ITR-dtv radar forward-looking super-resolution imaging method based on renyi entropy

Abstract

The present application relates to a kind of ITR-DTV radar forward-looking super-resolution imaging methods based on Renyi entropy, imaging method includes: based on the motion geometry model of radar forward-looking imaging, echo signal is expressed as the form of antenna directional diagram convolution target scattering coefficient in azimuth direction, radar observation model is constructed;Target scattering coefficient is constructed target function;Combined with radar observation model, direction total variation operator is used as the regularization term of target function, while adding positive definite weighting matrix in the loss function of target function, and Renyi entropy is selected as another regularization term of target function, and target optimization model is obtained;ADMM method is used to iteratively solve target optimization model, and model function is obtained, and the relaxation variable in model function, target phase and target amplitude are updated;Target scattering coefficient is calculated using target phase and target amplitude, and the super-resolution imaging of target is realized.The imaging method has strong target image direction texture detail recovery ability, strong scene adaptability and small error.

Description

Technical Field

[0001] This invention belongs to the field of radar imaging technology, specifically relating to an ITR-DTV radar forward-looking super-resolution imaging method based on Renyi entropy. Background Technology

[0002] Forward-looking radar imaging is a crucial component of radar imaging, and improving the azimuth resolution of the forward-looking area is urgently needed in practical engineering applications. To address this technical challenge, domestic and international scholars have primarily proposed solutions including real-beam scanning imaging, single-pulse imaging, and forward-looking scanning deconvolution super-resolution imaging. While real-aperture radar can provide forward-looking images, and large-scale array antennas can be used to obtain high-resolution images, the resolution still falls short of practical application requirements. Although single-pulse sharpening technology can sharpen the target scene, it doesn't strictly improve the resolution of forward-looking radar imaging. Conversely, deconvolution provides a new technical approach for achieving forward-looking super-resolution imaging. Deconvolution-based super-resolution imaging reconstructs the azimuth echo convolution model using a forward-looking scanning time series containing target azimuth information, transforming the azimuth resolution improvement problem into the inverse problem of deconvolution. Deconvolution-based super-resolution imaging can achieve super-resolution without hardware changes, achieving both low cost and high efficiency. Only a signal processing module needs to be added to ensure compatibility with existing radar platforms, facilitating widespread application.

[0003] Deconvolution techniques are highly sensitive to noise. To address this ill-conditioned problem, Richards M. proposed an iterative noncorrelated super-resolution imaging method and a corresponding fast algorithm in 1988. This algorithm can improve angular resolution by about 3 times, but it requires a high scene signal-to-noise ratio. In the 1990s, the Wright-Patterson Military Research Base in the United States proposed a super-resolution imaging method using nonlinear compensation filters, which improved angular resolution by 2-3 times. Subsequently, Yang Jianyu et al. from the University of Electronic Science and Technology of China (UESTC) used a generalized filtering method to improve radar imaging angular resolution by about 4 times. However, this algorithm suffers from poor convergence controllability during iteration due to the inability to accurately select convergence parameters, resulting in angular shifts in the recovered target azimuth signal and poor noise suppression. In recent years, researchers at UESTC have applied Bayesian statistical optimization methods from the field of optical super-resolution to radar super-resolution imaging algorithms. Relevant literature uses maximum a posteriori probability (MAP)... The APosteriori (MAP) criterion is used to estimate the target azimuth signal. Based on the statistical characteristics of the echo data, a Bayesian model is established, and the MAP criterion is used to predict the target azimuth signal, so that the azimuth information can be quickly converged during the iterative calculation. However, when there is a lot of noise in the receiver, the noise inside the system will be amplified after the deconvolution operation, resulting in a ringing effect, which leads to a large deviation between the reconstructed target azimuth signal and the theoretical data. Due to this defect, researchers proposed a regularized super-resolution method based on constrained optimization theory, which effectively alleviates the ill-conditioned problem in deconvolution.

[0004] Solving the deconvolution super-resolution problem using regularization methods hinges on optimizing the objective function to more accurately and efficiently describe the target scene. Reference 1 proposes an L1-norm-based model, which can reconstruct the target orientation signal in sparse scenes with low signal-to-noise ratios; however, this method has limited application scenarios and relatively high computational complexity. Reference 2 proposes a Tikhonov regularization algorithm, which is relatively simple to solve, but its super-resolution performance is insufficient in practical applications. Reference 3 proposes an improved Tikhonov algorithm, which uses the L2 norm of the target solution as a constraint, employs an extended error function to describe the solution's accuracy, and uses a weighted stability term to ensure the stability of the numerical solution. Different weights are assigned to each measurement data point based on its error level, further ensuring stability. The stability of the numerical solution was proven, and the interference of noise was reduced. However, its constraint term was too strong for images with large gradient changes, which caused many details and edge features in the image to be unable to be well recovered. Reference 4 proposed the Total Variation (TV) image denoising algorithm. This algorithm uses the total variation operator as a regularization term and can effectively recover the contour feature information of the image. However, the TV algorithm is prone to staircase effect and does not preserve the texture components of the image ideally. Reference 5 proposed a regularization algorithm based on maximum entropy. Since the influence of noise in the echo was not considered when verifying its performance, its performance in noisy environments is limited.

[0005] In summary, traditional super-resolution imaging methods suffer from poor ability to restore directional texture details in target images, simply providing a uniform description of errors across all measurement data, and poor adaptability to different scenes. Summary of the Invention

[0006] To address the aforementioned problems in the existing technology, this invention provides a forward-looking super-resolution imaging method for ITR-DTV radar based on Renyi entropy. The technical problem to be solved by this invention is achieved through the following technical solution:

[0007] This invention provides a forward-looking super-resolution imaging method for ITR-DTV radar based on Renyi entropy, comprising the following steps:

[0008] S1. Based on the motion geometry model of radar forward-looking imaging, the echo signal in the azimuth direction is represented as the form of antenna pattern convolved with the target scattering coefficient, and the radar observation model is constructed.

