Multi-criteria joint constrained range image sequence super-resolution method

Abstract

The application discloses a multi-criterion joint constraint range image sequence super-resolution method, and relates to the technical field of radar signal processing, and solves the problems that the range image super-resolution reconstruction precision is not high and the robustness is poor under a complex configuration in the prior art; the method comprises the following steps: acquiring a radar echo signal, and constructing a multi-criterion joint constraint range image super-resolution reconstruction model about the radar echo signal; constructing a non-convex relaxation penalty function to solve the range image super-resolution reconstruction model, and obtaining a cost function corresponding to the range image super-resolution reconstruction model; solving the cost function, and obtaining a super-resolution range image sequence of a target; the Doppler information between multi-frame range image sequences is utilized, the range image super-resolution reconstruction precision is improved, the range image super-resolution reconstruction robustness is enhanced, and robust range super-resolution imaging is realized.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of radar signal processing, and particularly relates to a multi-criterion joint constraint range profile sequence super-resolution method. BACKGROUND

[0002] High resolution range profile (HRRP) is a vector sum of target scattering point subechoes on radar ray obtained by using wideband radar signals, which contains rich physical structure features of the target. Therefore, the radar target recognition method based on HRRP has the advantage of high recognition accuracy, and has great value for target recognition and classification. However, in actual engineering application, due to the requirements of target detection distance, hardware device capacity and other indicators or system parameter limitations, the bandwidth of radar transmitting signals cannot meet the HRRP recognition demand of the target. In addition, in the electromagnetic interference environment of modern electronic warfare, the spectrum of radar HRRP may be interfered, which leads to the limitation of the actually available target signal bandwidth, thereby seriously affecting the target recognition performance. In summary, when the radar system resources are limited due to internal or external factors, the performance of the HRRP-based target recognition algorithm is seriously degraded, thereby seriously affecting the national defense capability, strategic early warning capability and long-range guided strike capability of the radar equipment applying the algorithm. Therefore, it is of great significance to study the robust range profile super-resolution algorithm under the condition of limited radar resources, and to obtain the target HRRP from low resolution range profile (LRRP) through super-resolution.

[0003] For range super-resolution, the existing algorithms such as bandwidth extrapolation, Prony, RELAX and MUSIC are usually susceptible to noise and model errors, and the super-resolution multiple is low. Therefore, in recent years, the sparse reconstruction-based super-resolution method based on compressed sensing (CS) has been widely studied by domestic and foreign scholars in order to realize more robust and high-multiple range super-resolution. According to the different sparse reconstruction technologies used, these super-resolution technologies are mainly divided into three categories: greedy algorithm class, Lp norm class and sparse Bayesian learning class.

[0004] The existing range profile super-resolution methods based on compressed sensing are all based on single-pulse range profile super-resolution, and do not use the Doppler information of the target. Therefore, the above super-resolution methods have the disadvantages of low super-resolution reconstruction accuracy and poor robustness when dealing with complex configuration range profiles. SUMMARY

[0005] The application solves the problems of low reconstruction precision and poor robustness of the distance image super-resolution reconstruction under complex configurations in the prior art by providing a multi-criteria joint constraint distance image sequence super-resolution method, realizes the use of the Doppler information between multiple distance image sequences, improves the reconstruction precision of the distance image super-resolution, enhances the robustness of the distance image super-resolution reconstruction, and realizes robust distance super-resolution imaging.

[0006] The application provides a multi-criteria joint constraint distance image sequence super-resolution method, which comprises the following steps:

[0007] obtaining a radar echo signal and constructing a multi-criteria joint constraint distance image super-resolution reconstruction model about the radar echo signal;

[0008] solving the distance image super-resolution reconstruction model by constructing a non-convex relaxation penalty function, to obtain a cost function corresponding to the distance image super-resolution reconstruction model;

[0009] solving the cost function to obtain a super-resolution distance image sequence of a target.

