constraints, which is expressed as:

[0192] ;

[0193] In the formula, λ1 is the regularization parameter of the non-convex sparse constraint, and λ2 is the regularization parameter of the generalized total variation constraint.

[0194] Since the aforementioned joint regularization optimization problem simultaneously includes non-convex, non-smooth sparse terms and generalized total variational terms, direct solution is quite difficult. To facilitate the solution, this embodiment employs an alternating iterative optimization method with variable splitting to process the joint regularization optimization problem. Therefore, in this embodiment, the method of using alternating iterative optimization with variable splitting to solve the joint regularization optimization problem of non-convex sparse constraints and generalized total variational terms to obtain the target scattering coefficient estimation result includes:

[0195] The non-convex sparse constraint and generalized total variational joint regularized optimization problem is equivalently split, and auxiliary variables z1, z2, and z3 corresponding to the structural constraints and sparse constraints are introduced, and z1 = Dx - v, z2 = Dv, and z3 = x are set.

[0196] The original problem is transformed into the following constrained optimization problem:

[0197] ;

[0198] By constructing an equivalent optimization function with a penalty term and alternately updating the main variable, auxiliary variable, and Lagrange multiplier, the iterative solution of the joint regularization optimization problem is achieved.

[0199] In this embodiment, the equivalent optimization function with a penalty term can be expressed as:

[0200] ;

[0201] In the formula, u1, u2, u3 are scaled Lagrange multipliers, and ρ1, ρ2, ρ3 are penalty parameters.

[0202] Specifically, the alternating update of the main variable, auxiliary variable, and Lagrange multiplier refers to:

[0203] In the (k+1)th iteration, with the other variables fixed, the update formula for the main variable x is:

[0204] ;

[0205] The update formula for the auxiliary variable v is:

[0206] ;

[0207] For the auxiliary variables z1 and z2 related to the generalized total variation, their subproblems are updated using a threshold shrinkage method, where the threshold shrinkage function is defined as:

[0208] ;

[0209] Therefore, the update formulas for z1 and z2 are as follows:

[0210] ;

[0211] For non-convex L q The sparsely correlated auxiliary variable z3 is updated using a non-convex sparse thresholding method for its subproblems:

[0212] ;

[0213] In the formula, Represents a non-convex sparse thresholding function;

[0214] After updating the main variables and auxiliary variables, the Lagrange multipliers are updated, as shown below:

[0215] ;

[0216] ;

[0217] .

[0218] It should be noted that after each iteration, it is determined whether the iteration termination condition has been met. In this embodiment, the iteration termination condition refers to the relative error between two adjacent target scattering coefficient estimation results, which is expressed as:

[0219] ;

[0220] When the above iteration termination condition is met, or the number of iterations reaches the preset maximum number of iterations, the iteration stops, and the current iteration result is used as the final estimated value of the target scattering coefficient, which is expressed as:

[0221] .

[0222] Example 2

[0223] Based on Example 1, to verify the effectiveness of the method provided in the example, this example constructs a two-dimensional extended target scene including abrupt edge regions and continuous smooth regions, and compares the method of this example with L2 regularization, TV regularization, L1-TV regularization, L2-TV regularization, and L... q The simulation experiment compared the -TV regularization method with the main parameters of the radar system used, as shown in Table 1.

[0224] Table 1 Simulation Parameters

[0225]

[0226] like Figure 3 As shown, the simulated original scene consists of three target regions: the upper one is a rectangular extended target with grayscale transition characteristics, the lower left one is a rectangular target with sharp edges and strong scattering, and the lower right one is a rectangular target with sharp edges and weak scattering. Figure 4 This is the real beam echo after range pulse compression and range migration correction. Figures 5 to 9 Imaging results from different contrast methods. Based on Figures 5-9 It can be seen that, Figure 5 The L2 regularization method shown exhibits obvious artifacts in the background region, and the target contour recovery is not clear enough. Figure 6 , Figure 7 and Figure 9 These correspond to the TV regularization method, the L1-TV regularization method, and the L... q -TV regularization methods, these types of methods are insufficient for maintaining the rectangular extended target with transition characteristics above. They are prone to restoring the originally continuously changing transition area to an over-sharpened segmented structure, resulting in the loss of gray-scale gradient features inside the extended target. Figure 8 The L2-TV regularization method shown can preserve the grayscale transition area of ​​the upper rectangular extended target well, but it is not effective in restoring the two lower black rectangular targets with sharp edges. The target position is expanded to a certain extent, and the originally sharp-edged strong scattering and weak scattering targets are restored to a blurred structure with transition characteristics.

[0227] In comparison, Figure 10 The method described in Example 1 can balance the preservation of continuous structure and the restoration of sharp targets. While maintaining the grayscale gradient features of the upper transition rectangle target, it also restores the clear boundaries of the lower strong and weak scattering rectangle targets, resulting in a reconstruction that is closer to the original scene. Therefore, the method in this embodiment achieves a better balance between preserving continuous structure and restoring sharp targets, and the reconstruction result is closer to the original target scene.