[0009] S2. Construct an objective function for the target scattering coefficients using regularization methods;

[0010] S3. Combining the radar observation model, the direction total variation operator is used as the regularization term of the objective function to constrain the target amplitude. At the same time, a positive definite weighting matrix is ​​added to the loss function of the objective function, and Renyi entropy is selected as another regularization term of the objective function to constrain the target amplitude, thus obtaining the target optimization model.

[0011] S4. Use the ADMM method to iteratively solve the target optimization model, construct the augmented Lagrangian function, obtain the solution model function, and solve for the slack variables, target phase, and target amplitude in the solution model function;

[0012] S5. Calculate the target scattering coefficient using the target phase and the target amplitude to achieve super-resolution imaging of the target.

[0013] In one embodiment of the present invention, step S1 includes:

[0014] S11. Based on the aforementioned motion geometry model, a Taylor series expansion is performed on the distance between the carrier aircraft and the target point to obtain an approximate linear slant range:

[0015]

[0016] Where H is the height of the aircraft above the horizontal plane, r is the distance from the target point to the projection of the aircraft on the XY plane, R0 is the distance between the aircraft and the target point, v is the speed of the aircraft, t is the moment of the aircraft's movement, and ψ0 is the angle between OQ and the Y-axis. The elevation angle of the radar antenna beam;

[0017] S12. The radar echo signal at the target time is sequentially processed by carrier frequency removal, pulse compression, motion correction, and replacement of the time variable with a spatial variable to obtain the echo signal between the azimuth angle and the approximate linear slant range:

[0018]

[0019] Where θ is the azimuth variable and R is the slant distance variable. Weighted reflectance coefficient for the target This represents the convolution operation. Let f0 represent the impulse response function, f0 be the frequency modulation of the carrier frequency, c be the speed of light, and v be the velocity of the moving platform. Let θ be the elevation angle of the radar antenna beam, and θ0 be the initial azimuth angle of the target. This refers to the radar beam scanning angular velocity;

[0020] S13. The echo signal is represented in the azimuth direction as the antenna pattern convolved with the target scattering coefficient. Considering noise and the fact that the radar-received echo is a discrete point, the echo signal is represented in a one-dimensional convolution form, resulting in the radar forward-looking imaging echo model:

[0021]

[0022] Where n(t) represents the random noise in the imaging process, a(t) is the antenna pattern, and σ(t) is the target scattering coefficient;

[0023] S14. Based on the fact that the echo data obtained by the radar through forward-looking scanning is a complex number, the target scattering coefficient is expressed as:

[0024] σ=φf

[0025] Where σ is the target scattering coefficient. A diagonal matrix, σ is the phase of σ, and f is the amplitude of the target scattering coefficient σ, |σ|.

[0026] S15. The radar observation model is obtained from the target scattering coefficient and the radar forward-looking imaging echo model:

[0027] s=Aφf+n

[0028] Where s is the echo signal, A is the antenna pattern, and n is the noise.

[0029] In one embodiment of the present invention, the objective function is:

[0030]

[0031] Where A is the antenna pattern, σ is the target scattering coefficient, s is the echo signal, λ is the regularization parameter, Γ(σ) is a function of σ, and q represents the norm operation.

[0032] In one embodiment of the present invention, step S3 includes the following steps:

[0033] S31. Combining the radar observation model, and using the total direction variation operator as the regularization term of the objective function to constrain the target amplitude, the objective function after adding the total direction variation operator is expressed as:

[0034]

[0035] Where f is the amplitude |σ| of the target scattering coefficient σ. Here, s is the non-differentiable term, s is the echo signal, and A is the antenna pattern. A diagonal matrix, It is the phase of σ, and ε is a positive number approaching 0;

[0036] S32. Add a positive definite weighting matrix W1 to the loss function of the objective function and introduce a slack variable ω to obtain the intermediate optimization model:

[0037]

[0038] Where f is the amplitude |σ| of the target scattering coefficient σ, W is the positive definite weighting matrix, s is the echo signal, A is the antenna pattern matrix, φ is the target phase, ω is the relaxation variable, and β1 is the regularization parameter;

[0039] S33. Select Renyi entropy as another regularization term of the objective function to constrain the objective magnitude, thus obtaining the objective optimization model:

[0040]

[0041] Where λ1 is the regularization parameter, α is a variable parameter, α≥0 and α≠1.

[0042] In one embodiment of the present invention, step S4 includes:

[0043] S41. Use the ADMM method to iteratively solve the objective optimization model, construct the augmented Lagrangian function, and obtain the solved model function:

[0044]

[0045] Where λ is a Lagrange multiplier;

[0046] S42. Using the method of separating variables, the update of the slack variable, the update of the target phase, and the update of the target amplitude are transformed into subproblems of solving the slack variable, solving the target amplitude, and solving the target phase, respectively, and the Lagrange multiplier is updated in each update process.

[0047] In one embodiment of the present invention, solving the subproblem of the slack variable in step S42 includes:

[0048] The subproblem of the slack variables is:

[0049]

[0050] Where n is the number of iterations, ω (n) Let be the slack variable for the nth iteration;

[0051] The subproblem of the slack variable is solved using the standard contraction formula, yielding a closed-form solution to the subproblem of the slack variable:

[0052]

[0053] Where, ω (n+1) Let be the slack variable for the (n+1)th iteration.

[0054] In one embodiment of the present invention, solving the sub-problem of the target amplitude in step S42 includes:

[0055] The subproblem of the target magnitude is:

[0056]

[0057] Among them, f (n+1) The target magnitude for the (n+1)th iteration;

[0058] The update formula for the target amplitude is:

[0059]

[0060] in, G = diag{g1,…,g} n}, σ i Let P be the i-th element in the target scattering coefficient vector, where P ∈ U. 2×2 , It is a weighted matrix, ξ∈U 2 ,||ξ i ||≤γ<1 is a direction-determining vector, D is the total variation operator, λ is the Lagrange multiplier, β1 is the regularization parameter, and ω is the slack variable.

