A radar forward-looking super-resolution imaging method

Abstract

The present invention discloses a radar forward-looking super-resolution imaging method. The method utilizes the insensitivity of the L2 norm to outliers, combines sparse prior constraints and total variation prior constraints to construct an imaging objective function, and adopts an iterative threshold shrinkage method to complete the optimization solution of the objective function. The method includes an initialization step, a range pulse compression step, a migration correction step, a target echo model construction step, an imaging objective function construction step, and a super-resolution imaging result output step. A sparse constraint term, a total variation constraint term, and an L2 norm constraint term are added to the imaging objective function. The L2 norm of the scattering coefficient σ of the target forms the L2 norm constraint term, the accumulation of the absolute values ​​of the differences between two pairs of adjacent elements in σ forms the total variation constraint term, and the L1 norm of σ forms the sparse constraint term. The present invention can effectively suppress noise amplification while completing high-quality super-resolution imaging of the target scene, and the iterative solution process maintains convergence, thereby having good robustness.

Description

Technical Field

[0001] The present invention belongs to the field of radar technology, and in particular relates to regularized super-resolution imaging of a real aperture scanning radar in a radar forward imaging scenario. Background Art

[0002] Radar imaging systems offer advantages such as all-day, all-weather capability, long detection range, and high-resolution imaging, playing an increasingly important role in military and civilian applications such as terrain mapping and battlefield surveillance. However, traditional synthetic aperture radar (SAR) and Doppler sharpening (DBS) technologies are unable to achieve high-resolution imaging of the forward-facing area directly in front of an aircraft due to a lack of effective Doppler bandwidth and the "left-right blur" phenomenon, resulting in a "blind spot" in the imaging area.

[0003] Radar forward-looking super-resolution imaging refers to the construction of an echo convolution model based on the convolution of the azimuth scanning echo, which is the antenna pattern and the target scattering coefficient, on the premise of obtaining the real aperture scanning radar echo. The deconvolution method is then used to estimate the target scattering coefficient, thereby improving the azimuth resolution of the real aperture scanning radar.

[0004] In the past decade, domestic and foreign scholars have been increasingly interested in the research of radar forward-looking super-resolution imaging. A variety of forward-looking super-resolution algorithms have been proposed, and the degree of image quality enhancement has been continuously improved. The paper "Sparse super-resolution imagingfor airborne single channel forward-looking radar in expanded beam space vialp regularisation" (Chen HM, Li M., Wang Z, et al. Electronics Letters, 2015, 51(11): 863-865) proposed a sparse super-resolution imaging method, which uses the sparse characteristics of key targets in the scene and models the targets through the L1 norm to achieve effective resolution of cluster targets. However, due to the excessive emphasis on scene sparsity, this method will cause certain damage to the background contour while resolving targets; the paper "A TV forward-looking super-resolution imaging method based on TSVD strategy for scanning radar" (Zhang Y., Tuo X., Huang Y., Yang J., IEEE Transactions on Geoscience and RemoteSensing, 2020, 58(7): 4517-4528) proposed a sparse TV regularization method, which introduces a total variation constraint to solve the scene contour recovery problem. The target scene is modeled and solved by the regularization method, which can effectively retain the contour features of the scene. However, whether it is a super-resolution method based on sparse prior or total variation constraint, it cannot effectively suppress the noise in the case of strong noise, and as the solution iteration proceeds, noise amplification will occur, that is, a semi-convergence state, which will seriously damage the imaging quality. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a radar forward-looking super-resolution imaging method that can suppress the influence of noise amplification.

[0006] The technical solution adopted by the present invention to solve the above technical problems is a radar forward-looking super-resolution imaging method, comprising the steps of:

[0007] Initialization steps: Set the transmit signal bandwidth B, radar transmit signal pulse width T and frequency modulation slope K r ; Sample the azimuth echo to obtain the real beam scanning echo;

[0008] Range-dimensional pulse compression steps: Perform Fourier transform on the real beam scanning echo along the range dimension; then construct a range-dimensional pulse compression reference function, multiply the Fourier-transformed real beam scanning echo with the conjugate of the range-dimensional pulse compression reference function, and inversely transform the multiplication result into the time domain to obtain the pulse compressed echo;

[0009] Migration correction steps: First, perform Fourier transform on the pulse compression echo along the range dimension. Then, construct a range migration correction reference function. Multiply the Fourier transformed pulse compression echo with the range migration correction reference function. Then, inversely transform the multiplication result to the time domain to complete the range migration correction of the echo and obtain the migration-corrected echo.