[0228] Furthermore, this embodiment conducts multiple Monte Carlo experiments on the aforementioned two-dimensional target scene under different signal-to-noise ratio conditions, and statistically analyzes the mean square error and structural similarity index of each method. The results are as follows: Figure 11 and Figure 12 As shown. (Through) Figure 11 and Figure 12 It can be seen that the method in this embodiment has lower MSE and higher SSIM under different signal-to-noise ratio conditions, indicating that the method in this embodiment is superior to the comparative method in terms of imaging accuracy, structure preservation capability and noise robustness.

[0229] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A forward-looking super-resolution imaging method for real aperture scanning radar based on joint constraints of non-convex sparsity and generalized total variation, characterized in that, Includes the following steps: The parameters of the real aperture scanning radar forward-looking imaging system are initialized, and radar forward-looking scan echo data are acquired. The radar forward-looking scan echo data are sequentially subjected to range pulse compression and range migration correction. For the migration-corrected echo data, azimuth echo data is extracted within the range cell where the target is located, and an azimuth convolution observation model is established; Based on the azimuth-oriented convolutional observation model, a joint regularization optimization problem of non-convex sparse constraints and generalized total variation is constructed. The joint regularization optimization problem of non-convex sparse constraints and generalized total variation is solved to obtain the target scattering coefficient estimation results; The radar forward-looking super-resolution imaging results are output based on the target coefficient estimation results.

2. The forward-looking super-resolution imaging method for real aperture scanning radar based on joint constraints of non-convex sparsity and generalized total variation as described in claim 1, characterized in that, The initialization of the parameters of the real aperture scanning radar forward-looking imaging system includes: Establish a forward-looking imaging geometric model of the moving platform radar. Assume that the radar platform is at a height of H above the ground, the platform moves along the positive Y-axis at a constant speed v, and the antenna beam scans in the azimuth direction at an angular velocity ω. Let the initial slant distance of the target point at the initial time be R0, the initial spatial azimuth angle between the target and the Y-axis be θ0, and the slow time be t; Based on the geometric relationship between the motion platform and the target point, the distance history of the target point at slow time t is obtained: ； Performing a Taylor expansion on the distance history around t=0 yields an approximate expression for the distance history: ； in, This represents a third-order or higher-order term with respect to slow time t.

3. The forward-looking super-resolution imaging method for real aperture scanning radar based on joint constraints of non-convex sparsity and generalized total variation as described in claim 1, characterized in that, The distance-oriented pulse compression includes: Let τ represent the range-long time and t represent the azimuth-slow time, then the linear frequency modulated signal transmitted by the radar can be expressed as: ； Among them, f c For carrier frequency, K r T is the frequency modulation slope. p Where is the pulse width, and rect(·) is the rectangular window function; The received echo signal is quadrature demodulated to obtain the baseband echo signal. A matched filter is then constructed based on the baseband form of the transmitted signal, as shown below: ； The baseband echo signal is transformed to the range frequency domain, multiplied by the frequency domain response of the matched filter, and then subjected to an inverse Fourier transform to obtain the range-compressed echo signal, the approximate expression of which is: ； Where u(R0,θ0) represents the target scattering coefficient, h a (·) represents the antenna pattern, B represents the signal bandwidth, c represents the electromagnetic wave propagation speed, λ represents the carrier wavelength, and R(t) represents the instantaneous slant range of the target. After range pulse compression, the target echo is compressed in the range direction to a position centered on the target's instantaneous slant range R(t).

4. The forward-looking super-resolution imaging method for real aperture scanning radar based on joint constraints of non-convex sparsity and generalized total variation as described in claim 3, characterized in that, The distance migration correction includes: Based on the target point's distance history, the target's distance migration relative to the initial time within slow time t is defined as: ； Under the condition that the distance between the radar platform and the target is much greater than the platform displacement during the beam dwell time and the scanning azimuth angle is small, ignoring the higher-order terms in the range history, we obtain an approximate expression for the range migration: ； When the range migration amount is greater than the range resolution unit, it is determined that the target echo has experienced range migration, wherein the range migration criterion is: ； Based on the time-shift property of Fourier transform, a distance migration correction phase compensation factor is constructed: ； Will Substituting, we get: ； The range-compressed echo signal is transformed to the range frequency domain, multiplied by the range migration correction phase compensation factor, and then subjected to an inverse Fourier transform to obtain the range migration-corrected echo signal. ； In the formula, f τ Indicates distance frequency; After range migration correction, the echo energy of the same target at different slow times is aligned to the initial reference range cell.