[0061] In one embodiment of the present invention, solving the subproblem of the target phase in step S42 includes:

[0062] The subproblem of the target phase is transformed into a subproblem of column vectors consisting of the diagonal elements of the target phase diagonal matrix:

[0063]

[0064] Where α is a column vector consisting of the diagonal elements of the target phase diagonal matrix. s is the echo signal, K is a diagonal matrix diag(f) with amplitude as the diagonal element, and A is the antenna pattern matrix;

[0065] The iterative update formula for the column vector composed of the diagonal elements of the target phase diagonal matrix is ​​as follows:

[0066] α (n+1) =α (n) -γ[H(α (n) )] -1▽α (n)

[0067] Where γ is the iteration step size.

[0068] In one embodiment of the present invention, the formula for updating the Lagrange multipliers in each update process is: λ n+1 =λ n +β1(ω-PDf).

[0069] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0070] This invention proposes an ITR-DTV deconvolution super-resolution imaging method based on Renyi entropy, utilizing regularization. By introducing directional total variation and Renyi entropy as constraint terms to constrain the target amplitude, this method not only more accurately recovers the edge texture details of the image but also enhances its applicability in different scenarios, significantly improving the target recovery capability of airborne radar in low signal-to-noise ratio environments. Furthermore, by adding a positive definite weighting matrix to the loss function, the error degree of each measurement value in the loss function is more accurately reflected. Therefore, this imaging method has the advantages of strong ability to recover directional texture details of target images, strong scene adaptability, and small error. Attached Figure Description

[0071] Figure 1 A flowchart illustrating an ITR-DTV radar forward-looking super-resolution imaging method based on Renyi entropy, provided for an embodiment of the present invention.

[0072] Figures 2a-2b A schematic diagram of a radar scanning imaging geometric model of a motion platform provided in an embodiment of the present invention;

[0073] Figure 3 This invention provides a point target distribution map under the same distance conditions as an embodiment of the invention;

[0074] Figure 4 This invention provides a two-dimensional dot matrix target distribution map under different distance conditions.

[0075] Figures 5a-5d Comparison of one-dimensional point target super-resolution imaging results of different methods provided in the embodiments of the present invention at a signal-to-noise ratio of 15dB;

[0076] Figures 6a-6d Comparison of two-dimensional lattice target super-resolution results provided by different methods in embodiments of the present invention;

[0077] Figure 7 Error variation curves for different methods provided in embodiments of the present invention. Detailed Implementation

[0078] The present invention will be further described in detail below with reference to specific embodiments, but the implementation of the present invention is not limited thereto.

[0079] Example 1

[0080] Forward-looking super-resolution imaging is a challenging and hot topic in radar imaging research. Limited by Doppler bandwidth and platform size, traditional high-resolution synthetic aperture imaging and real aperture imaging are not suitable for forward-looking imaging. Therefore, this embodiment focuses on forward-looking super-resolution imaging technology based on deconvolution, and conducts an in-depth study and analysis of the problems existing in the algorithm from a signal processing perspective. The construction process of the imaging method in this embodiment is as follows: To extract target information more accurately and suppress the staircase effect of the image, a total variation operator is first added as a regularization term; then, since using a single maximum or minimum entropy as a regularization term can only achieve good super-resolution results under specific target scenarios, to enhance the adaptability of the algorithm to different application scenarios, Renyi entropy with an adjustable parameter α is added as another regularization term; finally, the error term in the traditional objective function is analyzed. The same weight is applied to the error term, but in the actual system, each measurement value has a different degree of error. Therefore, to more accurately describe the error, a weighting matrix W1 is introduced into the error term in the objective function. Thus, this embodiment constructs an optimization function to solve the target problem, aiming to further preserve the directional texture and edge characteristics of the image, enhance the scene adaptability of the algorithm, and reduce the impact of errors.

[0081] Please see Figure 1 , Figure 1 This is a flowchart illustrating a forward-looking super-resolution imaging method for ITR-DTV radar based on Renyi entropy, provided as an embodiment of the present invention. This improved Tikhonov-directional total variation (ITR-DTV) radar forward-looking super-resolution imaging method based on Renyi entropy includes the following steps:

[0082] S1. Based on the motion geometry model of radar forward-looking imaging, the echo signal in the azimuth direction is represented as the antenna pattern convolved with the target scattering coefficient, thus constructing the radar observation model. Specific steps include:

[0083] S11. Based on the motion geometry model, the distance between the carrier and the target point is expanded using a Taylor series to obtain an approximate linear slant range between the carrier and the target point.

[0084] Specifically, this embodiment mainly addresses the super-resolution problem of radar forward-looking imaging. In most cases, the radar platform is in motion; a stationary state can be considered a special type of motion. Therefore, this embodiment primarily derives and explains the motion geometry model for radar forward-looking imaging. Please refer to [link to relevant documentation]. Figures 2a-2b , Figures 2a-2b This is a schematic diagram of a radar scanning imaging geometric model of a moving platform provided in an embodiment of the present invention. Figure 2a This is a diagram of the radar scanning process. Figure 2b This is the geometric model of the relative position of the motion platform and the target. Figure 2a In the middle, the aircraft is at a height H above the target plane, the platform moves along the positive Y-axis at a velocity v, and the radar beam scans at an angular velocity ω. Figure 2b In the middle, the beam pitch angle is The azimuth angle at the start of the scan is θ0.

