Multi-criterion joint constraint range profile sequence super-resolution method

Abstract

The invention discloses a multi-criterion joint constraint range profile sequence super-resolution method, relates to the technical field of radar signal processing, and solves the problems of low super-resolution reconstruction precision and poor robustness of a range profile 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 profile super-resolution reconstruction model about the radar echo signal; constructing a non-convex relaxation penalty function to solve the range profile super-resolution reconstruction model to obtain a cost function corresponding to the range profile super-resolution reconstruction model; solving the cost function to obtain a super-resolution range profile sequence of the target; according to the method, Doppler information among multiple frames of range profile sequences is utilized, the precision of range profile super-resolution reconstruction is improved, the robustness of range profile super-resolution reconstruction is enhanced, and robust range super-resolution imaging is realized.

Description

Technical Field

[0001] The invention relates to the technical field of radar signal processing, and in particular to a multi-criteria joint-constrained range image sequence super-resolution method. Background Art

[0002] High-resolution range profile (HRRP) is the vector sum of the target scattering point sub-echoes projected on the radar ray obtained by broadband radar signals. It contains rich physical structural characteristics of the target. Therefore, the radar target recognition method based on high-resolution range profile (HRRP) has the advantage of high recognition accuracy and is of great value for target recognition and classification. However, in actual engineering applications, due to the requirements of indicators such as target detection distance, hardware equipment capabilities, or system parameter limitations, the radar transmission signal bandwidth cannot meet the HRRP recognition requirements for targets. In addition, in the electromagnetic interference environment of modern electronic warfare, the spectrum of radar HRRP may be interfered, resulting in the actual available target signal bandwidth being limited, which seriously affects the target recognition performance. In summary, when the radar system resources are limited due to the influence of itself or external factors, the performance of the target recognition algorithm based on HRRP is seriously reduced, which has a serious impact on the homeland security capability, strategic early warning capability, and long-range guided strike capability of the radar equipment using the algorithm. Therefore, it is of great significance to study the robust range profile super-resolution algorithm under limited radar resources and obtain the target HRRP through super-resolution of the low-resolution range profile (LRRP).

[0003] For distance super-resolution, existing algorithms such as bandwidth extrapolation, Prony, RELAX and MUSIC are usually easily affected by noise and model errors, and the super-resolution multiple is low. Therefore, in order to achieve more robust and high-multiple distance super-resolution, sparse reconstruction super-resolution methods based on compressed sensing (CS) have been widely studied by scholars at home and abroad in recent years. According to the different sparse reconstruction technologies used, these super-resolution technologies are mainly divided into three categories: greedy algorithm type, Lp norm type and sparse Bayesian learning type.

[0004] Existing range image super-resolution methods based on compressed sensing are all based on single-pulse range image super-resolution, without using 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 targeting complex configuration range images. Summary of the invention

[0005] The present invention solves the problems of low accuracy and poor robustness of super-resolution reconstruction of range images under complex configurations in the prior art by providing a range image sequence super-resolution method with multi-criteria joint constraints, realizes the use of Doppler information between multi-frame range image sequences, improves the accuracy of range image super-resolution reconstruction, and enhances the robustness of range image super-resolution reconstruction, thereby realizing robust range super-resolution imaging.

[0006] The present invention provides a multi-criteria joint constraint range image sequence super-resolution method, the method comprising:

[0007] Acquire a radar echo signal, and construct a range image super-resolution reconstruction model with multi-criteria joint constraints on the radar echo signal;

[0008] 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;

[0009] The cost function is solved to obtain the super-resolution range image sequence of the target.

[0010] In a possible implementation, the step of constructing a range profile super-resolution reconstruction model with multi-criteria joint constraints on the radar echo signal includes:

[0011] The radar echo signal Y s (n,m) is converted into a frequency domain signal matrix of a short bandwidth range image sequence;

[0012] Performing Fourier transformation on the frequency domain signal matrix of the short bandwidth range image sequence to obtain a first matrix Y;

[0013] The first matrix Y is solved according to the constraint conditions to obtain a range image super-resolution reconstruction model.

