SAR jamming self-elimination method based on weak background prior

Abstract

The application discloses a SAR interference self-elimination method based on weak background prior, constructs an interference suppression optimization model based on weak background prior by detecting homologous weak background prior interference to be suppressed, protects useful signals by sparse regularization with hyperparameters, constructs an equivalent unconstrained optimization model by using a Lagrange, obtains an iterative relationship by an alternating direction multiplier method, and calculates a closed-form solution of a low-rank component of the interference suppression model to the useful signals by a soft threshold operator. The method can well utilize information of homologous interference to complete interference suppression on a specified area in SAR data polluted by interference, and has a certain energy protection for useful signals.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of radio frequency interference suppression, in particular to a SAR interference self-elimination method based on weak background prior. BACKGROUND

[0002] Synthetic aperture radar (SAR) has been widely concerned and applied due to its all-weather and all-time high resolution capability. However, in a complex electromagnetic environment, synthetic aperture radar is inevitably interfered by other radio frequency signals. Such as enemy active jammer signals, wireless communication, broadcast television and other radar signals will seriously affect the observation imaging capability of the SAR system. In today's increasingly fierce electronic countermeasures, interference suppression has become one of the abilities that radar systems must have. For the radio frequency interference (RFI) faced in SAR imaging, a series of signal decomposition methods based on nuclear norm minimization (NNM) have appeared in recent years. The traditional nuclear norm minimization method cannot accurately estimate the rank of the interference signal, which will lead to unsatisfactory interference suppression effect, and needs to be solved urgently. SUMMARY

[0003] The present application provides a SAR interference self-elimination method based on weak background prior, which can effectively suppress the interference of SAR received echoes and can realize relatively accurate estimation of radio frequency interference in SAR received signals.

[0004] The present application provides a SAR interference self-elimination method based on weak background prior, which comprises the following steps:

[0005] Detecting that the region to be suppressed of the SAR echo signal has a weak background homologous interference signal, and taking the weak background homologous interference signal as a prior interference signal;

[0006] Taking the SAR echo signal equal to the decomposed low-rank component matrix and sparse component matrix as a constraint condition, constructing an optimization model for minimizing the difference between the target to be suppressed and the rank of the prior interference signal, and setting a sparse regularization term in the optimization model;

[0007] By using the augmented Lagrange multiplier method, the optimization model is converted into an unconstrained problem to obtain a new optimization model;

[0008] Taking the similarity matrix of the prior interference signal as an auxiliary variable, using the alternating direction multiplier method, substituting the auxiliary variable into the update relationship of each variable of the new optimization model, and establishing an iterative update expression related to the auxiliary variable of the new optimization model;

[0009] The soft threshold operator is used to calculate the iterative update expression to obtain a closed-form solution of the low-rank component matrix of the SAR echo signal, and the SAR echo signal is subtracted by the closed-form solution of the low-rank component matrix to obtain the SAR echo signal after interference elimination.

[0010] Optionally, in an embodiment of the present application, the optimization model is:

[0011]

[0012] s.t X = R + S,

[0013] wherein Dif(R, R') represents the difference between the ranks of the target to be suppressed and the prior interference signal, λRe(S) is a sparse regularization term, X is the original signal matrix, R represents the low-rank component matrix, R' represents the prior interference signal, S represents the sparse matrix of the useful signal, and λ is a hyperparameter of the model.

[0014] Optionally, in an embodiment of the present application, the optimization model is converted into an unconstrained problem by using the augmented Lagrange multiplier method, comprising:

[0015] The optimization model under the constraint condition is solved by using the Lagrange function, the constraint condition is combined with the optimization target to be solved by using the Lagrange parameter, and a new unconstrained optimization model is constructed.

[0016] Optionally, in an embodiment of the present application, the expression of the soft threshold operator is:

[0017]

[0018] wherein x is a variable to be solved, and ε is a preset threshold.

[0019] Optionally, in an embodiment of the present application, after obtaining the SAR echo signal after interference elimination, the method further comprises:

[0020] The SAR echo signal after interference elimination is evaluated by using an evaluation index to determine the total energy loss and the interference suppression accuracy of the SAR echo signal after interference elimination.

[0021] Optionally, in an embodiment of the present application, the evaluation index comprises an interference energy suppression ratio for evaluating the total energy loss, and the calculation method is:

[0022]

[0023] wherein x m,n is the SAR echo signal, s m,n is a sparse component matrix after matrix decomposition, and m and n represent the matrix dimensions.