[0010] The target echo model is constructed by discretizing the azimuth signal x(t) extracted from the motion-corrected echo into a rectangular vector to obtain the azimuth convolution signal vector x. The target echo model is represented as follows: the azimuth convolution signal vector x is the product of the convolution matrix H determined by the antenna pattern and the target's scattering coefficient σ, plus the discretized radar receiver noise n.

[0011] Imaging objective function construction steps: adding sparse constraint terms, total variation constraint terms, and L2 norm constraint terms to the imaging objective function for solving the discretized radar receiver noise minimum; wherein, the L2 norm of the target scattering coefficient σ forms the L2 norm constraint term, the accumulation of the absolute value of the difference between two pairs of adjacent elements in the target scattering coefficient σ forms the total variation constraint term, and the L1 norm of the target scattering coefficient σ forms the sparse constraint term;

[0012] Super-resolution imaging result output step: calculate the gradient of the imaging objective function through iterative solution, and output the radar forward-looking super-resolution imaging result formed by the final target scattering coefficient σ distribution.

[0013] Specifically, the specific method for iteratively solving the gradient of the imaging objective function is:

[0014]

[0015] Among them, σ k is the kth iteration result of the target scattering coefficient σ, is the iterative threshold shrinkage operator, is the derivative of the imaging objective function, γ is the iteration step, 0<γ<2 / ||Η T Η||2, T represents transpose, ||·||2 is the L2 norm;

[0016]

[0017] Intermediate amount δ is the upper threshold.

[0018] Derivation of imaging objective function Specifically:

[0019]

[0020] Where diag(·) is a diagonal matrix, σ i is the i value of σ, ε is a constant introduced to solve the L1 norm non-differentiable problem, and the intermediate vector Represents σ i The difference between two pairs of adjacent elements of β1, β2, and β3 are the regularization parameters corresponding to the sparse constraint term, total variation constraint term, and L2 norm constraint term, respectively.

[0021] The present invention utilizes the insensitivity of the L2 norm to outliers, combines sparse constraints and total variation constraints to describe the scene, and adopts an iterative threshold shrinkage algorithm for optimization and solution.

[0022] The beneficial effects of the present invention are that, while better imaging of the target scene is performed, noise amplification can be effectively suppressed, good convergence characteristics are maintained, and the robustness and stability of super-resolution imaging are improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 It is a flowchart of the method provided by the present invention.

[0024] Figure 2 It is a schematic diagram of a simulation imaging scene adopted in a specific embodiment of the present invention.

[0025] Figure 3 It is the original echo signal in the specific implementation manner of the present invention.

[0026] Figure 4 It is the echo after pulse compression in the specific implementation manner of the present invention.

[0027] Figure 5 It is the echo after range migration correction in the specific implementation mode of the present invention.

[0028] Figure 6 yes Figure 5 The distance unit section of the target.

[0029] Figure 7 These are the imaging results after processing using the method of the present invention and the existing method; (a) is the super-resolution result of the method of the present invention; (b) is the super-resolution result of the Richard-Lucy (RL) method; (c) is the super-resolution result of the sparse regularization method; and (d) is the super-resolution result of the sparse TV regularization method.

