Radar foresight super-resolution imaging method based on adaptive hybrid regularization

Abstract

The invention relates to the technical field of radar imaging, in particular to a radar foresight super-resolution imaging method based on adaptive hybrid regularization. According to the method, firstly, gradient amplitude information of a directional diagram and gradient structure information of an original signal are combined through a gradient domain fusion preprocessing method, and the quality of an input signal is improved; and then, in a hybrid non-convex regularization deconvolution method, realizing parameter self-adaption by comprehensively utilizing noise estimation and image content analysis. In this way, radar foresight super-resolution imaging which is high in adaptability, good in noise robustness and high in imaging quality under the condition of the low signal-to-noise ratio is achieved.

Description

Technical Field

[0001] This invention relates to the field of radar imaging technology, and more specifically to a radar forward-looking super-resolution imaging method based on adaptive hybrid regularization. Background Technology

[0002] Forward-looking radar imaging has significant applications in precision guidance, topographic mapping, and other fields. However, due to limitations of the mounting platform, the antenna aperture of forward-looking radars is typically small, resulting in a much lower azimuth resolution than range resolution. While traditional methods such as monopulse angle measurement can improve resolution to some extent, their performance is severely limited by antenna beam shape and system noise.

[0003] Regularized deconvolution methods are an effective way to improve resolution. Common methods include L1 regularization, which utilizes scene sparsity, and total variational (TV) regularization, which utilizes the piecewise smoothness of the scene. However, L1 regularization is prone to artifacts in continuous surface target imaging and is sensitive to noise; TV regularization tends to be over-smoothing, which is insufficient in separating neighboring point targets and its edge preservation effect deteriorates at low signal-to-noise ratios. In addition, most methods use fixed regularization parameters, which are difficult to adapt to different signal-to-noise ratios and scene characteristics (sparse point targets vs. continuous surface targets), resulting in poor generalization ability. Non-convex regularization (such as Lp norm, p<1) can more accurately approximate the L0 norm and has better sparsity promotion ability, but its solution is complex, and the construction and efficient solution of hybrid models with constraints such as TV are even more challenging.

[0004] Therefore, there is an urgent need for a radar forward-looking super-resolution imaging method that can adapt to different scenarios and noise levels, while also possessing high resolution, strong noise reduction, and good edge preservation capabilities. Summary of the Invention

[0005] To address the aforementioned problems, this invention proposes a radar forward-looking super-resolution imaging method based on adaptive hybrid regularization.

[0006] The technical solution of this invention is as follows:

[0007] A radar forward-looking super-resolution imaging method based on adaptive hybrid regularization includes the following steps:

[0008] S1: Acquire the raw radar forward-looking echo signal I and the antenna pattern B, and calculate sign(∇I) and |∇B| respectively; where |∇B| is the magnitude of the antenna pattern gradient, defined as... The gradient of the original echo signal. The original echo signal gradient after setting the directional zero threshold is represented by sign(∇I), which represents the direction of the original echo signal gradient after setting the directional zero threshold. The calculation method is as follows:

[0009] ,

[0010] ,

[0011] ,

[0012] Where N is the length of the radar forward-looking raw echo signal I and the antenna pattern B; a zero-direction threshold is set, and fluctuations below this value are ignored to suppress random direction flipping at small gradients.

[0013] S2: Construct the fused gradient field G:

[0014] G = |∇B|·sign(∇I),

[0015] Among them, |∇B| preserves the inherent structural information of the antenna beam; sign(∇I) preserves the changing trend of the target scene;

[0016] S3: Based on Neumann boundary conditions, signal reconstruction is achieved by solving the Poisson equation; the objective function is:

[0017] ∫|∇Y - G|² dx + ∫|Y - I|² dx,

[0018] Where Y is the fused signal, Here, dx is the regularization parameter, dx is the differential element of the one-dimensional integral, which refers to the accumulation over every position in the entire azimuth space of a certain range cell, and I is the original radar forward-looking echo signal; taking the variational factor of the energy functional Y, substituting it into the specific form, and simplifying, we get:

[0019] ,

[0020] in, For the Laplace operator;

[0021] S4: Solve the objective function using the DCT method. The specific steps are as follows:

[0022] 1) Calculate the divergence divG of the fused gradient field;

[0023] 2) Perform DCT transformation:

[0024] = DCT( ),

[0025] 3) Calculate the frequency domain eigenvalues ​​λ of the Laplace operator under Neumann boundary conditions. k :

[0026] ;

[0027] 4) Frequency domain solution:

[0028] ;

[0029] 5) Obtain the fused signal by inverse DCT transformation. :

[0030] ;

[0031] S5: Construct an objective function with a hybrid non-convex regularization term based on the fused signal Y. The hybrid non-convex regularization objective function integrates sparse priors and local smoothness priors to adapt to complex target structures. The expression of the hybrid non-convex regularization objective function is as follows:

[0032] ,

[0033] Where H is the measurement matrix of the radar system, and x is the original target signal to be recovered. It is an estimate of x; , is the regularization weight parameter; p and q are the orders of the nonconvex norm; x D is a non-convex sparse regularization term used to extract sparse target information and suppress small-amplitude noise; D is the gradient operator. Dx This is a non-convex TV regularization term used to constrain the local smoothness of the signal and preserve the target edge;

[0034] S6: Add regularization weight parameters to the objective function , Represented as: = , = (1− ),in ∈[0,1]; The noise level is determined by noise level estimation, specifically by estimating the noise level using the finite difference method. z :

[0035] z ,

[0036] Where Δr is the current residual r = y − Hx k The difference, x k It is the estimated value of x in the k-th iteration of ADMM. z It is the estimated noise standard deviation. y is the number of units, i.e., the number of effective observation points; λ is positively correlated with the noise level, and its expression is:

[0037] ,

[0038] in, To prevent small amounts with a denominator of zero, C is an adjustment factor; if the current residual is less than the noise energy, it indicates that the estimate of the noise's impact is insufficient, meaning the regularization is too weak, and it should be increased. Strengthen regularization constraints; conversely, reduce them. To retain more target details;

[0039] Determined by structure estimation, the L1 / L2 ratio is used as the sparsity index to calculate the pixel-domain sparsity. and gradient domain sparsity :

[0040] ,

[0041] ,

[0042] Describing the sparsity of the pixel domain, A large value indicates that the target scene is sparse and dominant; Describing the sparsity of the gradient domain, Large values ​​indicate sparse gradients, meaning the segments are smooth but the edges are steep. x represents the number of units, which is also the number of effective observation points.

[0043] Related to sparse signal structure:

[0044] , σ ∈ (0,1)

[0045] To achieve regularization weights that are tilted towards sparser dimensions;

[0046] S7: The alternating direction multiplier method (ADMM) is used to solve the mixed nonconvex regularized objective function to obtain an estimate of the original target signal x. The super-resolution imaging is completed, and the specific process is as follows:

[0047] 1) Introduce auxiliary variables Z1=Dx and Z2=x to transform the objective function into a constrained optimization problem;

[0048] 2) Update X: Take the derivative of the augmented Lagrangian function with respect to x, set the gradient to zero, and solve the linear equation;

[0049] ,

[0050] in, It is the ADMM penalty parameter. They are Lagrange multipliers;

[0051] 3) Update Z1:

[0052] The subproblems are:

[0053]

[0054] The subproblem structure combines smoothing terms with non-convex / non-smooth regularization terms. For non-convex / non-smooth regularization terms, smoothing non-convex regularization is applied, and the solution is obtained through inner iterations within the outer iteration of ADMM.

[0055] Introducing a smooth approximation:

[0056] ,

[0057] in The smoothing parameter is set to a small constant.