[0024] The evaluation index includes a singular value loss ratio for evaluating interference suppression accuracy, and the smaller the singular value loss ratio is, the higher the interference suppression accuracy is, and the calculation manner is:

[0025]

[0026] Wherein, sigma i Indicates the singular value of the low-rank component matrix after decomposition, Indicates the singular value of the prior interference signal, and abs(·) is an absolute value operator.

[0027] The SAR interference self-elimination method based on weak background prior of the embodiment of the application can detect homologous weak background prior interference of the interference to be suppressed, construct an interference suppression optimization model based on weak background prior, protect useful signals through sparse regularization with hyperparameters, use an augmented Lagrange to construct an equivalent unconstrained optimization model, obtain an iterative relationship through an alternating direction multiplier method, and calculate a closed-form solution of the low-rank component of the interference suppression model to the useful signal through a soft threshold operator. The method can well utilize the information of homologous interference to complete interference suppression of a specified region in SAR data polluted by interference, and also has the energy of protecting useful signals.

[0028] Additional aspects and advantages of the application will be set forth in part in the description which follows, and in part will become apparent to those skilled in the art upon examination of the following and / or can be learned by practice of the application. BRIEF DESCRIPTION OF DRAWINGS

[0029] The above and / or additional aspects and advantages of the application will become apparent and be readily appreciated from the following description, taken in conjunction with the accompanying drawings, in which:

[0030] Figure 1 A flowchart of a SAR interference self-elimination method based on weak background prior according to an embodiment of the application is shown in FIG. 1;

[0031] Figure 2 A different region and different region singular value comparison result schematic diagram according to an embodiment of the application is shown in FIG. 2;

[0032] Figure 3 A prior interference selection schematic diagram according to an embodiment of the application is shown in FIG. 3;

[0033] Figure 4 A prior interference and region to be suppressed relationship schematic diagram in an implementation process according to an embodiment of the application is shown in FIG. 4;

[0034] Figure 5 An interference suppression result schematic diagram according to an embodiment of the application is shown in FIG. 5;

[0035] Figure 6The method for suppressing SAR interference according to the embodiment of the present application Figure 5 An enlarged result diagram in the box in the figure. DETAILED DESCRIPTION

[0036] Embodiments of the present application are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar notations represent the same or similar elements or elements having the same or similar functions throughout. The embodiments described below by referring to the drawings are exemplary and are intended to explain the present application, and cannot be understood as a limitation of the present application.

[0037] The method for suppressing SAR interference according to the embodiment of the present application

[0038] Specifically, Figure 1 The method for suppressing SAR interference according to the embodiment of the present application

[0039] As Figure 1 shown, the method for suppressing SAR interference according to the embodiment of the present application includes the following steps:

[0040] In step S101, the weak background homologous interference signal of the SAR echo signal to be suppressed is detected, and the weak background homologous interference signal is taken as the prior interference signal.

[0041] According to the received SAR echo signal, the weak background homologous interference of the region to be suppressed is detected. The weak background homologous interference can be considered as pure interference without useful signal, and is denoted as R'. The weak background homologous interference is taken as the prior interference.

[0042] Specifically, the embodiment of the present application uses the homologous interference of the contaminated region as the prior, and the homologous interference has a weak background energy compared with the useful signal, and is considered as pure interference.

[0043] In step S102, an optimization model of minimizing the difference between the target to be suppressed and the prior interference signal in rank is constructed with the constraint condition of the SAR echo signal being equal to the decomposed low-rank component matrix and the sparse component matrix, and a sparse regularization term is set in the optimization model.

[0044] Embodiments of the present application use rank difference minimization to separate the interference component, and further convert it into singular value difference minimization. A minimization model of the difference between the target to be suppressed and the prior interference in rank is constructed, which is further constructed as a more rigorous singular value difference minimization model, i.e. a most similar model, in the present application. At the same time, the sparse regularization term with a hyperparameter is introduced in the model constructed in the present application to protect the useful signal, so that the algorithm can retain useful radar detection information in interference suppression. And according to the relationship between the original received signal and the low-rank component and the sparse component, the model constraint condition is set.

[0045] The optimization model is a rank difference minimization model of the target to be suppressed and the prior interference, which is specifically as follows:

[0046]

[0047] s.t X=R+S,

[0048] Wherein, Dif(R,R') represents the difference in rank between the target to be suppressed and the prior interference signal, λRe(S) is a sparse regularization term, X is an original signal matrix, R represents a low-rank component matrix, R' represents a prior interference signal, S represents a sparse matrix of a useful signal, and λ is a hyperparameter of the model. In order to make the interference component obtained by the algorithm more similar to the prior interference, the difference between the singular values of the interference component and the singular values of the prior interference is considered in the form of minimization.