[0030] Figure 8The method of the present invention and the existing method are used to iteratively solve the curve. DETAILED DESCRIPTION

[0031] The present invention utilizes the insensitivity of the L2 norm to outliers, combines a sparse prior with a total variation prior to construct an imaging objective function to alleviate the noise sensitivity amplification in the deconvolution process, and then uses an iterative threshold shrinkage method to optimize the objective function, ultimately obtaining a stable, high-quality super-resolution image. The present invention provides a radar forward-looking super-resolution imaging method, comprising the following steps:

[0032] Step 1: Perform range-dimensional pulse compression on the real beam scanning echo

[0033] Assume that the pulse width of the radar transmission signal is T, the signal bandwidth is B, the wavelength of the transmission signal is λ, the center frequency of the radar transmission signal is f0 and the frequency modulation slope is K. r =B / T;

[0034] The radar transmits a linear frequency modulation signal, and the antenna beam scans the imaging area. The received real beam scanning echo x0(τ,t) is:

[0035]

[0036] Among them, τ represents the time variable of radar sampling in the range dimension, t is the time variable of radar sampling in the azimuth dimension, and the total sampling in the azimuth dimension is N. and are the integral variables of τ and t, σ(·) represents the target echo scattering coefficient, h(·) represents the antenna pattern of the scanning antenna, c is the speed of light, r P (·) is the target slant distance, sinc(·) is the sine basis function, and exp(·) is the exponential function.

[0037] The above real beam scanning echo is subjected to range-dimensional pulse compression, that is, the real beam scanning echo is first Fourier transformed along the range dimension; then the range-dimensional pulse compression reference function is constructed, and then the real beam scanning echo after Fourier transformation is multiplied by the conjugate of the range-dimensional pulse compression reference function, and the multiplication result is inversely transformed into the time domain to obtain the pulse compressed echo x rc (τ, t), and finally the echo x after pulse compression can be obtained rc (τ,t) expression:

[0038]

[0039] Step 2: Perform migration correction on the echo after pulse compression

[0040] In a platform with fast scanning time but slow movement speed, Among them, r0 is the initial distance between the target and the radar, is the radar viewing angle, and v is the platform speed. According to this approximate formula, the echo x after pulse compression can be rc (τ,t) is written as:

[0041]

[0042] Perform linear migration correction on it and obtain the echo x after migration correction rcc (τ,t) is:

[0043]

[0044] in, is the target scattering coefficient after phase weighting.

[0045] Step 3: Construct target echo model

[0046] Since the present invention only performs super-resolution on azimuth, it only processes the azimuth signal amplitude. rcc The azimuth signal x(t) of (τ, t) is extracted:

[0047]

[0048] The azimuth signal is the convolution of the scattering coefficient of the target and the antenna pattern of the scanning antenna:

[0049] x(t)=σ(t*)h(t) (6)

[0050] Where * is the convolution operation. Considering the influence of noise, the azimuth signal expression is rewritten as

[0051] x(t)=σ(t)*h(t)+n(t) (7)

[0052] where n(t) is the radar receiver noise.

[0053] First, discretize formula (7) and express it in rectangular vector form to obtain the azimuth convolution signal vector x as the target echo model:

[0054] x=Hσ+n (8)

[0055] Where x, σ, and n are 1×N-dimensional column vectors, n is the discretized radar receiver noise, N is the total number of sampling points of the two-dimensional echo matrix in the azimuth dimension, and H is the convolution matrix determined by the antenna pattern:

[0056]

[0057] Among them, h i ,i=1,2…l is the i-th sampling point of the vector, where l is the total number of sampling points in the antenna pattern.

[0058] Step 4: Construct imaging objective function

[0059] For the noise sensitivity problem in the deconvolution operation, that is, when solving the target scattering coefficient σ when the discretized radar receiver noise x-Hσ is minimized, a regularization method is usually used to solve it. The regularization of the existing sparse TV method is expressed in the data fidelity term On the basis of , sparse constraint term and total variation constraint term are added; among them, the total variation constraint term is formed by the accumulation of the absolute value of the difference between two pairs of adjacent elements in the scattering coefficient σ of the target, and the sparse constraint term is formed by the L1 norm of the target scattering coefficient σ;

[0060] for:

[0061]

[0062] Among them, ||·||2 is the L2 norm, ||·||1 is the L1 norm, is the data fidelity term, ||σ||1 is the sparse constraint term, is the total variation constraint term, β1 and β2 are the regularization parameters controlling the sparse constraint term and the total variation constraint term respectively. This patent focuses on one-dimensional super-resolution signal processing in the azimuth dimension, so the total variation constraint term can be expressed as follows:

[0063]

[0064] where σ i+1 , σ i and σ i-1 are the i+1th, ith, and i-1th values ​​of σ, respectively. To address the semi-convergence and noise amplification issues of existing methods, a sparse TV method with a joint L2 norm is proposed, utilizing the insensitivity of the L2 norm to outliers. This method introduces the L2 norm of the target's scattering coefficient to form an L2 norm constraint term to suppress outliers that appear during the iterative solution, thereby effectively alleviating the noise amplification phenomenon. A new regularized objective function is constructed as follows:

[0065]

[0066] in Where is the L2 norm constraint term, and β3 is the regularization parameter that controls the L2 norm constraint term.

[0067] Step 5: Iteratively solve the objective function gradient to output super-resolution imaging results

[0068] To optimize the objective function and find the extreme solution that minimizes the objective function, it is obviously quite difficult to solve it directly. Therefore, an iterative method can be used to gradually approach the true solution. This paper adopts the iterative threshold shrinkage IST method. Because the L1 norm is not differentiable, to differentiate the objective function (12), it is first necessary to introduce a very small constant ε to solve the non-differentiability of the L1 norm and rewrite the objective function E β (σ) is:

[0069]

[0070] Among them, the intermediate Then solve the gradient of the modified objective function:

[0071]

[0072] Among them, the intermediate vector diag(·) is a diagonal matrix.

[0073] Then the basic iteration formula of the IST method is as follows:

[0074]

[0075] Among them, σ k and σ k+1 is the result of two adjacent iterations, γ is the iteration step size, and to ensure the convergence of the algorithm, it should satisfy 0<γ<2 / ||Η T Η||2, is the iterative threshold shrinkage operator, the intermediate quantity

[0076]

[0077] Where δ is the upper threshold, which is usually taken as an estimated value smaller than the noise standard deviation. The regularization parameter can be determined using the L-curve method, that is, the regularization parameter is taken as the optimal value when it is at the best position between the data fidelity term and the regularization term.

[0078] After the iterative solution is completed, the output target scattering coefficient σ=σ k After obtaining the target scattering coefficient distribution, the radar forward-looking super-resolution imaging result can be output.

[0079] Example

[0080] The present invention is mainly verified by simulation experiment, and all steps and conclusions are verified to be correct on Matlab2020. The following is a further detailed description of the implementation process of the embodiment. Figure 1 shown.

[0081] The simulation parameters of the target scenario and radar system include: carrier frequency 10 GHz, platform speed 50 m / s, transmission signal bandwidth 40 MHz, transmission signal pulse width 2 μs, sampling rate 100 MHz, pulse repetition frequency 2000 Hz, main lobe beamwidth -2.5°, antenna scanning speed 50° / s, antenna scanning range ±10°, and target initial distance 3000 m.

[0082] Step 1: Target scenario such as Figure 2 As shown in the figure, in order to examine the sparse target resolution capability of the algorithm of the present invention, two impulse targets were set between -7° and -6° and between -5° and -4°, respectively, to simulate sparse discrete point targets in actual scenes, such as cars, tanks, etc.; in addition, in order to simultaneously examine the scene contour preservation capability of the algorithm of the present invention, a trapezoidal expansion target was set between -2° and 6° to simulate surface targets with relatively obvious contours in actual scenes, such as airports, mountains, etc., and the distance from the radar was uniformly set to 3000m. The radar transmit signal is a linear frequency modulation signal with a signal bandwidth B of 40MHz, a radar transmit signal pulse width T of 2us, and a frequency modulation slope K. r =20MHz / μs. When the radar receives, the sampling rate is f r =100MHz to sample the range dimension echo, and the azimuth dimension echo is sampled at a pulse repetition frequency prf = 2000Hz to obtain the real beam scanning echo x0(τ,t), whose size is 440×800, as shown in Figure 3 shown.