[0010] In a possible implementation manner, the step of constructing the multi-criteria joint constraint distance image super-resolution reconstruction model about the radar echo signal comprises the following steps:

[0011] converting the radar echo signal Y s (n,m) into a short-bandwidth distance image sequence frequency domain signal matrix;

[0012] performing Fourier transform on the short-bandwidth distance image sequence frequency domain signal matrix to obtain a first matrix Y;

[0013] solving the first matrix Y according to a constraint condition to obtain a distance image super-resolution reconstruction model.

[0014] In a possible implementation manner, the step of solving the first matrix Y according to the constraint condition comprises the following steps:

[0015] determining a constraint condition for solving according to the sparsity of a target scattering point and the low-rank property of the distance image sequence, and solving the first matrix Y according to the constraint condition.

[0016] In a possible implementation manner, the step of solving the distance image super-resolution reconstruction model by constructing a non-convex relaxation penalty function comprises the following steps:

[0017] constructing a non-convex relaxation penalty function by using a continuously smooth approximate hyperbolic tangent function;

[0018] jointly solving the distance image super-resolution reconstruction model according to the non-convex relaxation penalty function.

[0019] The solving result is optimized by using a Lagrange multiplier method to obtain a cost function corresponding to the range image super-resolution reconstruction model.

[0020] In a possible implementation, the solving of the cost function to obtain the super-resolution range image sequence of the target comprises:

[0021] A recursive error related to compressed sensing in the cost function is calculated, and a first cost function is determined according to the recursive error;

[0022] An update iteration formula of a weight coefficient matrix is determined according to the first cost function;

[0023] The first cost function is optimized under a constraint condition to obtain a second cost function;

[0024] The update iteration formula is optimized by using a gradient descent method according to the second cost function to obtain a second update iteration formula;

[0025] The second update iteration formula and the cost function are combined to be solved to obtain the super-resolution range image sequence of the target.

[0026] In a possible implementation, the radar echo signal is represented as:

[0027]

[0028] wherein P represents a total number of scattering points; δ p represents a scattering intensity of the pth scattering point; exp(·) represents an exponential function; f n represents a distance frequency; c represents a light speed; R p represents a slant range of the pth scattering point; represents a Doppler frequency of the pth scattering point; t m represents a slow time; Y s (n, m) represents a range image super-resolution reconstruction model.

[0029] In a possible implementation, the range image super-resolution reconstruction model is represented as:

[0030]

[0031] wherein Σ represents a diagonal matrix composed of singular values of S; G represents a target range-Doppler domain image; ||·||0 represents an l0 norm; γ represents a regularization parameter; Y represents a first matrix; Ψ represents a partial Fourier transform matrix; S represents a range image sequence matrix; F M represents an M-dimensional Fourier transform matrix; U represents a left orthogonal matrix; V represents a right orthogonal matrix, Hdenotes a transpose operation.

[0032] In a possible implementation, the cost function is represented as:

[0033]

[0034] wherein Y represents a first matrix; S represents a distance image sequence matrix; represents a partial Fourier transform matrix; ||·||0represents an l0norm; represents a Frobenius norm; represents a regularization coefficient; F represents a penalty function; G represents a target range-doppler domain image; represents a scale coefficient; represents a regularization parameter; and represents a scale coefficient. F wherein Y represents a first matrix; S represents a distance image sequence matrix; represents a partial Fourier transform matrix; ||·||0represents an l0norm; represents a Frobenius norm; represents a regularization coefficient; F represents a penalty function; G represents a target range-doppler domain image; represents a scale coefficient; represents a regularization parameter; and represents a scale coefficient.