[0014] In a possible implementation manner, solving the first matrix Y according to the constraint condition includes:

[0015] According to the sparsity of the target scattering points and the low rank of the range image sequence, the constraint conditions for solving are determined, and the first matrix Y is solved according to the constraint conditions.

[0016] In a possible implementation, constructing a non-convex relaxation penalty function to solve the range image super-resolution reconstruction model to obtain a cost function corresponding to the range image super-resolution reconstruction model includes:

[0017] A non-convex relaxation penalty function is constructed using a continuous and smooth approximate hyperbolic tangent function;

[0018] Jointly solving the range image super-resolution reconstruction model according to the non-convex relaxation penalty function;

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

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

[0021] Using the MMV-NAGLMS model, calculating a recursive error in a cost function related to compressed sensing, and determining a first cost function of the MMV-NAGLMS model according to the recursive error;

[0022] Determine an update iterative formula for a weight coefficient matrix according to the first cost function;

[0023] Optimizing the first cost function based on the constraint condition to obtain a second cost function;

[0024] According to the second cost function, the update iterative formula is optimized by using a gradient descent method to obtain a second update iterative formula;

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

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

[0027]

[0028] 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 distance of the pth scattering point; represents the Doppler frequency of the pth scattering point; t m Indicates slow time; Y s (n,m) represents the range image super-resolution reconstruction model.

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

[0030]

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

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

[0033]

[0034] Where Y represents the first matrix; S represents the range image sequence matrix; Ψ represents the partial Fourier transform matrix; ||·|| F represents the Frobenius norm; λ1 represents the regularization coefficient; F represents the penalty function; G represents the target range-Doppler domain image; α1 represents the scale coefficient; λ2 represents the regularization parameter; α2 represents the scale coefficient.

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

[0036]

[0037] Among them, W opt represents the optimal weight coefficient matrix.

[0038] One or more technical solutions provided in the present invention have at least the following technical effects or advantages:

[0039] (1) The present invention adopts a range image super-resolution reconstruction model to solve the problem of poor range image reconstruction accuracy under complex configurations. The model uses the Doppler information between the target multi-frame range image sequences and constrains the sparsity of the range-Doppler image and the low rank of the range image sequence. It can achieve fast and high-precision super-resolution reconstruction of the target range image sequence under limited resources.

[0040] (2) The present invention adopts a continuous and smooth approximate hyperbolic tangent function to approximate the l0 norm and construct a non-convex penalty function, unifying the sparsity and low rank of the signal into the cost function. Compared with other penalty functions, this penalty function is closer to the l0 norm model when the hyperparameters approach 0. Therefore, it can fully reflect the sparse and low rank characteristics of the signal to be reconstructed, thereby obtaining better performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 A flowchart of the steps of the range image sequence super-resolution method with multi-criteria joint constraints provided by an embodiment of the present invention;

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

[0043] FIG3( a ) is a schematic diagram of range image super-resolution simulation experiment results of a high-resolution range image sequence with a bandwidth of 400 MHz provided by an embodiment of the present invention;

[0044] FIG3( b ) is a schematic diagram of range image super-resolution simulation experiment results of a low-resolution range image sequence with a bandwidth of 100M under resource-constrained conditions provided by an embodiment of the present invention;

[0045] FIG3( c ) is a schematic diagram of a range image super-resolution simulation experiment result of a 400M bandwidth super-resolution range image sequence reconstructed by the SBL algorithm provided in an embodiment of the present invention;

[0046] FIG3( d ) is a schematic diagram of a high-resolution range image sequence with a bandwidth of 400 MHz provided by an embodiment of the present invention;

[0047] FIG4( a ) is a graph showing the correlation coefficients between a super-resolution range image sequence and a high-resolution range image sequence obtained by the SMV-SBL algorithm provided in an embodiment of the present invention;

[0048] FIG4( b ) is a graph showing the correlation coefficients between the super-resolution range image sequence and the high-resolution range image sequence obtained by the method provided in an embodiment of the present invention;

[0049] FIG5( a ) is a schematic diagram of super-resolution performance analysis of an original broadband range image sequence under low signal-to-noise ratio provided by an embodiment of the present invention;