[0049] By optimizing the model, a low-rank component similar to the prior can be obtained, and the received echo minus the low-rank component can obtain the required useful signal, and the interference component in the signal is largely suppressed by interference.

[0050] In step S103, the optimization model is converted into a new optimization model by using the augmented Lagrange multiplier method.

[0051] In embodiments of the present application, the optimization model is converted into an unconstrained problem by using the augmented Lagrange multiplier method, including:

[0052] The extreme value of the optimization model under the constraint condition is solved by using the Lagrange function, the constraint condition is combined with the optimization target to be solved by using the Lagrange parameter, and a new unconstrained optimization model is constructed.

[0053] The extreme value of a function under a constraint condition can be solved by using a Lagrange function, a Lagrange parameter is introduced to combine the original constraint condition and an optimization target to be solved together to form a new unconstrained target function. Based on the above operation, the algorithm model to be solved in the application can be converted into an unconstrained minimization problem, a penalty close to a boundary is constructed by using a Lagrange first-order term and a second-order term, so that the new unconstrained model is still in the boundary range of a feasible region.

[0054] In step S104, the alternating direction multiplier method is used with the aid of the similarity matrix of the prior interference signal as an auxiliary variable, the auxiliary variable is substituted into the update relationship of each variable of a new optimization model, and an iterative update expression related to the auxiliary variable of the new optimization model is established.

[0055] The similarity matrix of the prior interference is introduced as the auxiliary variable, so that the algorithm can conveniently solve a closed-form solution by using the alternating direction.

[0056] In the application, the Lagrange multiplier is introduced for the target problem, which also increases the number of variables to be solved. When calculating the optimal solution of each variable, the iterative update idea is used, that is, when solving a certain variable, other variables are regarded as a fixed parameter, and by this method, multiple variables in a target function can be solved. When each variable is solved, it can be regarded as a sub-optimization function. The optimal solution of each variable can be obtained through each iteration, and the final value of each variable can be obtained through multiple iteration calculations.

[0057] In step S105, the soft threshold operator is used to calculate the iterative update expression to obtain a closed-form solution of the low-rank component matrix of the SAR echo signal, and the SAR echo signal is subtracted from the closed-form solution of the low-rank component matrix to obtain the SAR echo signal after interference elimination.

[0058] For each iteration, the singular value difference minimization model can be changed into a minimization model of the auxiliary matrix by means of the auxiliary matrix. By using the soft threshold operator, a closed-form solution of the extracted echo signal low-rank component can be obtained.

[0059] In an embodiment of the application, the expression of the soft threshold operator is:

[0060]

[0061] Wherein, x is a variable to be solved, and ε is a preset threshold.

[0062] In the embodiment of the application, after obtaining the SAR echo signal after interference elimination, the following steps are further included:

[0063] The SAR echo signal after interference elimination is evaluated by the evaluation index to determine the total energy loss and interference suppression accuracy of the SAR echo signal after interference elimination.

[0064] In order to objectively evaluate the interference suppression effect, the interference energy suppression ratio is used as an evaluation index of the algorithm RFI suppression capability, and the interference singular value loss ratio is used to show that the part removed by the algorithm is the radio frequency interference. By comprehensively measuring the two indexes, it can be evaluated whether the result obtained after the algorithm processing of the received contaminated SAR signal is reliable. After the completion of interference suppression, the greater the energy suppression ratio and the smaller the singular value loss ratio mean that the algorithm has better interference suppression capability.

[0065] The interference energy suppression ratio (IESR) for evaluating the total energy loss is calculated as follows:

[0066]

[0067] Wherein, x m,n is the SAR echo signal, s m,n is the sparse component matrix after matrix decomposition, and m and n represent the matrix dimensions.

[0068] The singular value loss ratio (SVLR) for evaluating the interference suppression accuracy is calculated as follows:

[0069]

[0070] Wherein, σ i represents the singular value of the low-rank component matrix after decomposition, represents the singular value of the prior interference signal, and abs(·) is the absolute value operator. The smaller the singular value loss ratio means that the singular values are closer, and the low-rank matrix obtained by decomposition is more similar to the prior interference matrix.

[0071] The interference elimination capability of the algorithm can be evaluated by the interference energy suppression ratio, and the accuracy of interference elimination can be measured by the singular value loss ratio. By comprehensively measuring the two indexes, the interference suppression ability of the algorithm can be objectively evaluated.