[0035] In a possible implementation, the super-resolution distance image sequence is represented as:

[0036]

[0037] wherein W represents an optimal weight coefficient matrix. opt

[0038] The one or more technical solutions provided in the present application have at least the following technical effects or advantages:

[0039] (1) The present application adopts a distance image super-resolution reconstruction model for the problem of poor distance image reconstruction accuracy under a complex configuration, the model uses the Doppler information between multiple frames of distance image sequences of a target, simultaneously constrains the sparsity of a range-doppler image and the low rank of a distance image sequence, and can realize fast and high-precision super-resolution reconstruction of the distance image sequence of the target under limited resources.

[0040] (2) The present application adopts a continuously smooth approximate hyperbolic tangent function to approximate an l0norm and construct a non-convex penalty function, unifies the sparsity and low rank of a signal into a cost function, and compared with other penalty functions, the penalty function is closer to an l0norm model when the super parameter approaches 0, and thus can fully reflect the sparsity and low rank characteristics of a signal to be reconstructed, thereby obtaining better performance. BRIEF DESCRIPTION OF DRAWINGS

[0041] Figure 1 A multi-criteria joint constraint distance image sequence super-resolution method step flowchart provided for an embodiment of the present application;

[0042] Figure 2 A multi-measurement vector reconstruction framework schematic diagram based on an adaptive filtering algorithm provided for an embodiment of the present application;

[0043] FIG. 3(a) is a distance image super-resolution simulation experiment result schematic diagram of a 400M bandwidth high-resolution distance image sequence provided for an embodiment of the present application; ​

[0044] Fig. 3(b) is a schematic diagram of the range profile super-resolution simulation results of the low-resolution range profile sequence of 100M bandwidth under the resource-restricted condition according to an embodiment of the present application;

[0045] Fig. 3(c) is a schematic diagram of the range profile super-resolution simulation results of the super-resolution range profile sequence of 400M bandwidth reconstructed by the SBL algorithm according to an embodiment of the present application;

[0046] Fig. 3(d) is a schematic diagram of the high-resolution range profile sequence of 400M bandwidth according to an embodiment of the present application;

[0047] Fig. 4(a) is a correlation coefficient curve of the super-resolution range profile sequence and the high-resolution range profile sequence obtained by the SMV-SBL algorithm according to an embodiment of the present application;

[0048] Fig. 4(b) is a correlation coefficient curve of the super-resolution range profile sequence and the high-resolution range profile sequence obtained by the method according to an embodiment of the present application;

[0049] Fig. 5(a) is a schematic diagram of the super-resolution performance analysis of the original wideband range profile sequence under low signal-to-noise ratio according to an embodiment of the present application;

[0050] Fig. 5(b) is a schematic diagram of the super-resolution performance analysis of the sparse range profile sequence under low signal-to-noise ratio according to an embodiment of the present application;

[0051] Figure 6 Fig. 6 is a schematic diagram of the super-resolution performance analysis of the Yak-42 measured data according to an embodiment of the present application;

[0052] Fig. 7(a) is a schematic diagram of the range profile super-resolution results of the original bandwidth and narrowband range profile according to an embodiment of the present application;

[0053] Fig. 7(b) is a schematic diagram of the range profile super-resolution results of the Yak-42 measured data under different algorithms according to an embodiment of the present application; DETAILED DESCRIPTION

[0054] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0055] The present application provides a range profile sequence super-resolution method with multiple criteria combined constraints, as shown in the formula (1), which comprises the following steps S101-S103. Figure 1

[0056] ​S101, obtain a radar echo signal, and construct a multi-criteria joint constraint range image super-resolution reconstruction model for the radar echo signal.

[0057] Specifically, in step S101, the multi-criteria joint constraint range image super-resolution reconstruction model for the radar echo signal is constructed, including the following steps S1011 to S1013.

[0058] S1011, convert the radar echo signal Y s (n,m) into a short-bandwidth range image sequence frequency domain signal matrix.