[0083] Step 2: Perform Fourier transform on the real beam scanning echo along the range dimension. Then construct the range dimension pulse compression reference function refer(τ)=exp(jπK r τ 2 ), where -1μs≤τ≤1μs. Then compare the real beam scanning echo after Fourier transformation with the reference * (f) Multiply, and then transform the multiplication result back to the time domain to complete the distance dimension pulse compression of the simulated echo, and obtain the echo x after pulse compression rc (τ,t), whose size remains unchanged, such as Figure 4 As shown in the figure, f represents the distance dimension frequency domain variable, and * represents conjugate.

[0084] Step 3: First, perform Fourier transform on the echo after pulse compression along the distance dimension, denoted as X rc (f, t). Then construct the range migration correction reference function correct(f, t) = exp(-if2vt / c), where t is the scanning time t≤0.4s. rc(f, t) is multiplied by the range migration correction reference function correct(f, t), and then the multiplication result is inversely transformed into the time domain to complete the range migration correction of the simulated echo. The data after migration correction is recorded as x rcc (τ,t), the matrix size remains unchanged, such as Figure 5 At this time, the signal-to-noise ratio of the target distance unit is 15dB, as shown in Figure 5 and Figure 6 shown.

[0085] Step 4: Obtain the antenna pattern convolution matrix, discretize the scanning antenna pattern according to the main lobe width θ between the first zero points of the antenna pattern, the pulse repetition frequency prf and the scanning speed ω, and obtain The number of discretized antenna pattern points l = 100, then h = [h0,h1,…,h 100 ], thus constructing the convolution matrix H:

[0086]

[0087] Step 5: x rcc The amplitude of the data in the jth row (the initial value of j is 1) of (τ, t) is the original echo vector x to be processed. The imaging objective function is constructed according to expression (13). H is the convolution matrix constructed in the specific implementation step 4.

[0088] Step 6: Obtain the objective function gradient according to expression (14). First, assign x to σ 1 , ε is 10 -8 , the three regularization parameters β1, β2, and β3 are determined using the L curve method. We can first use empirical values ​​to assign initial values ​​to the three regularization parameters, and then fix two of the regularization parameters and use the L curve method to determine the value of the other one. The optimal solution is obtained by iterative solution using formula (15), γ is 1, and δ can be estimated based on the standard deviation of the noise. When the results of two iterations meet the following formula

[0089] ||σ k -σ k-1 || 2 <κ (17) The result converges, that is, the target solution is obtained, where the convergence threshold κ is set to 0.015 based on the empirical value. If formula (17) is not satisfied, k=k+1 is updated and the iteration is continued until the iteration termination condition is met and the target solution is obtained.

[0090] Step 7: Determine whether all distance unit data are processed completely, that is, whether j is greater than 440. If so, it means that the processing is complete, and the super-resolution imaging result is output. If not, it means that the processing is not complete, update j=j+1 and return to step 5.

[0091] The echo signal is super-resolved using the existing Richard-Lucy method, sparse regularization method, sparse TV regularization method and the method proposed in this invention. The imaging results are as follows: Figure 7 As shown. Figure 7 It can be found that although the three existing technical methods used for comparison can distinguish two impulse targets, the distortion of the extended target in the results of the RL method and the sparse regularization method is more serious, and some false targets appear in the results; although the sparse TV method can roughly maintain the contour shape, there are serious burrs, and the impulse target is also distorted; the algorithm proposed in the present invention has better recovery of impulse targets and extended targets, not only can it distinguish impulse targets and restore the shape of extended targets, but also has a good smoothing suppression effect on noise. It can be seen from the figure that the method provided by the present invention can well complete the super-resolution imaging of radar. Figure 8 The displayed MSE convergence curve also shows that compared with the existing technology methods, the method proposed in the present invention can achieve the lowest MES value in the iterative solution process, with a lower scene distortion rate. Moreover, it can maintain stable convergence characteristics when other methods are semi-convergent or even non-convergent. It has good convergence characteristics and strong robustness.