[0058] ,

[0059] Where m is the inner iteration number. Step size;

[0060] The inner iteration termination condition is:

[0061] ,

[0062] It is the inner iteration convergence threshold;

[0063] 4) Update Z2:

[0064] Similar in form to the Z1 subproblem, both are point-separable non-convex sparse regularization problems, and their inner-layer solution methods are consistent.

[0065] Subproblems:

[0066] ,

[0067] The subproblem structure combines smoothing terms with non-convex / non-smooth regularization terms. For non-convex / non-smooth regularization terms, smoothed non-convex regularization is applied, and the solution is obtained through inner iterations within the outer iteration of ADMM.

[0068] Introducing a smooth approximation:

[0069] ,

[0070] in The smoothing parameter is set to a small constant.

[0071] ,

[0072] Where γ is the step size and m is the inner iteration number;

[0073] The inner iteration termination condition is:

[0074] ,

[0075] It is the inner iteration convergence threshold;

[0076] 5) Update the Lagrange multipliers:

[0077] ,

[0078] Iterative convergence is driven by penalizing violations of constraints;

[0079] 6) Update according to the description in step S6 , , ;

[0080] 7) Convergence is determined using the dual residual criterion, with the original residuals used to measure the degree of constraint violation:

[0081] and ,

[0082] It is the convergence threshold of the original residual in the outer iteration of ADMM;

[0083] Dual residuals measure the degree of change in multipliers:

[0084] and ,

[0085] It is the convergence threshold of the dual residual of the outer iterative layer of ADMM;

[0086] When the convergence or iteration count reaches the set maximum M (M=1000), the estimated value of the current x is output, and the super-resolution imaging is completed.

[0087] The beneficial effects of this invention are as follows:

[0088] 1) This invention uses gradient domain fusion preprocessing to organically combine the structural prior of the antenna pattern with the target information of the original echo, effectively suppressing the random gradient of noise, adapting to low signal-to-noise ratio environments, and improving the noise resistance of the input signal; at the same time, it makes the initial value of the subsequent optimization objective function closer to the optimal solution, reduces the number of iterations, and improves the convergence efficiency of the algorithm.

[0089] 2) Construct a hybrid non-convex regularization objective function that integrates non-convex sparse terms and non-convex TV terms. This balances the ability to distinguish sparse point targets with the ability to preserve the edges of continuous surface targets, solving the problem of poor adaptability of single regularization methods. It can accurately restore the contour information of complex targets and reduce the generation of false targets.

[0090] 3) A two-dimensional parameter adaptive strategy is proposed, which dynamically adjusts the regularization intensity based on the noise level and assigns regularization weights based on the sparsity of the target structure. This strategy can adapt to different noise environments and target types without manual parameter tuning, significantly improving the versatility and stability of the algorithm. Attached Figure Description

[0091] Figure 1 This is a schematic diagram of the process of the present invention.

[0092] Figure 2 This is a schematic diagram of Y after gradient domain fusion.

[0093] Figure 3 The imaging effect of this method on concave targets under L1 regularization, TV regularization, and a signal-to-noise ratio of 10dB is shown.

[0094] Figure 4 The image shows the imaging performance of this method on concave targets in environments with signal-to-noise ratios of 15dB, 10dB, and 5dB. Detailed Implementation

[0095] The technical solution of the present invention will now be described in detail with reference to the accompanying drawings and embodiments:

[0096] Since the method of the present invention is applied to forward vision imaging, an application example of the method of the present invention in forward vision imaging will be used to illustrate this below.

[0097] Example

[0098] The parameter used in this example: pulse width ,bandwidth FM slope sampling frequency Pulse repetition period carrier frequency speed of light The scanning speed is 20° / s, and the antenna beamwidth is 2°. A concave target is set up, located at... At point m, the target's azimuth coordinates on the concave surface range from -0.2° to 0.2°, with 0° being the lowest point. N=500. =0.5, , =0.2, = , = , = , = , = The directional zero threshold is , 1 = .