[0059] Here, the radar echo signal is represented as:

[0060]

[0061] where P represents the total number of scattering points; δ p represents the scattering intensity of the pth scattering point; exp(·) represents the exponential function; f n represents the distance frequency; c represents the speed of light; R p represents the slant range of the pth scattering point; represents the Doppler frequency of the pth scattering point; t m represents the slow time; Y s (n,m) represents the range image super-resolution reconstruction model. The distance frequency f n =[n-N / 2] / N·B,n=0,1,…,N-1, where B is the signal bandwidth, and N is the number of sampling points.

[0062] Then, the short-bandwidth range image sequence frequency domain signal matrix under limited resources can be represented as:

[0063] Y=D Y s (2)

[0064] In the formula, is a partial sampling matrix, K is the number of sampling points, and K<N.

[0065] S1012, Fourier transform the short-bandwidth range image sequence frequency domain signal matrix to obtain a first matrix Y.

[0066] Here, the first matrix Y is represented as:

[0067] Y=D F N S (3)

[0068] In the formula, is a range image sequence matrix, is an N-dimensional Fourier transform matrix, so Ψ=D F N is a partial Fourier transform matrix.

[0069] S1013, solve the first matrix Y according to the constraint condition to obtain a range image super-resolution reconstruction model.

[0070] Specifically, solving the first matrix Y according to the constraint condition comprises: determining the constraint condition for solving according to the sparsity of the target scattering point and the low rank of the range image sequence, and solving the first matrix Y according to the constraint condition.

[0071] Here, solving formula (3) can obtain the expected range image super-resolution reconstruction model.

[0072] However, formula (3) is an underdetermined equation, and direct solving will obtain infinite solutions, so it is necessary to add a constraint condition to the equation.

[0073] It is considered to introduce the sparsity of the target scattering point and the low rank of the range image sequence to constrain formula (3), and the following constrained optimization problem is obtained.

[0074]

[0075] In the formula, is a target range-doppler domain image, is an M-dimensional Fourier transform matrix, γ is a regularization parameter, and Rank(·) represents the rank of the matrix.

[0076] The singular value decomposition of the range image sequence matrix S can approximate the rank of the range image sequence matrix S through the number of non-zero singular values.

[0077] Therefore, the singular value decomposition of the range image sequence matrix S is obtained as S=UΣV H , where Σ is a diagonal matrix composed of singular values of the range image sequence matrix S; U represents a left orthogonal matrix; V represents a right orthogonal matrix, (·) H represents the transpose operation.

[0078] Then formula (4) can be written as:

[0079]

[0080] Where, Σ represents a diagonal matrix composed of singular values of S; G represents a target range-doppler domain image; ||·||0 represents the l0 norm; γ represents a regularization parameter; Y represents a first matrix; Ψ represents a partial Fourier transform matrix; S represents a range image sequence matrix; F M represents an M-dimensional Fourier transform matrix; U represents a left orthogonal matrix; V represents a right orthogonal matrix, (·) H represents the transpose operation.

[0081] S102, a non-convex relaxation penalty function is constructed to solve the distance image super-resolution reconstruction model, and a cost function corresponding to the distance image super-resolution reconstruction model is obtained.

[0082] In order to obtain the super-resolution distance image sequence, a constrained optimization problem (5) needs to be solved, however, the l0 norm of the matrix is an NP-hard problem, so the constraint condition in formula (5) needs to be relaxed.

[0083] It is common to use the l1 norm and the kernel norm to convexly relax formula (5), however, using two convex relaxations to solve the sparse low rank (SLR) problem is over-relaxed. Therefore, in order to obtain better reconstruction performance, a suitable relaxation function needs to be found to accurately depict the sparse characteristics of the signal.

[0084] In the present application, a continuously smooth approximation hyperbolic tangent function is used to approximate the l0 norm and construct a non-convex penalty function.

[0085] Specifically, in step S102, a non-convex relaxation penalty function is constructed to solve the distance image super-resolution reconstruction model, and a cost function corresponding to the distance image super-resolution reconstruction model is obtained, including the following steps S1021 to S1023.

