Synthetic aperture radar interference suppression method based on kurtosis weighted nuclear norm

Abstract

The invention discloses a synthetic aperture radar interference suppression method based on a kurtosis weighted nuclear norm, and the method innovatively combines a sparse low-rank recovery theory with radar signal statistical characteristics, and constructs a unified interference suppression optimization problem model based on kurtosis statistics. Meanwhile, the residual kurtosis of interference and the sparse characteristic of echoes are restrained, and an optimization problem closed-form solution based on an alternating direction multiplier method (ADMM) framework is given. Compared with an existing interference suppression method, the SAR image result recovered by the interference suppression method is less in interference residue, the original scene recovery effect is better, and the method has more effective interference suppression capability. In addition, the method provided by the invention can effectively overcome the problems of excessive shrinkage and performance reduction during processing of non-ideal low-rank data in the existing method.

Description

Technical Field

[0001] The invention belongs to the technical field of SAR interference suppression, and in particular relates to a synthetic aperture radar interference suppression method based on kurtosis weighted nuclear norm. Background Art

[0002] Radar is an important electromagnetic detection equipment. With the continuous development and popularization of electronic technology, radar is increasingly used in military and people's livelihood fields, including air defense warning, weather monitoring, terrain mapping, automatic driving, smart home, etc., and is becoming more and more important to human production and life. Synthetic aperture radar (SAR) is an all-weather, all-day, high-resolution electromagnetic detection technology with unique advantages in many aspects, so it is increasingly valued by countries around the world.

[0003] Synthetic aperture radar continuously emits electromagnetic waves, and uses the movement of the platform to perform coherent imaging processing on the echo data received at different locations over a period of time. This technology achieves aperture synthesis through long-distance movement, forming a very large antenna aperture and achieving higher resolution. The principle of this technology utilizes time resources and space resources in exchange for high resolution.

[0004] The main challenge facing the current SAR system is the interference of more and more signals, including unintentional radio frequency interference from civilian equipment and intentional interference from military equipment, which have a great impact on the SAR system. Therefore, SAR interference suppression technology has received more and more attention. Existing SAR interference suppression technology can be mainly divided into non-parametric methods, parametric methods and semi-parametric methods. The non-parametric method mainly uses techniques such as setting thresholds for filtering, which is easier to implement and has relatively low computational complexity. However, due to the loss of some useful information, it cannot achieve the best performance; the parametric method considers the amplitude information and phase information of the signal at the same time, with high computational complexity and better performance, but it requires accurate modeling of the signal to achieve good results; the semi-parametric method transforms the interference suppression problem into a convex optimization problem, which protects the real echo while suppressing the interference, and has good effect and efficiency. However, there are two problems with the semi-parametric method. One is that too many useful signals are lost due to excessive shrinkage during the interference suppression process, and the other is that the low-rank characteristics of the interference are not significant, and the interference and echo cannot be effectively separated. Summary of the invention

[0005] Purpose of the invention: In view of the problem that current SAR imaging systems are easily affected by various types of complex interference, the purpose of the present invention is to provide a synthetic aperture radar interference suppression method based on the kurtosis weighted nuclear norm, which can adaptively process SAR data containing complex interference and can still effectively suppress interference signals while protecting useful echo signals when the interference does not have ideal low-rank characteristics.

[0006] Technical solution: To achieve the above-mentioned invention objective, the specific technical solution of the present invention is as follows:

[0007] A synthetic aperture radar interference suppression method based on kurtosis weighted nuclear norm, which can adaptively process SAR data containing interference and suppress interference while protecting the useful echo signal. It includes the following steps:

[0008] Step 1: Obtain the SAR image data containing interference and use it as the input in the form of a two-dimensional matrix.

[0009] Step 2: Set hyperparameters according to the input interference matrix and initialize the echo matrix, auxiliary matrix, and auxiliary variables.

[0010] Step 3: Construct an interference suppression optimization problem model based on kurtosis weighted nuclear norm according to the input hyperparameters and data, and at the same time constrain the residual kurtosis of the interference and the sparse characteristics of the echo.

[0011] Step 4: Use the ADMM framework to solve the optimization problem constructed in Step 3, and alternately optimize the interference matrix, echo matrix, auxiliary matrix, and auxiliary variables. Among them, the interference matrix is extracted using the kurtosis weighted nuclear norm, and the echo matrix is extracted through the sparse term.