[0099] The technical solution of this invention is carried out sequentially as follows:

[0100] 1. Obtain the radar forward-looking echo signal I and the antenna pattern signal B, calculate their discrete gradients ∇I and ∇B according to formula (1), and then obtain sign(∇I) and |∇B|;

[0101] 2. Follow the steps " "Construct a fused gradient field;

[0102] 3. Set the regularization parameter λ=0.1 for solving the Poisson equation, and follow the steps... The solution steps of the method are as follows: The equation in the equation yields the fused signal Y, as shown below. Figure 2 As shown;

[0103] 4. Construction Steps The mixed nonconvex regularization objective function in "";

[0104] 5. Solve the objective function using the Alternating Direction Multiplier Method (ADMM) as described in step "S7": First, initialize the variables x0, Z1, Z2, ... 1. Both are zero vectors. The initial value is set to 1;

[0105] 6. For the objective function in S5, update x, Z1, Z2, and the Lagrange multipliers according to S7. According to the steps " "step" "step" "Update parameters" The convergence is checked using the double residual criterion. If convergence is achieved, the estimated value of x is output as the imaging result. If convergence is not achieved, this step is repeated until convergence is achieved or the number of iterations reaches its maximum, at which point the current estimated value of x is output as the imaging result.

[0106] Figure 3These are the imaging results of L1 regularization, TV regularization, and our proposed method at an SNR of 10 dB. It can be seen that, at the same signal-to-noise ratio, compared to other methods, our proposed method better restores concave targets at a lower SNR, demonstrating better edge preservation and undulation restoration capabilities, and also exhibiting better noise filtering adaptability.

[0107] Figure 4 These are the imaging results of concave targets using the method presented in this paper at signal-to-noise ratios of 15dB, 10dB, and 5dB. It can be seen that the method basically achieves the function of target resolution and contour reconstruction under different signal-to-noise ratios. The experiments confirm the effectiveness of the preprocessing and hybrid regularization methods, demonstrating good noise robustness.