[0086] S1021, a continuously smooth approximation hyperbolic tangent function is used to construct a non-convex relaxation penalty function;

[0087] Here, it is a mixed form of a Gaussian function and a hyperbolic tangent function, and is expressed as:

[0088]

[0089] Wherein, α represents a scale coefficient; x represents an independent variable.

[0090] Formula (6) is a non-convex approximation of the l0 norm, and the function value becomes steeper as the value of α decreases, and the function value is closer to the l0 norm. Therefore, when α→0, f(x; α)≈||x||0 is approximately true.

[0091] For the matrix The following function is defined:

[0092]

[0093] In formula (7), x nm is the nth row and mth column element of the matrix X. Similarly, when α→0, F(X; α)≈||X||0 is approximately true.

[0094] S1022, the distance image super-resolution reconstruction model is jointly solved according to the non-convex relaxation penalty function.

[0095] Here, the l0 norm in equation (5) is replaced by the function F(X; α) to jointly solve the range image super-resolution reconstruction model.

[0096] S1023, the solution results are optimized using the Lagrange multiplier method to obtain the cost function corresponding to the range image super-resolution reconstruction model.

[0097] Here, the l0 norm in equation (5) is replaced by the function F(X; α), and the optimization problem is transformed into minimizing the cost function using the Lagrange multiplier method. The cost function is expressed as:

[0098]

[0099] Where Y represents the first matrix; S represents the distance image sequence matrix; Ψ represents the partial Fourier transform matrix; ||·|| F Let F denote the Frobenius norm; λ1 denote the regularization coefficient; F denote the penalty function; G denote the target range-Doppler domain image; α1 denotes the scaling coefficient; λ2 denotes the regularization parameter; and α2 denotes the scaling coefficient. S103, solve the cost function to obtain the super-resolution range image sequence of the target.

[0100] Specifically, in step S103, the cost function is solved to obtain the super-resolution range image sequence of the target, including the following steps S1031 to S1035.

[0101] S1031, Calculate the recursive error in the cost function with respect to compressed sensing, and determine the first cost function based on the recursive error;

[0102] S1032, Determine the update iterative formula for the weight coefficient matrix based on the first cost function;

[0103] S1033, optimize the first cost function under the constraints to obtain the second cost function;

[0104] S1034, Based on the second cost function, the update iteration formula is optimized using the gradient descent method to obtain the second update iteration formula;

[0105] S1035, combined with the second update iteration formula and cost function, is solved to obtain the super-resolution range image sequence of the target.

[0106] For example, to solve the constrained optimization problem in equation (8), this invention proposes the DSL0-NAGLMS algorithm based on the MMV-LMS framework, combined with a Double smoothed l0-norm non-convex penalty function, and using the steepest descent method for parameter updating. The specific details are as follows:

[0107] Table 1 Corresponding relationship between parameters of adaptive filtering algorithm and compressed sensing

[0108]

[0109]

[0110] In Table 1, d represents a desired signal; x represents an input signal; W represents a weight coefficient matrix; and e represents a measurement error.

[0111] To solve the compressed sensing problem Y = ΨS, where:

[0112]

[0113] y j = [y j1 , y j2 , …, y jM ], ψ j = [ψ j1 , ψ j2 , …, ψ jN ], j = 1, 2, …, K (11)

[0114] S = [s 11 , s 12 , …, s NM ] (12)

[0115] The multi-measurement vector reconstruction framework of the adaptive filtering algorithm adopted is shown in Fig. 1. Table 1 shows the corresponding relationship between parameters of the adaptive filtering algorithm and the compressed sensing problem. Then the recursive error is: Figure 2 e = d - xW (13)

[0116] wherein,

[0117] Thus, the cost function is:

[0118] ξ MMV-NAGLMS = f(W) = ||e|| 2 = (d - xW)(d - xW) H (14)

[0119] Then the W update iteration formula of the weight coefficient matrix is:

[0120]

[0121]

[0122] wherein, μ is an iteration step size.