[0012] Step 5: Repeat Step 4 until the convergence condition is met or the maximum number of iterations is reached to obtain the SAR echo data after suppressing interference.

[0013] Further, in the kurtosis weighted nuclear norm, by subtracting the kurtosis of the data after removing a singular value component from the reference kurtosis, it is distinguished whether the removed singular value component belongs to interference or echo, and the calculation result is limited to a monotonically changing positive real number interval by an exponential function to obtain the corresponding weighted value.

[0014] Further, the interference suppression optimization problem model constructed in Step 3 can be defined as:

[0015]

[0016] Among them, RK( ) represents the regularization processing based on residual kurtosis, ‖ ‖1 represents the L1 norm regularization processing, ‖ ‖ F represents the Frobenius norm regularization processing, λ represents the hyperparameter for constraining the low-rank sparse degree, R represents the interference matrix, X represents the echo matrix, Y represents the original input data matrix, and δ represents the error limit.

[0017] Further, the regularization processing RK( ) based on residual kurtosis in the constructed interference suppression optimization problem model can be defined as:

[0018]

[0019] where m and n respectively represent the number of samples in the range dimension and azimuth dimension of the data matrix, and k i represents the weighting value corresponding to the i-th singular value, and σ i (R) represents the i-th singular value of the interference matrix.

[0020] Furthermore, the constructed interference suppression optimization problem model can be iteratively solved through the ADMM (Alternating Direction Method of Multipliers) framework, and the augmented Lagrangian equation constructed is:

[0021]

[0022] where Y1 represents the auxiliary matrix, μ represents the penalty factor, and <·> represents the matrix inner product.

[0023] Furthermore, the closed-form solution of the interference matrix in the constructed augmented Lagrangian equation is:

[0024]

[0025] where is the SVD (Singular Value Decomposition) result of G (p) , the superscript (p) represents the p-th iteration, k represents the weighting value k i forming a vector, and SVT represents the singular value threshold function, which can be expressed as:

[0026]

[0027] The weighting value k i is calculated by computing the residual kurtosis (RK) of each singular value component of the interference matrix, and is defined as:

[0028]

[0029] where c represents a positive real scaling coefficient, represents the kurtosis of the reference complex signal calculated with G (p) , represents the kurtosis of the complex signal after removing the component corresponding to the i-th singular value of the interference matrix.

[0030] Furthermore, the method for calculating the kurtosis of the complex signal is:

[0031]

[0032] where RSK represents the kurtosis of the real signal, and is defined as:

[0033]

[0034] where M pDenote the p-th order sample central moment, x represents the input real random variable, E[ ] represents XXX; in addition, μ m,l Denote the (m + l)-th order sample central moment, defined as where σ represents the standard deviation of the data, z represents the input complex random variable, (·) * represents the operation of taking the complex conjugate.

[0035] Furthermore, the closed-form solutions of the echo matrix, auxiliary matrix, and auxiliary variables in the constructed augmented Lagrangian equation are

[0036]

[0037] μ (p+1) = min{ρμ (p) , μ max}

[0038] where is the soft threshold function, used to characterize the sparse characteristics of the echo signal, F represents the input matrix, β represents the threshold, ρ represents the algorithm acceleration factor, and μ max represents the upper limit of the penalty factor.

[0039] Beneficial effects: A synthetic aperture radar interference suppression method based on kurtosis-weighted nuclear norm provided by the present invention utilizes the characteristic that there are significant differences in the kurtosis statistics between the interference signal and the echo signal. By comparing the difference between the residual kurtosis and the reference kurtosis of each signal component, it is determined whether the signal component belongs to interference or echo, and the weighting value is calculated based on this value. For different signal components, the components closer to the interference are more easily extracted, and the components closer to the echo are more easily protected, thereby achieving more accurate interference separation. Compared with the prior art, it has the following advantages: 1. The present invention combines the SAR signal statistical characteristics and distribution with the interference suppression technology, differentiates using the difference in kurtosis statistics between the interference-containing data and the interference-free data, and more effectively extracts the interference data by constructing the kurtosis-weighted nuclear norm. On this basis, combined with the sparse characteristics of the echo data, accurate separation of interference and echo is achieved. 2. The present invention constructs a new interference suppression optimization problem model based on kurtosis-weighted nuclear norm, solves the problem that the existing interference suppression methods overly shrink and lose useful signals, and can also handle the situation where the low-rank characteristics of the interference are not ideal. 3. The present invention can adaptively process the input interference-containing SAR data, effectively suppress various complex interference signals, and simultaneously protect the useful echo signals. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 is a schematic flow chart of an embodiment of the present invention;