[0085] Assume there exists a target point Q on the target plane, and the target remains within the beam range. At t = 0, the carrier aircraft is at its initial position O', the distance between the carrier aircraft and target point Q is R0, and the angle between OQ and the Y-axis is θ0. After the carrier aircraft has moved along the Y-axis for time t, the instantaneous distance when the radar reaches point B is R(t), and the distance from the carrier aircraft's projection onto point Q in the XY plane is r. Therefore, from... Figure 2b From the geometric relationships, we can derive that, at time t, the approximate linear slant range expression for the distance between the carrier aircraft and the target point Q, expressed as a Taylor series expansion, is:

[0086]

[0087] Where H is the height of the aircraft above the horizontal plane, r is the distance from the target point to the projection of the aircraft on the XY plane, R0 is the distance between the aircraft and the target point, v is the speed of the aircraft, t is the moment of the aircraft's movement, and ψ0 is the angle between OQ and the Y-axis. This represents the elevation angle of the radar antenna beam.

[0088] S12. The radar echo signal at the target time is sequentially processed by removing the carrier frequency, pulse compression, movement correction, and replacing the time variable with a spatial variable to obtain the echo signal between the azimuth angle and the approximate linear slant range.

[0089] Specifically, the radar transmits a linear frequency modulated signal at a certain pulse repetition frequency, therefore the expression for the transmitted signal is:

[0090]

[0091] Where τ is the distance-time vector, and T r For the transmitted signal pulse width, f0 and K r These are the modulation frequencies of the carrier frequency and the linear frequency modulation signal, respectively.

[0092] For the radar echo signal at target time t, the following processes are performed sequentially: carrier frequency removal, pulse compression, travel correction, and replacement of time variables with spatial variables. This yields the echo signal expression for the relationship between the azimuth angle θ and the approximately linear slant range R:

[0093]

[0094] Where θ is the azimuth variable and R is the slant distance variable. Weighted reflectance coefficient for the target This represents the convolution operation. Let f0 represent the impulse response function, f0 be the frequency modulation of the carrier frequency, c be the speed of light, and v be the velocity of the moving platform. Let θ be the elevation angle of the radar antenna beam, and θ0 be the initial azimuth angle of the target. This refers to the radar beam scanning angular velocity.

[0095] S13. The echo signal is represented in the azimuth direction as the antenna pattern convolution target scattering coefficient. Considering noise and that the echo received by the radar is a discrete point, the echo signal is represented in a one-dimensional convolution form to obtain the radar forward-looking imaging echo model.

[0096] Specifically, as shown in equation (3), the preprocessed echo signal in the azimuth direction can be represented as the antenna pattern convolved with the target scattering coefficient. Considering the presence of noise and the fact that the radar-received echo is a discrete point, the echo signal is re-represented as a one-dimensional convolution:

[0097]

[0098] Where n(t) represents random noise in the imaging process, a(t) is the antenna pattern, and σ(t) is the target scattering coefficient.

[0099] Thus, the super-resolution problem of forward-looking radar imaging is transformed into the problem of estimating the target scattering coefficient σ.

[0100] S14. Based on the fact that the echo data obtained by the radar through forward-looking scanning is a complex number, the target scattering coefficient is re-represented.

[0101] Specifically, in practice, the echo data obtained by radar through forward-looking scanning is a complex number, so the target scattering coefficient can be rewritten as follows:

[0102] σ= φf (5)

[0103] Where σ is the target scattering coefficient. A diagonal matrix, σ is the phase of σ, and f is the amplitude of the target scattering coefficient σ, |σ|.

[0104] S15. The radar observation model is obtained from the target scattering coefficient and the radar forward-looking imaging echo model as follows:

[0105] s=Aφf+n (6)

[0106] Where s is the echo signal, A is the antenna pattern, and n is the noise.

[0107] S2. Using regularization, construct an objective function for the target scattering coefficients.

[0108] Specifically, as shown in step S1, the radar forward-looking imaging super-resolution problem can be transformed into an estimation problem of the target scattering coefficient σ, i.e., deriving the input from the output. This type of problem is well-suited for modeling using deconvolution. However, in practical engineering applications, noise inevitably exists in the system. When noise enters the system, the input data information cannot be directly reconstructed using the deconvolution algorithm. This means that the deconvolution method has a noise sensitivity problem, and the signal will be submerged in strong noise. In addition, the non-full-rank characteristic of the antenna pattern means that even a small disturbance in the system can cause a large error in the final recovery result. Therefore, a regularization method is used to analyze and solve the ill-conditioned deconvolution problem.

[0109] Regularization theory essentially introduces constraints on minimizing the loss function and provides a regularization parameter to adjust the relationship between the two, thereby making the solution in the original problem closer to the desired result, and thus reducing the solution space and the impact of noise on the result. Therefore, solving the radar forward-looking super-resolution imaging problem based on regularization can effectively improve the ill-conditioned nature of convolution inversion. The constructed objective function can be expressed as:

[0110]

[0111] Where A is the antenna pattern, σ is the target scattering coefficient, s is the echo signal, λ is the regularization parameter, Γ(σ) is a function of σ, and q represents the norm operation.

[0112] S3. Combining the radar observation model, the direction total variation operator is used as the regularization term of the objective function to constrain the target amplitude. At the same time, a positive definite weighting matrix is ​​added to the loss function of the objective function, and Renyi entropy is selected as another regularization term of the objective function to constrain the target amplitude, thus obtaining the target optimization model.