[0123] ​Corresponding to the constraint optimization problem in formula (8), the sparsity and low rank constraint are added into the MMV-NAGLMS framework, and two Gaussian functions are used as the approximation function of zero norm. The new cost function is:

[0124] ξ DSL0-NAGLMS =||e|| 2 +λ1F(G;α1)+λ2F(Σ;α2) (16)

[0125] where

[0126]

[0127] g nm represents the element of the nth row and the mth column of the matrix G, σ l represents the lth element on the main diagonal of the diagonal matrix Σ, L = min(M, N).

[0128] The steepest descent direction of the function f(x; a) is obtained as follows:

[0129]

[0130] The negative gradient direction of the function makes the independent variable x tend to 0, which is called zero-attracting phenomenon, which is called zero attractor, which always attracts the weight coefficient in the adaptive filtering framework to zero, and can accelerate the convergence of the algorithm when the signal is sparse. Accordingly, the zero attractor is extended to the matrix form, and the following is obtained:

[0131]

[0132] By using the gradient descent method, combining formula (15), (17)-(21) and minimizing formula (16), the new weight coefficient matrix iteration formula is obtained as follows:

[0133]

[0134] In addition, as the value of a decreases, the influence of the zero attractor increases, but the range of the zero attractor decreases, so a set of gradually decreasing {a} sequences are considered to be used to continuously approach the zero norm, so as to avoid falling into local minimum.

[0135] Specifically, the steps for solving the cost function are as follows:

[0136] (1) Determine the initialization input data Y, Ψ, λ1, λ2, initialization: W (0) = W (-1) = 0, i = 0, set μ, β, ε, α1, α2;

[0137] (2) Determine the input vector x of the i-th iteration (i) and the desired vector d (i) : j = mod(i, N) + 1; x (i) = ψ j ; d (i) = y j ;

[0138] (3) Calculate the current gradient matrix

[0139] (4) Calculate the range-doppler image matrix G (i) and the singular value matrix Σ (i) , G (i) = W (i) F M , UΣ (i) V H = W (i) ;

[0140] (5) Update the weight coefficient matrix W according to formula (22) (i+1) ;

[0141] (6) After a certain number of iterations, reduce α1 and α2, α1 = ρ1·α1, 0.5 < ρ1 < 1; α2 = ρ2·α2, 0.5 < ρ2 < 1;

[0142] (7) According to the judgment condition , if yes, W opt = W (i+1) and output; otherwise, increase the iteration number i = i + 1 and go to (2);

[0143] until the loop ends, and the output super-resolution range image sequence is represented as: wherein, W opt represents the optimal weight coefficient matrix.

[0144] In one simulation embodiment provided by the application, the experimental conditions are: the algorithm of the application is verified through simulation experiments. The experimental running system is Intel(R) Core(TM) i7-10700F CPU@2.90GHz and NVIDIA GeForce RTX 2070 SUPER GPU, 64-bit Windows 10 operating system, and the simulation software adopts MATLAB.

[0145] Experimental content and result analysis:

[0146] The present application takes a simple scattering point target model as an example, uses a single measurement vector sparse Bayesian learning (SMV-SBL) algorithm as a comparison algorithm, and performs super-resolution experiments on a range profile sequence of a moving target, and results are shown in FIG. 3. FIG. 3(a) is a high-resolution range profile sequence (HRRP) of 400M bandwidth, FIG. 3(b) is a low-resolution range profile sequence (LRRP) of 100M bandwidth under a resource-limited condition, FIG. 3(c) is a super-resolution range profile sequence (SRRP) of 400M bandwidth reconstructed by the SBL algorithm, and FIG. 3(d) is a SRRP of 400M bandwidth reconstructed by the algorithm.

