Radar foresight super-resolution imaging method

Abstract

The invention discloses a radar foresight super-resolution imaging method, which comprises the following steps of: constructing an imaging target function by combining sparse prior constraint and total variation prior constraint by utilizing the insensitivity of an L2 norm to a specific value, and finishing the optimal solution of the target function by adopting an iterative threshold shrinkage method. Comprising an initialization step, a range pulse compression step, a migration correction step, a target echo model construction step, an imaging target function construction step and a super-resolution imaging result output step, and a sparse constraint term, a total variation constraint term and an L2 norm constraint term are added into the imaging target function; wherein the L2 norm of the scattering coefficient sigma of the target forms an L2 norm constraint term, the accumulation of absolute values of differences of two pairs of adjacent elements in the sigma forms a total variation constraint term, and the L1 norm of the sigma forms a sparse constraint term; according to the method, the noise amplification phenomenon can be effectively suppressed while high-quality super-resolution imaging of the target scene is completed, convergence is kept in the iteration solving process, and good robustness is achieved.

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-looking imaging scenario. Background Art

[0002] Radar imaging systems have the advantages of all-day, all-weather, long detection distance, and high imaging resolution, and play an increasingly important role in military and civilian fields such as terrain mapping and battlefield surveillance. Traditional synthetic aperture radar (SAR) technology and Doppler sharpening (DBS) technology cannot perform high-resolution imaging of the forward-looking area directly in front of the aircraft due to the lack of effective Doppler bandwidth and the "left-right blur" phenomenon, forming a "blind spot" in the imaging area.

[0003] Radar forward-looking super-resolution imaging refers to building 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 acquiring the real aperture scanning radar echo, and using the deconvolution method 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 imaging for 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 "ATV 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 priors or total variation constraints, it cannot effectively suppress 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 cause serious damage to 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 capable of suppressing 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 real beam scanning echo after Fourier transform with the conjugate of the range-dimensional pulse compression reference function, and inversely transform the multiplication result to the time domain to obtain the echo after pulse compression;

[0009] Motion correction steps: first perform Fourier transform on the echo after pulse compression along the distance dimension, then construct a range motion correction reference function, multiply the pulse compression echo after Fourier transform with the range motion correction reference function, and then inversely transform the multiplication result to the time domain to complete the range motion correction of the echo and obtain the echo after motion correction;

[0010] The target echo model construction steps are as follows: the azimuth signal x(t) extracted from the echo after motion correction is discretized and expressed in the form of a rectangular vector to obtain the azimuth convolution signal vector x; the target echo model is expressed as follows: the azimuth convolution signal vector x is composed of the product of the convolution matrix H determined by the antenna pattern and the scattering coefficient σ of the target 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 minimum noise of the discretized radar receiver; wherein, the L2 norm of the scattering coefficient σ of the target forms the L2 norm constraint term, the accumulation of the absolute value of the difference between two pairs of adjacent elements in the scattering coefficient σ of the target forms the total variation constraint term, and the L1 norm of the scattering coefficient σ of the target forms the sparse constraint term;

[0012] 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.

[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, ▽E(·) is the derivative of the imaging objective function, γ is the iterative step size, 0<γ<2 / ||H T H||2, T represents transpose, ||·||2 is the L2 norm;

[0016]

[0017] Intermediate quantity σ′=σ k-1 -γ▽E(σ k-1), δ is the upper threshold value.

[0018] The specific derivation of the imaging objective function ▽E is:

[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 to optimize and solve.

[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 robustness 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 implementation manner 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 mode 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; (d) is the super-resolution result of the sparse TV regularization method.

[0030] Figure 8 The 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, and combines sparse priors and total variation priors 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, and finally obtains a stable high-quality super-resolution image. The present invention provides a radar forward-looking super-resolution imaging method, comprising the steps of:

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

[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 distance 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 subjected to Fourier transform along the range dimension; then a range-dimensional pulse compression reference function is constructed, and then the real beam scanning echo after Fourier transform 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 echo x after pulse compression. rc (τ, t), and finally the echo x after pulse compression can be obtained rc (τ,t) expression:

[0038]

[0039] Step 2: Perform motion 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 of the target from the radar, is the radar viewing angle, and v is the platform speed. According to this approximate formula, the pulse compression echo x rc (τ,t) can be written as:

[0041]

[0042] Perform linear motion correction on it and obtain the motion-corrected echo x 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( (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] Among them, x, σ and n are 1×N dimensional column vectors, n is the discretized radar receiver noise, N is the total 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 representation of the existing sparse TV method is 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, ∫|▽σ|dσ is the total variation constraint term, β1 and β2 are the regularization parameters for controlling the sparse constraint term and the total variation constraint term respectively. This patent focuses on the 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. Aiming at the semi-convergence and noise amplification problems of the existing methods, a sparse TV method with a joint L2 norm is proposed by utilizing the insensitivity of the L2 norm to outliers. This method introduces the L2 norm of the scattering coefficient of the target to form an L2 norm constraint term to suppress outliers that appear in the iterative solution process, thereby effectively alleviating the noise amplification phenomenon. The 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 above 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), we first need 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 middle 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 consecutive iterations, γ is the iteration step length, and to ensure the convergence of the algorithm, it should satisfy 0<γ<2|| / Η T H||2, is the iterative threshold shrinkage operator, the intermediate quantity σ′=σ k-1 -γ▽E(σ k-1 );

[0076]

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

[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 implementation process of the embodiment is further described in detail below. Figure 1 shown.