Claims

1. A radar forward-looking super-resolution imaging method based on adaptive hybrid regularization, characterized in that, Includes the following steps: S1: Obtain the radar forward-looking original echo signal I and the antenna pattern B, and calculate sign(∇I) and |∇B| respectively; wherein |∇B| is the amplitude of the antenna pattern gradient, and is defined as is the original echo signal gradient, is the original echo signal gradient after setting the direction zero threshold, and sign(∇I) is the direction of the original echo signal gradient after setting the direction zero threshold, and the calculation method is as follows: ， ， ， Where N is the length of the radar forward-looking raw echo signal I and the antenna pattern B; a zero-direction threshold is set, and fluctuations below this value are ignored to suppress random direction flipping at small gradients. S2: Construct the fused gradient field G: G = |∇B|·sign(∇I), Among them, |∇B| preserves the inherent structural information of the antenna beam; sign(∇I) preserves the changing trend of the target scene; S3: Based on Neumann boundary conditions, signal reconstruction is achieved by solving the Poisson equation; the objective function is: ∫|∇Y - G|² dx + ∫|Y - I|² dx, Where Y is the fused signal, Here, dx is the regularization parameter, dx is the differential element of the one-dimensional integral, which refers to the accumulation over every position in the entire azimuth space of a certain range cell, and I is the original radar forward-looking echo signal; taking the variational factor of the energy functional Y, substituting it into the specific form, and simplifying, we get: ， in, For the Laplace operator; S4: Solve the objective function using the DCT method. The specific steps are as follows: 1) Calculate the divergence divG of the fused gradient field; 2) Perform DCT transformation: = DCT( ), 3) Computing the frequency domain eigenvalues λ of the Laplace operator under Neumann boundary conditions k : ； 4) Frequency domain solution: ； 5) Obtain the fused signal by inverse DCT transformation. : ； S5: Construct an objective function with a hybrid non-convex regularization term based on the fused signal Y. The hybrid non-convex regularization objective function integrates sparse priors and local smoothness priors to adapt to complex target structures. The expression of the hybrid non-convex regularization objective function is as follows: ， Where H is the measurement matrix of the radar system, and x is the original target signal to be recovered. It is an estimate of x; , is the regularization weight parameter; p and q are the orders of the nonconvex norm; x D is a non-convex sparse regularization term used to extract sparse target information and suppress small-amplitude noise; D is the gradient operator. Dx This is a non-convex TV regularization term used to constrain the local smoothness of the signal and preserve the target edge; S6: Add regularization weight parameters to the objective function , Represented as: = , = (1− ),in ∈[0,1]; The noise level is determined by noise level estimation, specifically by estimating the noise level using the finite difference method. z : z ， Where Δr is the current residual r = y − Hx k The difference, x k It is the estimated value of x in the k-th iteration of ADMM. z It is the estimated noise standard deviation. y is the number of units, i.e., the number of effective observation points; λ is positively correlated with the noise level, and its expression is: ， in, To prevent small amounts with a denominator of zero, C is an adjustment factor; if the current residual is less than the noise energy, it indicates that the estimate of the noise's impact is insufficient, meaning the regularization is too weak, and it should be increased. Strengthen regularization constraints; conversely, reduce them. To retain more details of the target; Determined by structure estimation, the L1 / L2 ratio is used as the sparsity index to calculate the pixel-domain sparsity. and gradient domain sparsity : ， ， Describing the sparsity of the pixel domain, A large value indicates that the target scene is sparse and dominant; Describing the sparsity of the gradient domain, Large values ​​indicate sparse gradients, meaning the segments are smooth but the edges are steep. x represents the number of units, which is also the number of effective observation points; Related to sparse signal structure: ,σ ∈ (0,1) To achieve regularization weights that are tilted towards sparser dimensions; S7: The alternating direction multiplier method (ADMM) is used to solve the mixed nonconvex regularized objective function to obtain an estimate of the original target signal x. The super-resolution imaging is completed, and the specific process is as follows: 1) Introduce auxiliary variables Z1=Dx and Z2=x to transform the objective function into a constrained optimization problem; 2) Update X: Take the derivative of the augmented Lagrangian function with respect to x, set the gradient to zero, and solve the linear equation; ， in, It is the ADMM penalty parameter. They are Lagrange multipliers; 3) Update Z1: The subproblems are: ， The subproblem structure combines smoothing terms with non-convex / non-smooth regularization terms. For non-convex / non-smooth regularization terms, smoothing non-convex regularization is applied, and the solution is obtained through inner iterations within the outer iteration of ADMM. Introducing a smooth approximation: ， in The smoothing parameter is set to a small constant. ， Where m is the inner iteration number. Step size; The inner iteration termination condition is: ， It is the inner iteration convergence threshold; 4) Update Z2: Similar in form to the Z1 subproblem, both are point-separable non-convex sparse regularization problems, and their inner-layer solution methods are consistent. Subproblems: ， The subproblem structure combines smoothing terms with non-convex / non-smooth regularization terms. For non-convex / non-smooth regularization terms, smoothing non-convex regularization is applied, and the solution is obtained through inner iterations within the outer iteration of ADMM. Introducing a smooth approximation: ， in The smoothing parameter is set to a small constant. ， Where γ is the step size and m is the inner iteration number; The inner iteration termination condition is: ， It is the inner iteration convergence threshold; 5) Update the Lagrange multipliers: ， Iterative convergence is driven by penalizing violations of constraints; 6) Update according to the description in step S6 , , ; 7) Convergence is determined using the dual residual criterion, with the original residuals used to measure the degree of constraint violation: and , It is the convergence threshold of the original residual in the outer iteration of ADMM; Dual residuals measure the degree of change in multipliers: and , It is the convergence threshold of the dual residual of the outer iterative layer of ADMM; When the convergence or iteration count reaches the set maximum M, the estimated value of the current x is output, and the super-resolution imaging is completed.

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