[0050] FIG5( b ) is a schematic diagram of super-resolution performance analysis of a sparse range image sequence under low signal-to-noise ratio provided by an embodiment of the present invention;

[0051] Figure 6 A schematic diagram of super-resolution performance analysis of Yak-42 measured data provided by an embodiment of the present invention;

[0052] FIG. 7( a ) is a schematic diagram of super-resolution results of original bandwidth and narrow bandwidth range images provided by an embodiment of the present invention;

[0053] FIG7( b ) is a schematic diagram of range image super-resolution results of Yak-42 measured data under different algorithms provided by an embodiment of the present invention; DETAILED DESCRIPTION

[0054] The technical solutions in the embodiments of the present invention will be described clearly and completely below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0055] The present invention provides a multi-criteria joint constraint range image sequence super-resolution method, such as Figure 1As shown, the method includes the following steps S101 to S103.

[0056] S101, acquiring a radar echo signal, and constructing a range profile super-resolution reconstruction model with multi-criteria joint constraints on the radar echo signal.

[0057] Specifically, in step S101, a range profile super-resolution reconstruction model with multi-criteria joint constraints on radar echo signals is constructed, including the following steps S1011 to S1013.

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

[0059] Here, the radar echo signal is expressed 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 slope distance of the pth scattering point; f dp represents the Doppler frequency of the pth scattering point; t m Indicates slow time; Y s (n,m) represents the range image super-resolution reconstruction model. Range frequency f n =[nN / 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 frequency domain signal matrix of the short bandwidth range image sequence under limited resources can be expressed as:

[0063] Y=DY s (2)

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

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

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

[0067] Y=DF N S (3)

[0068] In the formula, is the distance image sequence matrix, is the N-dimensional Fourier transform matrix, so Ψ=DFN is the partial Fourier transform matrix.

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

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

[0071] Here, the desired range image super-resolution reconstruction model can be obtained by solving equation (3).

[0072] However, equation (3) is an underdetermined equation. Solving it directly will result in infinite solutions. Therefore, it is necessary to add constraints to the equation.

[0073] Considering the introduction of the sparsity of target scattering points and the low rank of the range image sequence to constrain equation (3), the following constrained optimization problem is obtained.

[0074]

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

[0076] By performing singular value decomposition on the range image sequence matrix S, the rank of the range image sequence matrix S can be approximated by the number of non-zero singular values.

[0077] Therefore, the singular value decomposition of the distance image sequence matrix S is performed to obtain S = UΣV H , where Σ is a diagonal matrix consisting of the singular values ​​of the range image sequence matrix S; U represents a left orthogonal matrix; V represents a right orthogonal matrix, (·) H Represents a transpose operation.

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

[0079]

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

[0081] S102, 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.

[0082] In order to obtain a super-resolution range image sequence, it is necessary to solve the constrained optimization problem (5). However, minimizing the l0 norm of the matrix is ​​an NP-hard problem, so it is necessary to relax the constraints in equation (5).

[0083] It is common to use the l1 norm and the nuclear norm to convexly relax equation (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, it is necessary to find a suitable relaxation function to accurately characterize the sparse characteristics of the signal.

[0084] In the present invention, a continuous and smooth approximate 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 range image super-resolution reconstruction model to obtain a cost function corresponding to the range image super-resolution reconstruction model, including the following steps S1021 to S1023.

[0086] S1021, constructing a non-convex relaxation penalty function using a continuous and smooth approximate hyperbolic tangent function;

[0087] Here, it is a mixture of Gaussian and hyperbolic tangent functions, expressed as:

[0088]

[0089] Among them, α represents the scale coefficient; x represents the independent variable.