5. The forward-looking super-resolution imaging method for real aperture scanning radar based on joint constraints of non-convex sparsity and generalized total variation as described in claim 4, characterized in that, The process of extracting azimuth echo data within the target's range cell from the migration-corrected echo data and establishing an azimuth convolutional observation model includes: Within a fixed range cell, the azimuth echo can be approximated as a convolution relationship between the target scattering coefficient distribution and the antenna pattern: ； In the formula, y(θ) represents the azimuth echo signal, x(θ) represents the target scattering coefficient distribution, h(θ) represents the antenna pattern function, n(θ) represents additive noise, and * represents convolution operation; Discretizing the azimuth convolution relationship yields the discrete azimuth convolution observation model: y = Hx + n; Where H represents the convolutional measurement matrix, and y, x, and n represent the discretized azimuth echo observation vector, target scattering coefficient vector, and noise vector, respectively. Specifically, y, x, and n are expressed as follows: ； ； ； The convolution measurement matrix H is composed of antenna pattern sampling vectors, which are expressed as follows: ； In the formula, L represents the number of sampling points corresponding to the coverage area of ​​the antenna main lobe, N represents the azimuth discrete dimension of the scene to be reconstructed, and M represents the sampling dimension of the observed echo, and satisfies: M = N + L - 1; Based on the beam scanning imaging relationship, we have: ； ； In the formula, Ω represents the angular domain range covered by the antenna scan, and θ b ω represents the antenna beamwidth, ω represents the scanning speed, and PRF represents the pulse repetition frequency.

6. The forward-looking super-resolution imaging method for real aperture scanning radar based on joint constraints of non-convex sparsity and generalized total variation as described in claim 5, characterized in that, The aforementioned optimization problem based on the azimuth-oriented convolutional observation model, which constructs a joint regularization optimization problem involving non-convex sparse constraints and generalized total variation, includes: Based on the aforementioned discrete azimuth convolutional observation model, the radar forward-looking super-resolution imaging inversion problem is expressed as a regularized optimization problem, which is as follows: ； in, For data fidelity items, λ is the regularization term, and λ is the regularization parameter; Introducing non-convex L q The sparse constraint is used as the first regularization term, and the non-convex L q Sparse constraints are represented as: ； In the formula, x i Let represent the i-th element in the target scattering coefficient vector x, and q be a non-convex sparse control parameter; Introducing a generalized total variation constraint as the second regularization term, the generalized total variation constraint is expressed as: ； In the formula, D represents the discrete difference operator, v represents the auxiliary variable, and α1 and α0 are used to adjust the first-order structural constraint and the higher-order smoothing constraint, respectively. The data fidelity item, non-convex L q A weighted combination of sparse constraints and generalized total variational constraints yields a joint regularized optimization problem of nonconvex sparse and generalized total variational constraints, which is expressed as: ； In the formula, λ1 is the regularization parameter of the non-convex sparse constraint, and λ2 is the regularization parameter of the generalized total variation constraint.

7. The forward-looking super-resolution imaging method for real aperture scanning radar based on joint constraints of non-convex sparsity and generalized total variation as described in claim 6, characterized in that, An alternating iterative optimization method involving variable splitting is used to solve the joint regularized optimization problem of non-convex sparse constraints and generalized total variation, and the target scattering coefficient estimation results are obtained. The method employs an alternating iterative optimization approach with variable splitting to solve the joint regularized optimization problem involving non-convex sparse constraints and generalized total variation, obtaining the target scattering coefficient estimation results, including: The non-convex sparse constraint and generalized total variational joint regularized optimization problem is equivalently split, and auxiliary variables z1, z2, and z3 corresponding to the structural constraints and sparse constraints are introduced, and z1 = Dx - v, z2 = Dv, and z3 = x are set. The original problem is transformed into the following constrained optimization problem: ； By constructing an equivalent optimization function with a penalty term and alternately updating the main variable, auxiliary variable, and Lagrange multiplier, the iterative solution of the joint regularization optimization problem is achieved.

8. The forward-looking super-resolution imaging method for real aperture scanning radar based on joint constraints of non-convex sparsity and generalized total variation as described in claim 7, characterized in that, The equivalent optimization function with a penalty term is expressed as: ； In the formula, u1, u2, u3 are scaled Lagrange multipliers, and ρ1, ρ2, ρ3 are penalty parameters.

9. The forward-looking super-resolution imaging method for real aperture scanning radar based on joint constraints of non-convex sparsity and generalized total variation as described in claim 7, characterized in that, The alternating update of the main variable, auxiliary variable, and Lagrange multiplier refers to: In the (k+1)th iteration, with the other variables fixed, the update formula for the main variable x is: ； The update formula for the auxiliary variable v is: ； For the auxiliary variables z1 and z2 related to the generalized total variation, their subproblems are updated using a threshold shrinkage method, where the threshold shrinkage function is defined as: ； Therefore, the update formulas for z1 and z2 are as follows: ； For non-convex L q The sparsely correlated auxiliary variable z3 is updated using a non-convex sparse thresholding method for its subproblems: ； In the formula, Represents a non-convex sparse thresholding function; After updating the main variables and auxiliary variables, the Lagrange multipliers are updated, as shown below: ； ； 。 10. The forward-looking super-resolution imaging method for real aperture scanning radar based on joint constraints of non-convex sparsity and generalized total variation, as described in any one of claims 7-9, is characterized in that... After each iteration, determine whether the iteration termination condition has been met; The iteration termination condition refers to the relative error between two consecutive target scattering coefficient estimation results, which is expressed as: ； When the above iteration termination condition is met, or the number of iterations reaches the preset maximum number of iterations, the iteration stops, and the current iteration result is used as the final estimated value of the target scattering coefficient, which is expressed as: 。

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