[0041] Figure 2 is a comparison graph of the residual kurtosis curve and the reference kurtosis of the interference matrix in an embodiment of the present invention;

[0042] Figure 3 The SAR image data containing interference input in the embodiment of the present invention;

[0043] Figure 4 The interference-free SAR image data referenced in the embodiment of the present invention;

[0044] Figure 5 is the result graph after processing Figure 3 using the notch filtering method;

[0045] Figure 6 is the result graph after processing Figure 3 using the RPCA method;

[0046] Figure 7 is the result graph after processing Figure 3 using the RNN method;

[0047] Figure 8 is the result graph after processing Figure 3 using the embodiment of the present invention. Specific embodiments

[0048] The present invention will be further clarified below in conjunction with the accompanying drawings and specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and not to limit the scope of the present invention. After reading the present invention, various equivalent modifications made by those skilled in the art fall within the scope defined by the appended claims of this application.

[0049] As Figure 1 shown, a synthetic aperture radar interference suppression method based on kurtosis weighted nuclear norm disclosed in the embodiment of the present invention includes the following steps:

[0050] Step 1: Obtain the SAR image data containing interference and use it as input in the form of a two-dimensional matrix;

[0051] Step 2: Set hyperparameters according to the input interference matrix and initialize the echo matrix, auxiliary matrix, and auxiliary variables;

[0052] Step 3: Construct an interference suppression optimization problem model based on kurtosis weighted nuclear norm according to the input hyperparameters and data, and at the same time constrain the residual kurtosis of the interference and the sparse characteristics of the echo;

[0053] Step 4: Use the ADMM framework to solve the constructed optimization problem, alternately optimizing the interference matrix, echo matrix, auxiliary matrix, and auxiliary variables; among them, the interference matrix is extracted using kurtosis weighted nuclear norm, and the echo matrix is extracted through the sparse term;

[0054] Step 5: Repeat Step 4 until the convergence condition is met or the maximum number of iterations is reached, and obtain the SAR echo data after interference suppression for subsequent processing.

[0055] The method innovatively combines the sparse low-rank recovery theory with the statistical characteristics of radar signals, can adaptively process SAR data with interference, and suppresses interference while protecting useful echo signals.

[0056] Next, the detailed implementation process of an embodiment will be described in detail using real SAR image data. The specific implementation method is as follows:

[0057] (1) Use Matlab software to read the input SAR data with interference. There are a large number of suppression interferences on the original data image.

[0058] (2) Set the input hyperparameters according to the required interference suppression effect and the characteristics of the SAR data, and construct an interference suppression optimization problem model based on the kurtosis-weighted nuclear norm. This model can be defined as:

[0059]

[0060] The purpose of this optimization problem is to simultaneously constrain the residual kurtosis of the interference and the sparse characteristics of the echo on the basis that the sum of the interference and the echo approaches the original input data. Among them, RK( ) represents the regularization processing based on the residual kurtosis, || ||1 represents the L1-norm regularization processing, || || F represents the Frobenius-norm regularization processing, λ represents the hyperparameter that constrains the degree of low-rank sparsity, R represents the interference matrix, X represents the echo matrix, Y represents the original input data matrix, δ represents the error limit, and is a very small positive real number.

[0061] (3) Solve the optimization problem in step (2) by the alternating direction method of multipliers for distributed iteration. The constructed augmented Lagrangian equation is:

[0062]

[0063] Among them, Y1 represents the auxiliary matrix, μ represents the penalty factor, and <·> represents the matrix inner product. The ADMM framework obtains the closed-form solution of the optimization problem by fixing other variables when optimizing one variable in each iteration and iteratively optimizing each variable in sequence until convergence.

[0064] Among them, the closed-form solution of the interference matrix is

[0065] Among them is the SVD (singular value decomposition) result of G (p) The superscript (p) represents the p-th iteration, and k represents the weighting value k iThe vector composed of, and SVT represents the singular value threshold function, which can be expressed as:

[0066]

[0067] The weighting value k i is calculated by computing the residual kurtosis (RK) of each singular value component of the interference matrix. Based on this, it is calculated, and its purpose is to suppress more interference components and retain more echo components. Its definition is:

[0068]

[0069] Figure 2 The figure shows the comparison of the residual kurtosis and the reference kurtosis of the singular values of different sizes (arranged in descending order from large to small) of the SAR data containing interference. Comparing the sizes of the residual kurtosis and the reference kurtosis can distinguish whether different singular values belong to interference or echo.