Claims

1. A radar forward-looking super-resolution imaging method, characterized in that: Including steps: Initialization steps: Set the radar transmit signal bandwidth B, transmit signal pulse width T and frequency modulation slope K r ; Sample the azimuth echo to obtain the real beam scanning echo; Range pulse compression steps: Perform Fourier transform on the real beam scanning echo along the range dimension; then construct the range-dimensional pulse compression reference function, multiply the Fourier-transformed real beam scanning echo with the conjugate of the range-dimensional pulse compression reference function, and inversely transform the multiplication result into the time domain to obtain the pulse compressed echo; Migration correction steps: First, the pulse compression echo is Fourier transformed along the range dimension. Then, a range migration correction reference function is constructed. The Fourier transformed pulse compression echo is multiplied by the range migration correction reference function. The multiplication result is then inversely transformed to the time domain to complete the range migration correction of the echo and obtain the migration-corrected echo. The target echo model is constructed by discretizing the azimuth signal x(t) extracted from the motion-corrected echo into a rectangular vector to obtain the azimuth convolution signal vector x. The target echo model is represented as follows: the azimuth convolution signal vector x is the product of the convolution matrix H determined by the antenna pattern and the target's scattering coefficient σ, plus the discretized radar receiver noise n. Imaging objective function construction steps: adding a sparse constraint term, a total variation constraint term, and an L2 norm constraint term to the imaging objective function for solving the discretized radar receiver noise minimum; wherein, the L2 norm of the target's scattering coefficient forms the L2 norm constraint term, the accumulation of the absolute value of the difference between two pairs of adjacent elements in the target's scattering coefficient σ forms the total variation constraint term, and the L1 norm of the target's scattering coefficient σ forms the sparse constraint term; Super-resolution imaging result output step: by iteratively solving and calculating the gradient of the imaging objective function, the final radar forward-looking super-resolution imaging result formed by the target scattering coefficient σ distribution is output; The specific method for iteratively solving the gradient of the imaging objective function is: Among them, σ k is the kth iteration result of the target scattering coefficient σ, is the iterative threshold shrinkage operator, is the derivative of the imaging objective function, γ is the iteration step, 0<γ<2 / ||Η T Η||2, T represents transpose, ||·||2 is the L2 norm; Intermediate amount δ is the upper threshold.

2. The method according to claim 1, wherein The specific derivative of the imaging objective function ▽E is: Where diag(·) is a diagonal matrix, σ i is the i value of σ, ε is a constant introduced to solve the L1 norm non-differentiable problem, and the intermediate vector Represents σ i The difference between two pairs of adjacent elements of β1, β2, and β3 are the regularization parameters corresponding to the sparse constraint term, total variation constraint term, and L2 norm constraint term, respectively.

3. The method according to claim 2, wherein: When iteratively solving the gradient of the imaging objective function, the L-curve method is used to determine the regularization parameters β1, β2, and β3 respectively.

4. The method according to claim 1, wherein: The imaging objective function is specifically: Among them, ||·||2 is the L2 norm, ||·||1 is the L1 norm, σ i+1 , σ i and σ i-1 are the i+1th, ith and i-1th values ​​of σ respectively, N is the total number of samples in the orientation dimension, ‖σ‖1 is the sparse constraint term, is the total variation constraint term, is the L2 norm constraint term; β1 is the regularization parameter of the sparse constraint term, β2 is the regularization parameter of the total variation constraint term, and β3 is the regularization parameter that controls the L2 norm constraint term.

5. The method according to claim 1, wherein: Pulse compression echo x rc (τ,t) is specifically: Among them, τ represents the time variable of radar sampling in the range dimension, t is the time variable of radar sampling in the azimuth dimension, and are the integral variables of τ and t, h(·) represents the antenna pattern of the scanning antenna, c is the speed of light, r P (·) is the target slant range, sinc(·) is the sine basis function, exp(·) is the exponential function, and λ is the wavelength of the transmitted signal.

6. The method according to claim 1, wherein: Echo x after migration correction rcc (τ,t) is specifically: Among them, τ represents the time variable of radar sampling in the range dimension, t is the time variable of radar sampling in the azimuth dimension, and are the integral variables of τ and t respectively, is the target scattering coefficient after phase weighting, exp(·) is the exponential function, r0 is the initial distance of the target from the radar; sinc(·) is the sine basis function, h(·) represents the antenna pattern of the scanning antenna, v is the platform movement speed, is the radar viewing angle, c is the speed of light, and λ is the wavelength of the transmitted signal.

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