[0113] Specifically, total variation regularization is a representative algorithm among regularization methods. However, the traditional total variation function is rotation-invariant, meaning that after any rotation transformation, the total variation function values ​​in all directions of the image are equal. Therefore, it is impossible to find a specific direction that minimizes the total variation function. Thus, a directional total variation algorithm is proposed based on the traditional total variation regularization algorithm. This algorithm better preserves and restores the image's contours and texture details, resulting in better target reconstruction. The directional total variation regularization term is defined as follows:

[0114]

[0115] Where f is the total variation functional, (i,j) is a point in the discrete image, and t is a vector inside the unit circle. Δ1 and Δ2 represent the interpolation operators in the horizontal and vertical directions, respectively, Δ1f(i,j)=f(i,j)-f(i-1,j), Δ2f(i,j)=f(i,j)-f(i,j-1), α>1, E α,θ Let B2 represent the region enclosed by an ellipse with a major axis of length α, a minor axis of length 1, and an inclination angle of θ. If B2 represents the set of all vectors within the unit circle, then E α,θ It can be seen as being obtained by stretching and rotating B2, therefore E α,θ The relationship between B2 and B2 is as follows:

[0116] E α,θ =R θ Λ α B (9)

[0117] in, Therefore, equation (8) can also be expressed as:

[0118]

[0119] In super-resolution imaging, the gradient weights used in the total variation regularization method depend on their orientation. The total variation operator increases the sensitivity to changes in the selected orientation, therefore, compared to the total variation operator, using the total variation operator as a regularization term can better suppress the staircase effect and perform better in preserving the texture and edge characteristics of the image.

[0120] In practical systems, each measurement has a different degree of error and should have a different weight in the error term. Therefore, a positive definite weighting matrix W1 is defined and added to the loss function term, and its expression is:

[0121] W1 = diag(|e1| p +η,,e m p+η) (11)

[0122] Among them, e j =s j -A j σ0, A j It is the j-th row of matrix A, s j σ is the j-th element of s, σ0 is an initial matrix value of σ, p≥0, η≥0.

[0123] Therefore, ||s-Aσ|| 2 The term is added to matrix W1, and the total variation operator is used as a regularization term to preserve the texture and edge characteristics of the image. By adjusting the direction vector in the total variation operator, a better super-resolution effect on the main texture direction in the image can be achieved, and the staircase effect can be suppressed to some extent. Thus, the optimization model can be expressed as:

[0124]

[0125] Among them, P i Δσ i This can be extended to mean:

[0126] P i Δσ i =Δσ i -〈ξ i ,Δσ i >ξ i (13)

[0127] Where 〈·,·〉 denotes the vector dot product, and Δ denotes the total variation operator; ξ∈U 2 ,||ξ i ||≤γ<1 is a vector that determines the direction; P∈U 2×2 , It is a weighted matrix. Represents the outer product of vectors.

[0128] Representing the total variation operator Δ in matrix form, firstly, if the continuous function of the scene satisfies... but:

[0129]

[0130] in, The dimension of a matrix operator is n x (n y -1)×n x n y I represents a length of n x The unit vector.

[0131] Therefore, the optimization model that needs to be solved can also be expressed as:

[0132]

[0133] Based on the above, and considering that the echo data obtained by radar through forward scanning is complex in practice, step S3 includes:

[0134] S31. Combining the radar observation model, the direction total variation operator is used as the regularization term of the objective function to constrain the target amplitude.

[0135] Specifically, combining the radar observation model of formula (6), the total variability operator is used as the regularization term of the objective function of formula (7) to constrain the target amplitude. Then, the objective function after adding the total variability operator is expressed as:

[0136]

[0137] Where f is the amplitude |σ| of the target scattering coefficient σ. Here, s is the non-differentiable term, s is the echo signal, and A is the antenna pattern. A diagonal matrix, It is the phase of σ, and ε is a positive number approaching 0.

[0138] S32. Add a positive definite weighting matrix W1 to the loss function of the objective function and introduce a slack variable ω to obtain an intermediate optimization model.

[0139] Specifically, a positive definite weighting matrix W1 is added to the loss function of the objective function. Simultaneously, considering the use of variable separation and penalty optimization, a slack variable ω is introduced to replace PΔσ, and constraints are applied to the residual terms of ω and PΔσ. The resulting intermediate optimization model can then be expressed as:

[0140]

[0141] Where f is the amplitude of the target scattering coefficient σ, W1 is the positive definite weighting matrix, s is the echo signal, A is the antenna pattern matrix, φ is the target phase, ω is the relaxation variable, and β1 is the regularization parameter.

[0142] S33. Select Renyi entropy as another regularization term of the objective function to constrain the objective magnitude, and obtain the objective optimization model.

[0143] Specifically, in information theory, Renyi entropy is an important indicator of diversity. Renyi entropy contains a variable parameter α, and the α-order Renyi entropy is defined as:

[0144]

[0145] Where X represents the set of all samples, α≥0 and α≠1, P i P represents the probability of the i-th variable occurring, hence P i >0,

[0146] (1) When α = 0, the probability of each event in set X is equal, and the entropy is at its maximum. The expression is:

[0147] R0(X)=lnn (19)

[0148] Where n is the total number of events in set X.

[0149] (2) When α→1, R0(X) degenerates into Shannon entropy, expressed as:

[0150]

[0151] (3) When α→∞, R α (X) converges to the minimum entropy, expressed as:

[0152] R ∞ (X)=-lnP i max (twenty one)

[0153] Among them, P i max This represents the probability of the event with the highest probability in set X occurring.

[0154] To maximize the use of prior information about the target, reduce sensitivity to noise disturbances, and enhance the algorithm's applicability to different scenarios, Renyi entropy is selected as another regularization term to constrain the target amplitude, resulting in the target optimization model:

[0155]

[0156] Where λ1 is the regularization parameter, α is a variable parameter, α≥0 and α≠1.

[0157] S4. Use the ADMM method to iteratively solve the target optimization model, construct the augmented Lagrangian function, obtain the solution model function, and solve for the slack variables, target phase, and target amplitude in the solution model function.

[0158] S41. Use the ADMM method to iteratively solve the objective optimization model, construct the augmented Lagrangian function, and obtain the solved model function:

[0159]

[0160] Where λ is a Lagrange multiplier.

[0161] S42. Using the method of separating variables, the update of the slack variable, the update of the target phase, and the update of the target amplitude are transformed into subproblems of solving the slack variable, solving the target amplitude, and solving the target phase, respectively, and the Lagrange multiplier is updated in each update process.