[0070] where c represents a positive real scaling coefficient, represents the reference complex signal kurtosis calculated with G (p) and represents the complex signal kurtosis after removing the component corresponding to the i-th singular value of the interference matrix. The calculation method of the complex signal kurtosis required for calculating the weighting value is:

[0071]

[0072] where RSK represents the real signal kurtosis, and its definition is:

[0073]

[0074] where M p represents the p-th order sample central moment, x represents the input real random variable, E[] represents calculating the expectation of the input random variable. In addition, μ m,l represents the m + l-th order sample central moment, and its definition is

[0075] where σ represents the standard deviation of the data, z represents the input complex random variable, and (·) * represents the operation of taking the complex conjugate.

[0076] The closed-form solution of the echo matrix is:

[0077]

[0078] where is the soft threshold function, used to characterize the sparse characteristics of the echo signal, F represents the input matrix, and β represents the threshold. The closed-form solutions of the auxiliary matrix and the auxiliary variable are:

[0079]

[0080] μ (p+1) = min{ρμ (p) , μ max}

[0081] And the overall algorithm iteration convergence condition is

[0082] where ρ represents the algorithm acceleration factor, μ max represents the upper limit of the penalty factor, η represents the error limit, and ||·|| represents the operation of calculating the two-norm of the input data.

[0083] (4) Use the matlab software. According to the closed-form solutions of each variable given in the ADMM framework in step (3), write a program to implement the complete processing flow of the algorithm.

[0084] (5) Through the processing of the matlab program written in step (4), the echo data after interference suppression output by the method of the embodiment of the present invention can be obtained, and this echo data can be used for further processing of subsequent algorithms.

[0085] In summary, for the synthetic aperture radar interference suppression method based on kurtosis-weighted nuclear norm in the embodiment of the present invention, interference suppression tests are carried out on real SAR images with interference. The original SAR images with interference are as Figure 3 shown, and the interference-free SAR images of the same area for reference are as Figure 4 shown. The image processed by the method of the embodiment of the present invention is as Figure 8 shown. Through the above method, the SAR data with interference is processed, and finally the effect of effective interference suppression is achieved. Among them, Figure 5 , Figure 6 , Figure 7 are the effects achieved by the notch filtering method, the RPCA (robust principal component analysis) method, and the RNN (weighted nuclear norm) method respectively, and are used to compare with the method proposed by the present invention. It can be seen that the method proposed by the present invention has better processing effects. The weighted nuclear norm method mainly weights according to the singular value size to reduce signal loss, and does not have the ability to distinguish interference from echoes. When the low-rank characteristic of interference is not ideal, the performance will decline. The method of the present invention can effectively distinguish interference from echoes, has better interference separation ability, can effectively cope with the situation where the low-rank characteristic of interference is not ideal, and at the same time reduces the loss of useful signals.

[0086] The embodiment of the present invention also discloses a computer program product, including a computer program, and when the computer program is executed by a processor, it implements the steps of the synthetic aperture radar interference suppression method based on kurtosis-weighted nuclear norm.

[0087] The program code for implementing the method of the present invention can be written in any combination of one or more programming languages. These program codes can be provided to the processor or controller of a general-purpose computer, a special-purpose computer, or other programmable data processing devices, such that when the program codes are executed by the processor or controller, the steps of the method of the present invention are implemented. The program codes can be executed entirely on the machine, partially on the machine, executed partially on the machine and partially on a remote machine as an independent software package, or executed entirely on a remote machine or server. Those parts not detailed in the present invention are well-known techniques to those skilled in the art.

[0088] The above are only the preferred embodiments of the present invention. It should be noted that the present invention is described through some embodiments. As is known to those skilled in the art, without departing from the spirit and scope of the present invention, various changes or equivalent replacements can be made to these features and embodiments. Additionally, under the teaching of the present invention, these features and embodiments can be modified to adapt to specific situations and materials without departing from the spirit and scope of the present invention. Therefore, the present invention is not limited by the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application belong to the scope protected by the present invention.