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

[0091] For the matrix Define the following function:

[0092]

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

[0094] S1022, jointly solving the range image super-resolution reconstruction model 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, optimizing the solution result by using the Lagrange multiplier method to obtain a 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 Lagrange multiplier method is used to transform the optimization problem into a problem of minimizing the cost function. The cost function is expressed as:

[0098]

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

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

[0101] S1031, using the MMV-NAGLMS model, calculating the recursive error of the cost function regarding compressed sensing, and determining the first cost function of the MMV-NAGLMS model according to the recursive error;

[0102] S1032, determining an update iterative formula for the weight coefficient matrix according to the first cost function;

[0103] S1033, optimizing the first cost function according to the constraint condition to obtain a second cost function;

[0104] S1034, optimizing the update iterative formula using a gradient descent method according to the second cost function to obtain a second update iterative formula;

[0105] S1035 , solving the second update iterative formula and the cost function to obtain a super-resolution range image sequence of the target.

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

[0107] Table 1 Correspondence between adaptive filtering algorithm and compressed sensing parameters

[0108]

[0109]

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

[0111] 1)MMV-NAGLMS model:

[0112] To solve the compressed sensing problem, Y = ΨS, where:

[0113]

[0114]

[0115] y j =[y j1 ,y j2 ,…,y jM ], ψ j =[ψ j1 ,ψ j2 ,…,ψ jN ], j=1,2,…,K (11)

[0116] S=[s 11 ,s 12 ,…,s NM ] (12)

[0117] The multi-measurement vector reconstruction framework of the adaptive filtering algorithm adopted, such as Figure 2 As shown. Table 1 gives the corresponding relationship between the parameters of the adaptive filtering algorithm and the compressed sensing problem. Then the recursive error is:

[0118] e=d-xW (13)

[0119] in,

[0120] So the cost function of MMV-NAGLMS is:

[0121] ξ MMV-NAGLMS =f(W)=||e|| 2 =(d-xW)(d-xW) H (14)

[0122] Then the W update iteration formula of the weight coefficient matrix is:

[0123]

[0124] Among them, μ is the iteration step size.

[0125] Corresponding to the constrained optimization problem in equation (8), the sparse and low-rank constraints are added to the MMV-NAGLMS framework, and two Gaussian functions are used as approximate functions of the zero norm. The new cost function is:

[0126] ξ DSL0-NAGLMS =||e|| 2 +λ1F(G;α1)+λ2F(Σ;α2) (16)

[0127] in

[0128]

[0129] g nm represents the element in the nth row and 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).

[0130] Find the direction of the fastest descent of the function f(x; α), and we can get:

[0131]

[0132] The negative gradient direction of this function makes the independent variable x tend to 0. This phenomenon is called zero-attracting. It is called the zero attractor, which always attracts the weight coefficients in the adaptive filtering framework to zero, and can accelerate the convergence of the algorithm when the signal is sparse. Based on this, the zero attractor is expanded to the matrix form, and we can get:

[0133]

[0134] Using the gradient descent method, combining equations (15), (17)-(21) and minimizing equation (16), we get the new weight coefficient matrix iteration formula:

[0135]

[0136] In addition, as the value of α decreases, the influence of the zero attraction factor increases, but the range of zero attraction decreases. Therefore, it is considered to use a set of gradually decreasing {α} sequences to continuously approach the zero norm to avoid falling into the local minimum.

[0137] Specifically, the steps of solving the cost function using the MMV-NAGLMS model are:

[0138] (1) Determine the initialization input data Y, Ψ, λ1, λ2, and initialize: W (0) =W(-1) =0, i=0, set μ, β, ε, α1, α2;

[0139] (2) Determine the input vector x for the i-th iteration (i) and the expected vector d (i) :j=mod(i,N)+1;x (i) =ψ j ;d (i) =y j ;

[0140] (3) Calculate the current gradient matrix

[0141] (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) ;

[0142] (5) Update the weight coefficient matrix W according to formula (22) (i+1) ;

[0143] (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;

[0144] (7) According to the judgment conditions Make a judgment, if so, then W opt =W (i+1) And output; if not, increase the number of iterations i=i+1 and go to (2);

[0145] Until the cycle ends, the output super-resolution range image sequence is expressed as: Among them, W opt represents the optimal weight coefficient matrix.

[0146] In a simulation embodiment provided by the present invention, the experimental conditions are as follows: the algorithm of the invention is verified by simulation experiments. The experimental operation system is Intel(R) Core(TM) i7-10700F CPU@2.90GHz and NVIDIAGeForce RTX2070SUPER GPU, 64-bit Windows 10 operating system, and the simulation software is MATLAB.