[0162] Specifically, in the solution process, three variables need to be updated iteratively: relaxation variable ω, target phase φ, and target amplitude f. Since the updates of these three variables do not affect each other, the method of separation of variables is used to transform the problem into a subproblem about ω, φ, and f, and the Lagrange multiplier λ is updated in each update of the three variables.

[0163] The subproblem of the slack variable ω is:

[0164]

[0165] Where n is the number of iterations, ω (n) Let be the slack variable for the nth iteration;

[0166] The isotropic shrinkage operator shrink2 is defined as follows: Using the standard shrinkage formula to solve the subproblem of the relaxation variable ω, the isotropic shrinkage operator shrink2 is:

[0167]

[0168] Where, b∈R N , μ>0.

[0169] Therefore, the closed-form solution of the relaxed variable ω subproblem in equation (24) can be expressed as:

[0170]

[0171] Where, ω (n+1) Let be the slack variable for the (n+1)th iteration.

[0172] The subproblem of the target magnitude f is:

[0173]

[0174] Among them, f (n+1) This represents the target magnitude for the (n+1)th iteration.

[0175] To solve the minimization problem shown in equation (27), we first differentiate f and find its stationary point, which gives:

[0176]

[0177] Where φ is the target phase and A is the antenna pattern matrix. f is the target amplitude, s is the echo signal, D is the total variation operator, and P∈U2×2 , It is a weighted matrix, ξ∈U 2 ,||ξ i ||≤γ<1 is a vector that determines the direction, λ is a Lagrange multiplier, β1 is a regularization parameter, ω is a slack variable, λ1 is a regularization parameter, and α is an adjustable parameter in Renyi entropy.

[0178] Further decomposition and combination of terms containing f yields:

[0179] ▽f=H(f)fD H P H λ-β1D H P H ω (29)

[0180] in, G = diag{g1,…,g} n}, σ i It is the i-th element in the target scattering coefficient vector.

[0181] Let ▽f = 0 in (29), and we get the update formula for the target amplitude f:

[0182] f (n+1) =H(f) (n) ) -1 (P H D H λ+β1P H D H ω) (30)

[0183] in, G = diag{g1,…,g} n}, σ i Let P be the i-th element in the target scattering coefficient vector, where P ∈ U. 2×2 , It is a weighted matrix, ξ∈U 2 ,||ξ i ||≤γ<1 is a direction-determining vector, D is the total variation operator, λ is the Lagrange multiplier, β1 is the regularization parameter, and ω is the slack variable.

[0184] For the subproblem of the target phase φ: let α represent the column vector consisting of the diagonal elements of the target phase diagonal matrix φ, and let K represent the diagonal matrix diag(f) with amplitude as the diagonal element. Solving the subproblem of the target phase φ is transformed into solving the subproblem of α.

[0185]

[0186] Where α is a column vector consisting of the diagonal elements of the target phase diagonal matrix. s is the echo signal, K is a diagonal matrix diag(f) with amplitude as the diagonal element, and A is the antenna pattern matrix.

[0187] Using the quasi-Newton algorithm to solve equation (31), its derivative is:

[0188] ▽α=2K H A H W 11 AKα-2K H A H W 11 s (32)

[0189] Where K is a diagonal matrix diag(f) with amplitude as its diagonal element.

[0190] Further simplifying equation (32), we get:

[0191] ▽α=H(α)α-2K H A H W 11 s (33)

[0192] Where H(α)=2K H A H W 11 AK.

[0193] Then the iterative update formula for α can be obtained as follows:

[0194] α (n+1) =α (n) -γ[H(α (n) )] -1 ▽α (n (34)

[0195] Where γ is the iteration step size.

[0196] Finally, the formula for updating the Lagrange multipliers in each update process is:

[0197] λ n+1 =λ n +β1(ω-PDf) (35)

[0198] Furthermore, through iterative updates, solutions for the slack variable ω, the target phase φ, and the target amplitude f can be obtained.

[0199] S5. Calculate the target scattering coefficient using the target phase and the target amplitude to achieve super-resolution imaging of the target.

[0200] Specifically, given the target phase φ and target amplitude f, the target scattering coefficient can be calculated using formula (5), and then the echo signal can be calculated using formula (4) to achieve super-resolution imaging of the target.

[0201] This embodiment addresses the shortcomings of traditional super-resolution imaging methods, such as poor recovery of directional texture details in target images, simplistic uniform description of errors across all measurement data, and poor adaptability to different scenarios. It proposes an ITR-DTV deconvolution super-resolution imaging method based on Renyi entropy, utilizing regularization. By introducing directional total variation and Renyi entropy as constraint terms to constrain the target amplitude, this method not only recovers edge texture details more accurately but also enhances its applicability in various scenarios, significantly improving the target recovery capability of airborne radar in low signal-to-noise ratio environments. Furthermore, by adding a positive definite weighting matrix to the loss function, the error level of each measurement value in the loss function is more accurately reflected. Therefore, this imaging method has the advantages of strong recovery of directional texture details in target images, strong scene adaptability, and small error.

[0202] Example 2

[0203] Building upon Example 1, to verify the super-resolution imaging performance of the proposed method, this example first uses Matlab to simulate the imaging process of a forward-looking scanning radar, taking point targets, array targets, and area targets as examples to compare the performance differences between the proposed algorithm and traditional imaging algorithms. Then, this example processes existing measured data from scanning radar to further verify the proposed super-resolution method.

[0204] 1. Experiment setup.

[0205] The simulation parameters for forward-looking radar imaging are shown in Table 1:

[0206] Table 1. Forward Imaging Simulation Parameter Settings

[0207] parameter numerical values dimension Antenna beamwidth 3π / 180 rad Antenna scanning speed 30π / 180 rad / s Transmitted signal carrier frequency 16.014 GHz Transmit signal bandwidth 5 MHz Antenna scanning range -4～4 ° Target range 5 Km

[0208] Please see Figure 3 , Figure 3 This invention provides a point target distribution map under the same distance conditions. The point target simulation experiment selects five points located at the same distance but in different directions, defining the positions of the five points as -0.7°, -0.3°, 0°, 0.5°, and 1.5° respectively.