Claims

1. A synthetic aperture radar interference suppression method based on kurtosis weighted nuclear norm, characterized in that, It includes the following steps: Step 1: Obtain SAR image data with interference and use it as input in the form of a two-dimensional matrix; Step 2: Set hyperparameters according to the input interference matrix, and initialize the echo matrix, auxiliary matrix, and auxiliary variables; Step 3: Construct an interference suppression optimization problem model based on kurtosis-weighted nuclear norm according to the input hyperparameters and data, while constraining the residual kurtosis of interference and the sparse characteristics of the echo; Step 4: Use the ADMM framework to solve the constructed optimization problem, alternately optimizing the interference matrix, echo matrix, auxiliary matrix, and auxiliary variables; among them, the interference matrix is extracted using the kurtosis-weighted nuclear norm, and the echo matrix is extracted through the sparse term; Step 5: Repeat Step 4 until the convergence condition is met or the maximum number of iterations is reached to obtain the SAR echo data after interference suppression.

2. The synthetic aperture radar interference suppression method based on kurtosis weighted nuclear norm according to claim 1, characterized in that In the kurtosis-weighted nuclear norm, by subtracting the kurtosis of the data after removing a singular value component from the reference kurtosis, it is distinguished whether the removed singular value component belongs to interference or echo, and the calculation result is limited to a monotonically changing positive real number interval by an exponential function to obtain the corresponding weighted value.

3. The synthetic aperture radar interference suppression method based on kurtosis weighted nuclear norm according to claim 1, characterized in that The interference suppression optimization problem model constructed in Step 3 is defined as: Among them, RK( ) represents the regularization process based on residual kurtosis, || ||1 represents the L1-norm regularization process, || || F represents the Frobenius-norm regularization process, λ represents the hyperparameter that constrains the low-rank sparsity degree, R represents the interference matrix, X represents the echo matrix, Y represents the original input data matrix, and δ represents the error limit value.

4. The synthetic aperture radar interference suppression method based on kurtosis weighted nuclear norm according to claim 3, characterized in that The regularization processing RK( ) based on residual kurtosis in the constructed interference suppression optimization problem model is defined as: where m and n respectively represent the number of samples in the range dimension and azimuth dimension of the data matrix, and k i represents the weighting value corresponding to the i-th singular value, and σ i (R) represents the i-th singular value of the interference matrix.

5. The synthetic aperture radar interference suppression method based on kurtosis weighted nuclear norm according to claim 4, characterized in that, The constructed interference suppression optimization problem model is iteratively solved through the ADMM framework, and the constructed augmented Lagrangian equation is: Where Y1 represents the auxiliary matrix, μ represents the penalty factor, and <·> represents the matrix inner product.

6. The synthetic aperture radar interference suppression method based on kurtosis weighted nuclear norm according to claim 5, characterized in that, The closed-form solution of the interference matrix in the constructed augmented Lagrangian equation is: Among them is the singular value decomposition result of G (p) The superscript (p) represents the p-th iteration, and k represents the weighting value k i The vector composed of, SVT represents the singular value threshold function, which is expressed as:

7. The method for suppressing synthetic aperture radar interference based on kurtosis weighted nuclear norm according to claim 6, wherein Weight value k i is calculated by computing the residual kurtosis of each singular value component of the interference matrix, and is defined as follows: where c represents a positive real scaling factor, denotes the kurtosis of the reference complex signal calculated with G (p) and denotes the kurtosis of the complex signal after removing the component corresponding to the i-th singular value of the interference matrix.​ 8. The synthetic aperture radar interference suppression method based on kurtosis weighted nuclear norm according to claim 7, wherein The calculation method of the complex signal kurtosis CSK is: Where RSK represents the real signal kurtosis, which is defined as: where M p represents the p-th order sample central moment, x represents the input real random variable, and E[] represents calculating the expectation of the input random variable; μ m,l represents the (m + l)-th order sample central moment, which is defined as where σ represents the standard deviation of the data, z represents the complex random variable of the input, and (·) * represents the operation of taking the complex conjugate.

9. The synthetic aperture radar interference suppression method based on kurtosis weighted nuclear norm according to claim 6, wherein The closed-form solutions of the echo matrix, auxiliary matrix, and auxiliary variables in the constructed augmented Lagrangian equation are: Among them is the soft threshold function, F represents the input matrix, β represents the threshold, ρ represents the algorithm acceleration factor, and μ max represents the upper limit of the penalty factor.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by a processor, it implements the steps of the synthetic aperture radar interference suppression method based on kurtosis-weighted nuclear norm according to any one of claims 1-9.

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