[0147] Experimental content and result analysis:

[0148] The present invention takes a simple scattered point target model as an example, uses the single measurement vector sparse Bayesian learning (SMV-SBL) algorithm as a comparison algorithm, and conducts a super-resolution experiment on the range image sequence of a moving target. The results are shown in Figure 3. Figure 3 (a) is a high-resolution range image sequence (HRRPs) with a bandwidth of 400M, Figure 3 (b) is a low-resolution range image sequence (LRRPs) with a bandwidth of 100M under resource-constrained conditions, Figure 3 (c) is a super-resolution range image sequence (SRRPs) with a bandwidth of 400M reconstructed by the SBL algorithm, and Figure 3 (d) is a SRRPs with a bandwidth of 400M reconstructed by the algorithm proposed in the present invention. In order to characterize the super-resolution reconstruction performance, we define the correlation coefficient (CC) between SRRP and HRRP:

[0149]

[0150] In the formula, <·> represents the inner product of two vectors, ||·||2 represents the l2 norm of the vector, |·| represents the absolute value of the vector, and g H For HRRP, It is SRRP.

[0151] Therefore, the average correlation coefficient (ACC) of the range image sequence can be obtained by formula (2):

[0152]

[0153] Where M is the number of pulses, CC m is the correlation coefficient between SRRP and HRRP of the mth pulse.

[0154] FIG4(a) shows the correlation coefficient curves of SRRPs and HRRPs obtained by the SMV-SBL algorithm and the algorithm proposed in the present invention. It can be seen from the figure that the reconstruction performance of 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 recognition accuracy of the target. However, the reconstruction performance of SRRPs obtained by the algorithm proposed in the present invention fluctuates little, and the average correlation coefficient ACC is improved from 0.79 to 0.94.

[0155] Figure 4(b) shows the correlation coefficient curves of SRRPs and HRRPs obtained by the SMV-SBL algorithm and the algorithm proposed in the present invention at different super-resolution magnifications. The results show that the algorithm proposed in the present invention also has good performance for high-magnification super-resolution problems and is more robust.

[0156] Figure 5(a) and Figure 5(b) show the original broadband range image sequence with 5dB Gaussian white noise, the noise-free original broadband range image sequence, the sparse low-rank constrained super-resolution range image sequence of the present invention, and the sparse constrained super-resolution range image sequence, where the super-resolution range image sequence is obtained by 4 times super-resolution from the 100M low-resolution range image sequence with 5dB noise. It can be seen from the figure that the range image sequence obtained by the algorithm proposed in this paper has a better correlation with the original broadband range image sequence, the rank of the range image sequence is lower, and it has good noise robustness.

[0157] Figure 6 The correlation coefficient curves of SRRPs and HRRPs obtained by the SMV-SBL algorithm and the algorithm of the present invention for 2000 range image sequences of Yak-42 are given. It can be seen from the figure that the reconstruction performance of 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 SRRPs obtained by the algorithm proposed in the present invention fluctuates little, and the average correlation coefficient ACC is increased from 0.72 to 0.89.

[0158] Figure 7(a) and Figure 7(b) show the super-resolution results of the Yak-42 range image sequence and a certain frame of the range image sample. The position of the sample is marked with a red frame. Figure 6 From the results, it can be seen that the super-resolution range image sequence (SRRPs) obtained by the algorithm proposed in the present invention has a higher similarity with the original range image, and the super-resolution reconstruction effect is better. And from the super-resolution results of single-frame range image samples, the super-resolution range image (SRRP) reconstructed by the algorithm of the present invention can better restore the structural feature information of the original broadband range image from the narrowband range image.

[0159] The various embodiments in this specification are described in a progressive manner, and the same or similar parts between the various embodiments can be referred to each other, and each embodiment focuses on the differences from other embodiments. All or part of the present invention can be used in many general or special computer system environments or configurations. For example: personal computers, server computers, handheld devices or portable devices, tablet devices, mobile communication terminals, multi-processor systems, microprocessor-based systems, programmable electronic devices, network PCs, minicomputers, mainframe computers, distributed computing environments including any of the above systems or devices, etc.