[0209] Please see Figure 4 , Figure 4 This invention provides a two-dimensional dot matrix target distribution map under different distance conditions. The dot matrix target simulation experiment selected nine points located at different distances and in different orientations, such as... Figure 4 As shown.

[0210] At the same signal-to-noise ratio, comparing the imaging results of the method proposed in this embodiment with those of other methods allows for a direct evaluation of the new algorithm's performance. Furthermore, the effectiveness of the super-resolution algorithm can be quantitatively described using relative imaging error, which can be expressed by the formula:

[0211]

[0212] in, σ represents the recovered scattering information, and σ represents the true scattering information.

[0213] 2. Simulation experiment.

[0214] Against the background, assuming the noise follows a Gaussian distribution, the radar platform moves at a speed of 1000 m / s.

[0215] Please see Figures 5a-5d , Figures 5a-5d This is a comparison image of one-dimensional point target super-resolution imaging results using different methods provided in embodiments of the present invention at a signal-to-noise ratio of 15 dB. Figure 5a It is the least squares method. Figure 5b For the ITR algorithm, Figure 5c For DTV algorithm, Figure 5d This is the method described in this embodiment. Figures 5a-5d As can be seen, in the super-resolution results of the least squares method, the target is completely submerged in noise, and it cannot distinguish point targets in different azimuth directions. The ITR algorithm can roughly distinguish the positions of five point targets, but the average noise amplitude is large and two false targets with high energy appear, resulting in a significant loss of the amplitude of the actual target. The DTV algorithm achieves better super-resolution of azimuth targets, distinguishing all point targets, but some noise points with large amplitudes still remain, and the target signal amplitude is also lost to some extent. When solving for the recovery using the method proposed in this embodiment, most of the energy is concentrated on the target point, and no false targets appear. This effectively suppresses noise and achieves super-resolution recovery of the target, demonstrating significant advantages.

[0216] Please see Figures 6a-6d , Figures 6a-6d This is a comparison image of the super-resolution results of two-dimensional lattice targets using different methods provided in the embodiments of the present invention, wherein... Figure 6a It is the least squares method. Figure 6b For the ITR algorithm, Figure 6c For the total variation algorithm of direction, Figure 6dThis is the method of this embodiment. Figure 6 shows that, affected by noise, the target information in the least squares super-resolution result is almost submerged in noise, and the target cannot be super-resolutiond; although the main information of the target is preserved in the ITR algorithm super-resolution result, some targets are still connected together, and the resolution is limited; the DTV algorithm can suppress noise to a certain extent and improve the effect of antenna pattern broadening, but some connections are still present, making it difficult to accurately determine the target position and analyze the target; the method proposed in this embodiment, under low signal-to-noise ratio conditions, recovers the target energy with almost no loss compared to the algorithms described above, and the azimuth resolution is greatly improved.

[0217] Please see Figure 7 , Figure 7 Error variation curves for different methods provided in embodiments of the present invention. Comparison. Figure 7 As shown by the four relative error curves, the least squares method is most susceptible to noise interference; even at a relatively high signal-to-noise ratio (SNR) of 30 dB, its relative error remains above 50%. The ITR algorithm exhibits relatively stable performance and is the best among the three methods at low SNRs; ​​however, its target recovery performance does not improve significantly with increasing SNR. Compared to the ITR algorithm, the DTV regularization algorithm performs better in target recovery under high SNR conditions, but its target recovery error is larger under low SNR conditions. Under all given SNR conditions, the method proposed in this embodiment has a smaller relative imaging error and superior imaging performance compared to the other three algorithms.

[0218] This embodiment proposes an ITR-DTV regularization method based on Renyi entropy. Building upon the minimum mean square error (MSE) loss function, it introduces a weighting matrix from the ITR algorithm to more accurately reflect the error level of each measurement in the loss function. Simultaneously, the DTV operator and Renyi entropy are incorporated as regularization terms. Experimental results show that, compared to other super-resolution imaging methods, the proposed method can more accurately recover image edge and texture details under low signal-to-noise ratio conditions, providing richer detail information, stronger adaptability to different target scenes, and better super-resolution results.

[0219] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A forward-looking super-resolution imaging method for ITR-DTV radar based on Renyi entropy, characterized in that, Including the following steps: S1. Based on the motion geometry model of radar forward-looking imaging, the echo signal in the azimuth direction is represented as the form of antenna pattern convolved with the target scattering coefficient, and the radar observation model is constructed. S2. Construct an objective function for the target scattering coefficients using regularization methods; S3. Combining the radar observation model, the direction total variation operator is used as the regularization term of the objective function to constrain the target amplitude. At the same time, a positive definite weighting matrix is ​​added to the loss function of the objective function, and Renyi entropy is selected as another regularization term of the objective function to constrain the target amplitude, thus obtaining the target optimization model. S4. Use the ADMM method to iteratively solve the target optimization model, construct the augmented Lagrangian function, obtain the solution model function, and solve for the slack variables, target phase, and target amplitude in the solution model function; S5. Calculate the target scattering coefficient using the solved target phase and target amplitude to achieve super-resolution imaging of the target.