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

[0082] Step 1: Target scenario Figure 2 As shown in the figure, in order to examine the sparse target resolution ability of the algorithm of the present invention, two impulse targets are set between -7° and -6° and between -5° and -4° respectively, simulating sparse discrete point targets in actual scenes, such as cars, tanks, etc.; in addition, in order to simultaneously examine the scene contour preservation ability of the algorithm of the present invention, a trapezoidal expansion target is set between -2° and 6° to simulate surface targets with obvious contours in actual scenes, such as airports, mountains, etc., and the distance to the radar is uniformly set to 3000m. The radar transmission signal is a linear frequency modulation signal, the signal bandwidth B is 40MHz, the radar transmission signal pulse width T is 2us, and the frequency modulation slope K r =20MHz / μs. When the radar receives, the sampling rate is f r =100MHz to sample the distance 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-dimensional pulse compression of the simulated echo, and obtain the echo x after pulse compression rc (τ,t), its 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(-if 2vt / c), where t is the scanning time t≤0.4s. rc(f, t) is multiplied by the range motion correction reference function correct(f, t), and then the multiplication result is inversely transformed into the time domain to complete the range motion correction of the simulated echo. The data after the motion 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 by 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 other value. The optimal solution is obtained by iterative solution from formula (15), γ is 1, and δ can be estimated based on the standard deviation of the noise. When the results of two iterations satisfy the following formula

[0089] ||σ k -σ k-1 || 2 <κ (17)

[0090] The result converges, that is, the target solution is obtained, wherein the convergence threshold κ is set to 0.015 according to 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 satisfied and the target solution is obtained.

[0091] 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.

[0092] The echo signal is super-resolved using the existing Richard-Lucy method, sparse regularization method, sparse TV regularization method and the method proposed in the present 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 as 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 both impulse targets and extended targets, and can not only distinguish impulse targets and restore the shape of extended targets, but also has a better 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. From Figure 8 It can also be seen from the displayed MSE convergence curve that compared with the prior art method, 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, when other methods are semi-convergent or even non-convergent, it can maintain stable convergence characteristics, has good convergence characteristics, and has strong robustness.

Claims

1. A radar forward-looking super-resolution imaging method, It is characterized in that Includes 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 a range-dimensional pulse compression reference function, multiply the real beam scanning echo after Fourier transform by the conjugate of the range-dimensional pulse compression reference function, and inversely transform the multiplication result into the time domain to obtain the echo after pulse compression; Steps for correcting movement: First, the echo after pulse compression is Fourier transformed along the range dimension, and then a range motion correction reference function is constructed. The echo after pulse compression after Fourier transformation is multiplied by the range motion correction reference function, and then the multiplication result is inversely transformed to the time domain to complete the range motion correction of the echo and obtain the echo after motion correction. The target echo model construction steps are as follows: the azimuth signal x(t) extracted from the echo after motion correction is discretized and expressed in the form of a rectangular vector to obtain the azimuth convolution signal vector x; the target echo model is expressed as follows: the azimuth convolution signal vector x is composed of the product of the convolution matrix H determined by the antenna pattern and the scattering coefficient σ of the target plus the discretized radar receiver noise n; 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 minimum noise of the discretized radar receiver; wherein, the L2 norm of the scattering coefficient of the target forms the L2 norm constraint term, the accumulation of the absolute value of the difference between two pairs of adjacent elements in the scattering coefficient σ of the target forms the total variation constraint term, and the L1 norm of the scattering coefficient σ of the target 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.

2. The method according to claim 1, It is characterized in that 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 H|| 2 , T represents transpose, ||·|| 2 is the L2 norm; Intermediate δ is the upper threshold value.

3. The method according to claim 2, It is characterized in that Derivation of imaging objective function Specifically: 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 β 1 , β 2 , β 3 are the regularization parameters corresponding to the sparse constraint term, total variation constraint term and L2 norm constraint term respectively.

4. The method according to claim 3, It is characterized in that When iteratively solving the gradient of the imaging objective function, the L curve method is used to determine the regularization parameter β 1 , β 2 , β 3 .

5. The method according to claim 1, It is characterized in that 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 samplings in the azimuth dimension, ||σ|| 1 is a sparse constraint term, is the total variation constraint term, is the L2 norm constraint; β 1 is the regularization parameter of the sparse constraint term, β 2 is the regularization parameter of the total variation constraint, β 3 is the regularization parameter that controls the L2 norm constraint.

6. The method according to claim 1, It is characterized in that Pulse compression echo x rc (τ,t) is specifically: Among them, τ represents the time variable of radar sampling in the distance dimension, and t is the time variable of radar sampling in the azimuth dimension. and are the integral variables of τ and t, respectively, 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.

7. The method according to claim 1, It is characterized in that Echo x after motion correction rcc (τ,t) is specifically: Among them, τ represents the time variable of radar sampling in the distance dimension, and 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, r 0 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, It is an under-the-radar perspective.

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