[0160] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, a person skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some or all of the technical features thereof may be replaced by equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the scope of the technical solutions of the present invention.

Claims

1. A multi-criteria joint constraint range image sequence super-resolution method, characterized in that: include: Acquire a radar echo signal, and construct a range image super-resolution reconstruction model with multi-criteria joint constraints on 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; The cost function is solved to obtain a super-resolution range image sequence of the target.

2. The multi-criteria joint constraint range image sequence super-resolution method according to claim 1, characterized in that: The method of constructing a range image super-resolution reconstruction model with multi-criteria joint constraints on the radar echo signal includes: The radar echo signal Y s (n,m) is converted into a frequency domain signal matrix of a short bandwidth range image sequence; Performing Fourier transformation on the frequency domain signal matrix of the short bandwidth range image sequence to obtain a first matrix Y; The first matrix Y is solved according to the constraint conditions to obtain a range image super-resolution reconstruction model.

3. The multi-criteria joint constraint range image sequence super-resolution method according to claim 2, characterized in that: The solving the first matrix Y according to the constraint condition includes: According to the sparsity of the target scattering points and the low rank of the range image sequence, the constraint conditions for solving are determined, and the first matrix Y is solved according to the constraint conditions.

4. The multi-criteria joint constraint range image sequence super-resolution method according to claim 1, characterized in that: The constructing of a non-convex relaxation penalty function to solve the range image super-resolution reconstruction model to obtain a cost function corresponding to the range image super-resolution reconstruction model includes: A non-convex relaxation penalty function is constructed using a continuous and smooth approximate hyperbolic tangent function; Jointly solving the range image super-resolution reconstruction model according to the non-convex relaxation penalty function; The solution is optimized using the Lagrange multiplier method to obtain a cost function corresponding to the range image super-resolution reconstruction model.

5. The multi-criteria joint constraint range image sequence super-resolution method according to claim 1, characterized in that: The cost function is solved to obtain a super-resolution range image sequence of the target, including: Using the MMV-NAGLMS model, calculating a recursive error in a cost function related to compressed sensing, and determining a first cost function of the MMV-NAGLMS model according to the recursive error; Determine an update iterative formula for a weight coefficient matrix according to the first cost function; Optimizing the first cost function based on the constraint condition to obtain a second cost function; According to the second cost function, the update iterative formula is optimized by using a gradient descent method to obtain a second update iterative formula; The second update iteration formula and the cost function are combined to solve and obtain a super-resolution range image sequence of the target.

6. The multi-criteria joint constraint range image sequence super-resolution method according to claim 1, characterized in that: The radar echo signal is expressed as: 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 slope distance of the pth scattering point; f dp represents the Doppler frequency of the pth scattering point; t m Indicates slow time; Y s (n,m) represents the range image super-resolution reconstruction model.

7. The multi-criteria joint constraint range image sequence super-resolution method according to claim 1, characterized in that: The range image super-resolution reconstruction model is expressed as: Where Σ represents the diagonal matrix composed of the singular values ​​of S; G represents the target range-Doppler domain image; ||·||0 represents the l0 norm; γ represents the regularization parameter; Y represents the first matrix; Ψ represents the partial Fourier transform matrix; S represents the range image sequence matrix; F M represents the M-dimensional Fourier transform matrix; U represents the left orthogonal matrix; V represents the right orthogonal matrix, (·) H Represents a transpose operation.

8. The multi-criteria joint constraint range image sequence super-resolution method according to claim 1, characterized in that: The cost function is expressed as: Where Y represents the first matrix; S represents the range image sequence matrix; Ψ represents the partial Fourier transform matrix; ||·|| F represents the Frobenius norm; λ1 represents the regularization parameter; F represents the penalty function; G represents the target range-Doppler domain image; α1 represents the scale coefficient; λ2 represents the regularization parameter; α2 represents the scale coefficient.

9. The multi-criteria joint constraint range image sequence super-resolution method according to claim 1, characterized in that: The super-resolution range image sequence is expressed as: Among them, W opt represents the optimal weight coefficient matrix.

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