2. The ITR-DTV radar forward-looking super-resolution imaging method based on Renyi entropy according to claim 1, characterized in that, Step S1 includes: S11. Based on the aforementioned motion geometry model, a Taylor series expansion is performed on the distance between the carrier aircraft and the target point to obtain an approximate linear slant range: Where H is the height of the carrier above the horizontal plane, r is the distance from the target point to the projection of the carrier onto the XY plane, R0 is the initial distance between the carrier and the target point, v is the speed of the carrier, t is the moment of the carrier's movement, and ψ0 is the angle between OQ and the Y-axis. The elevation angle of the radar antenna beam; S12. The radar echo signal at the target time is sequentially processed by carrier frequency removal, pulse compression, motion correction, and replacement of the time variable with a spatial variable to obtain the echo signal between the azimuth angle and the approximate linear slant range: Where θ is the azimuth variable and R is the slant distance variable. Weighted reflectance coefficient for the target This represents the convolution operation. Let f0 represent the impulse response function, f0 be the modulation frequency of the carrier frequency, and c be the speed of light. Let θ be the elevation angle of the radar antenna beam, and θ0 be the initial azimuth angle of the target. This refers to the radar beam scanning angular velocity; S13. The echo signal is represented in the azimuth direction as the antenna pattern convolved with the target scattering coefficient. Considering noise and the fact that the radar-received echo is a discrete point, the echo signal is represented in a one-dimensional convolution form, resulting in the radar forward-looking imaging echo model: Where n(t) represents the random noise in the imaging process, a(t) is the antenna pattern, and σ(t) is the target scattering coefficient; S14. Based on the fact that the echo data obtained by the radar through forward-looking scanning is a complex number, the target scattering coefficient is expressed as: σ=φf Where σ is the target scattering coefficient. A diagonal matrix, σ is the phase of σ, and f is the amplitude of the target scattering coefficient σ, |σ|. S15. The radar observation model is obtained from the target scattering coefficient and the radar forward-looking imaging echo model: s=Aφf+n Where s is the echo signal, A is the antenna pattern matrix, and n is the noise.

3. The ITR-DTV radar forward-looking super-resolution imaging method based on Renyi entropy according to claim 1, characterized in that, The objective function is: Where A is the antenna pattern matrix, σ is the target scattering coefficient, s is the echo signal, λ is the regularization parameter, Γ(σ) is a function of σ, and q represents the norm operation.

4. The ITR-DTV radar forward-looking super-resolution imaging method based on Renyi entropy according to claim 1, characterized in that, Step S3 includes the following steps: S31. Combining the radar observation model, and using the total direction variation operator as the regularization term of the objective function to constrain the target amplitude, the objective function after adding the total direction variation operator is expressed as: Where f is the amplitude |σ| of the target scattering coefficient σ. Here, s is the non-differentiable term, s is the echo signal, and A is the antenna pattern matrix. A diagonal matrix, σ is the phase of σ, ε is a positive number approaching 0, and D is the total variation operator; S32. Add a positive definite weighting matrix W1 to the loss function of the objective function and introduce a slack variable ω to obtain the intermediate optimization model: Where f is the amplitude |σ| of the target scattering coefficient σ, W1 is the positive definite weighting matrix, s is the echo signal, A is the antenna pattern matrix, ω is the relaxation variable, and β1 is the regularization parameter; S33. Select Renyi entropy as another regularization term of the objective function to constrain the objective magnitude, thus obtaining the objective optimization model: Where λ1 is the regularization parameter, α is a variable parameter, α≥0 and α≠1.

5. The ITR-DTV radar forward-looking super-resolution imaging method based on Renyi entropy according to claim 4, characterized in that, Step S4 includes: S41. Use the ADMM method to iteratively solve the objective optimization model, construct the augmented Lagrangian function, and obtain the solved model function: Where λ is a Lagrange multiplier; S42. Using the method of separating variables, the update of the slack variable, the update of the target phase, and the update of the target amplitude are transformed into subproblems of solving the slack variable, solving the target amplitude, and solving the target phase, respectively, and the Lagrange multiplier is updated in each update process.

6. The ITR-DTV radar forward-looking super-resolution imaging method based on Renyi entropy according to claim 5, characterized in that, The subproblem of solving the slack variable in step S42 includes: The subproblem of the slack variables is: Where n is the number of iterations, ω (n) Let be the slack variable for the nth iteration; The subproblem of the slack variable is solved using the standard contraction formula, yielding a closed-form solution to the subproblem of the slack variable: Where, ω (n+1) Let be the slack variable for the (n+1)th iteration.

7. The ITR-DTV radar forward-looking super-resolution imaging method based on Renyi entropy according to claim 5, characterized in that, The sub-problem of solving the target amplitude in step S42 includes: The subproblem of the target magnitude is: Among them, f (n+1) The target magnitude for the (n+1)th iteration; The update formula for the target amplitude is: f (n+1) =H(f (n) ) -1 (P H D H λ+β1P H D H ω) in, G = diag{g1,…,g} n }, σ i Let P be the i-th element in the target scattering coefficient vector, where P ∈ U. 2×2 , It is a weighted matrix, ξ∈U 2 ξ i It is a vector that determines direction, ||ξ i ||≤γ<1, where γ is the iteration step size, D is the total variation operator, λ is the Lagrange multiplier, β1 is the regularization parameter, and ω is the relaxation variable.

8. The ITR-DTV radar forward-looking super-resolution imaging method based on Renyi entropy according to claim 5, characterized in that, The subproblem of solving the target phase in step S42 includes: The subproblem of the target phase is transformed into a subproblem of column vectors consisting of the diagonal elements of the target phase diagonal matrix: a (n+1) =argmins H W 11 s+(a (n) ) H K H A H W 11 Aka (n) -s H W 11 AKα (n) -(α (n) ) H K H A H W 11 s Where α is a column vector consisting of the diagonal elements of the target phase diagonal matrix. s is the echo signal, K is a diagonal matrix diag(f) with amplitude as the diagonal element, and A is the antenna pattern matrix; The iterative update formula for the column vector composed of the diagonal elements of the target phase diagonal matrix is ​​as follows: Where γ is the iteration step size, H(α) = 2K H A H W 11 AK, 9. The ITR-DTV radar forward-looking super-resolution imaging method based on Renyi entropy according to claim 5, characterized in that, The formula for updating the Lagrange multipliers in each update process is: λ n+1 =λ n +β1(ω-PDf).

Images