[0147]

[0148] In the formula, <·> represents an inner product of two vectors, ||·||2 represents an l2 norm of a vector, |·| represents an absolute value of a vector, g H is an HRRP, is an SRRP.

[0149] Therefore, an average correlation coefficient (ACC) of the range profile sequence can be obtained from formula (2):

[0150]

[0151] In the formula, M is a pulse number, CC m is a correlation coefficient of the SRRP and the HRRP of the mth pulse.

[0152] FIG. 4(a) shows a correlation coefficient curve diagram of the SRRPs and the HRRPs obtained by the SMV-SBL algorithm and the algorithm. It can be seen from the diagram that the reconstruction performance of the SRRPs obtained by the SMV-SBL algorithm fluctuates greatly, and the average correlation coefficient ACC is only 0.79, which will seriously affect the imaging performance and the recognition accuracy of the target. The reconstruction performance of the SRRPs obtained by the algorithm fluctuates less, and the average correlation coefficient ACC is improved from 0.79 to 0.94.

[0153] FIG. 4(b) shows a correlation coefficient curve diagram of the SRRPs and the HRRPs obtained by the SMV-SBL algorithm and the algorithm under different super-resolution multiples. The results show that the algorithm has better performance on the high-multiple super-resolution problem, and is more robust.

[0154] Fig. 5(a) and Fig. 5(b) show the original wideband range profile sequence of 5dB Gaussian white noise, the original wideband range profile sequence without noise, the sparse low-rank constrained super-resolution range profile sequence of the present application, and the sparse constrained super-resolution range profile sequence, wherein the super-resolution range profile sequence is obtained by 4 times super-resolution from the 100M low-resolution range profile sequence of 5dB noise. As can be seen from the figures, the range profile sequence obtained by the algorithm in the present application has better correlation with the original wideband range profile sequence, lower rank of the range profile sequence, and good noise robustness.

[0155] Figure 6 The correlation coefficient curves of the SRRPs and HRRPs obtained by the SMV-SBL algorithm and the algorithm of the present application for 2000 range profile sequences of Yak-42 are shown in the figures. As can be seen from the figures, the reconstruction performance of the SRRPs obtained by the SMV-SBL algorithm fluctuates greatly, and the average correlation coefficient ACC is only 0.72, which will seriously affect the imaging performance and recognition accuracy of the target. The reconstruction performance of the SRRPs obtained by the algorithm of the present application fluctuates less, and the average correlation coefficient ACC is improved from 0.72 to 0.89.

[0156] Fig. 7(a) and Fig. 7(b) show the range profile sequence of Yak-42 and the super-resolution results of a certain frame range profile sample, which is marked by a red frame in Figure 6 As can be seen from the results, the super-resolution range profile sequence (SRRP) obtained by the algorithm of the present application has higher similarity with the original range profile, and the super-resolution reconstruction effect is better. And from the super-resolution results of the single frame range profile sample, the super-resolution range profile (SRRP) reconstructed by the algorithm of the present application can better recover the structural feature information of the original wideband range profile from the narrowband range profile.

[0157] The various embodiments in the specification are described in a progressive manner, and the same or similar parts between the various embodiments can be referred to each other. Each embodiment mainly explains the difference from other embodiments. The whole or part of the present application can be used in many general or special computer system environments or configurations. For example: personal computer, server computer, handheld device or portable device, tablet device, mobile communication terminal, multi-processor system, microprocessor-based system, programmable electronic device, network PC, minicomputer, mainframe computer, distributed computing environment including any of the above systems or devices, etc.

[0158] The above examples are only used to illustrate the technical solutions of the present application, and are not intended to limit the present application; although the present application has been described in detail with reference to the foregoing examples, those skilled in the art should understand that the technical solutions recorded in the foregoing examples can still be modified, or some or all of the technical features thereof can be replaced by equivalents; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the present application.

Claims

1. A method for super-resolution of a sequence of range images with multiple criteria joint constraints, characterized in that, The method comprises the following steps: The radar echo signal is acquired, and a multi-criteria joint constraint distance image super-resolution reconstruction model about the radar echo signal is constructed; the distance image super-resolution reconstruction model is represented as: ; wherein, represents a diagonal matrix composed of singular values of represents a target distance-Doppler domain image; represents a norm; represents a regularization parameter; represents a first matrix; represents a partial Fourier transform matrix; represents M a Fourier transform matrix of dimension represents a left orthogonal matrix; represents a right orthogonal matrix, represents a transposition operation;​ Solving the distance image super-resolution reconstruction model by constructing a non-convex relaxation penalty function to obtain a cost function corresponding to the distance image super-resolution reconstruction model; the cost function is represented as: ; wherein, represents a distance image sequence matrix; represents a Frobenius norm; represents a regularization parameter; represents a penalty function; represents a regularization parameter; represents a first scale coefficient; represents a second scale coefficient; calculating a recursive error of compressed sensing in a cost function, and determining a first cost function according to the recursive error; determining an updating iteration formula of a weight coefficient matrix according to the first cost function; optimizing the first cost function according to a constraint condition to obtain a second cost function; wherein the constraint condition comprises a multi-criteria joint constraint of a sparsity constraint of a target in a range-Doppler domain and a low-rank constraint of a multi-frame range image sequence matrix; wherein the second cost function is expressed as: ; wherein, represents a recursive error; According to the second cost function, the update iteration formula is optimized by using a gradient descent method to obtain a second update iteration formula; wherein the second update iteration formula is represented as: ; wherein, represents a distance Doppler image matrix; represents a singular value matrix; represents an updated weight coefficient matrix; represents a current gradient matrix; solving the second updating iteration formula and the cost function to obtain a target hyper-resolution range image sequence.

2. The method of claim 1, wherein the plurality of criteria are jointly constrained. The method of constructing a multi-criteria joint constraint range image hyper-resolution reconstruction model of the radar echo signal comprises the following steps: converting the radar return signals into a short bandwidth range profile sequence frequency domain signal matrix; performing Fourier transform on the short bandwidth range image sequence frequency domain signal matrix to obtain a first matrix ; solving the first matrix according to the constraint condition to obtain a distance image super-resolution reconstruction model.

3. The method of claim 2, wherein the plurality of criteria are combined to form a joint constraint, and the joint constraint is applied to the sequence of distance images to generate a sequence of super-resolved images. solving the first matrix according to the constraint condition includes: According to the sparsity of the target scattering point and the low rank of the range image sequence, a constraint condition for solving is determined, and the first matrix is solved according to the constraint condition .

4. The method of claim 1, wherein the plurality of criteria are combined to form a joint constraint. The method of constructing a non-convex relaxation penalty function to solve the range image hyper-resolution reconstruction model to obtain a cost function corresponding to the range image hyper-resolution reconstruction model comprises the following steps: a continuous smooth approximation hyperbolic tangent function is used to construct a non-convex relaxation penalty function; the range image hyper-resolution reconstruction model is jointly solved according to the non-convex relaxation penalty function; a Lagrange multiplier method is used to optimize the solving result to obtain the cost function corresponding to the range image hyper-resolution reconstruction model.

5. The method of claim 1, wherein the plurality of criteria are combined to form a joint constraint, and the joint constraint is applied to the sequence of range images to generate a sequence of super-resolved range images. The radar echo signal is represented as: ； wherein, denotes the total number of scatterers; denotes the scattering intensity of the th scatterer; denotes the exponential function; denotes the distance frequency; denotes the speed of light; denotes the slant range of the th scatterer; denotes the Doppler frequency of the th scatterer; denotes the slow time; denotes the range image super-resolution reconstruction model.

6. The method of claim 1, wherein the plurality of criteria are combined to form a joint constraint. The hyper-resolution range image sequence is represented as: ； wherein denotes the optimal weight coefficient matrix.

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