[0072] The SAR interference self-elimination method based on weak background prior art will be described in detail below through specific embodiments.

[0073] As Figure 2 (a) and Figure 2The different regions have different singular value distribution characteristics as shown in (b). Considering the spatial transformation of the SAR system view window from sea surface to land, the singular value of the echo signal is also gradually increasing. The echo signal of the open sea surface is weak, and the singular value of the sea surface region is small. When the land area in the window increases, the singular value of the corresponding receiving matrix also gradually increases. When the land area is observed completely, the singular value of the signal matrix is relatively larger than the previous two scenarios. Figure 2 (a) intercepts the sea surface (the leftmost box), half sea and half land (the middle box), and land (the rightmost box) three regions and shows the singular value distribution of the receiving signal matrix in the three scenarios. Among them, Figure 2 (b) the short dashed line, the long dashed line and the solid line respectively represent the singular value distribution of the sea surface signal, the half sea and half land signal and the land signal. The singular value distribution is very obvious in the figure. The singular value of the sea surface signal is almost the lowest at each index, and the singular value of the land signal is almost the highest at each index, and the value of the half sea and half land is between the two.

[0074] Due to the weak echo energy of the sea surface, its signal strength can be ignored compared to the land. It is considered that the S matrix of the sea surface area receiving interference is approximately a zero matrix. At this time, only the interference signal component is dominant in the region echo, which can be regarded as a pure RFI without target echo. According to this setting, the algorithm proposed by the embodiment of the present application uses the part of the RFI with the sea surface as the background as a priori, and calculates the singular value distribution thereof. The prior singular value distribution is used to realize interference suppression in different scenarios.

[0075] The prior interference acquisition schematic diagram is shown in Figure 3 According to Figure 4 , first, the same source interference with the sea surface as the background in the sea area near the to-be-processed region is intercepted as a priori, and the singular value distribution of the region is calculated. Then, the prior information and the data matrix are substituted into the solving model to obtain the interference suppression result.

[0076] With the help of the measured data of the SAR system, the present application carries out interference suppression based on priori for three different scenarios of islands, peninsulas and land. Figure 5 (a) of and Figure 5 (d) of are respectively an island covered by interference and the result of interference suppression on the island; Figure 5 (b) and Figure 5 (e) are respectively a peninsula with radio frequency interference and the result of interference suppression on the peninsula region; Figure 5 (c) and Figure 5 (f) are respectively land with radio frequency interference and the result of interference suppression on the land region. In order to more clearly and intuitively see the interference suppression effect, Figure 6 (a) toFigure 6 (f) corresponds to the area within the dashed line in (a)- Figure 5 Figure 5 (f) corresponds to the area within the dashed line in (a)- Figure 5 Figure 6 It can be seen that the interference suppression method used in the present application can effectively remove radio frequency interference in different scenarios, and can relatively clearly restore the echo signal of the SAR system.

[0077] The SAR interference self-elimination method based on weak background prior art according to the embodiment of the present application first calculates the singular value distribution of the homologous interference signal in the weak background area, and then minimizes the singular value of the prior singular value and the low-rank component according to the matrix similarity principle, and then separates the interference signal of the region to be suppressed, and retains the remaining effective signal. The method can realize relatively accurate estimation of radio frequency interference in the SAR receiving signal, and can well utilize the information of the homologous interference to complete the interference suppression of the specified region in the SAR data polluted by the interference, and also has a certain protection energy of the useful signal, and is more reliable than the existing same type of method.

[0078] In the description of the present specification, the description of the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" means that the specific features, structures, materials or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present application. In the present specification, the illustrative description of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or N embodiments or examples in a suitable manner. In addition, the skilled in the art can combine and combine the different embodiments or examples described in the present specification and the features of the different embodiments or examples without contradiction.

[0079] In addition, the terms "first", "second" are only for descriptive purposes, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of indicated technical features. Therefore, the features limited by "first", "second" can explicitly or implicitly include at least one feature. In the description of the present application, the meaning of "N" is at least two, for example, two, three, etc., unless otherwise specifically limited.

[0080] ​​Any processes or methods described in the flowcharts or otherwise described herein can be understood as representing code modules, segments, or portions of code which include one or more executable instructions for implementing specific logic functions (or steps) of the application, and / or that the various processes or methods described in connection with the preferred embodiments of the application can be embodied in a computer readable medium (e.g., magnetic or optical), that is, any non-transitory medium of expression that can be capable of being employed as a computational medium for implementing the processes or methods described in connection with the preferred embodiments of the application, regardless of the particular technology or techniques used to implement the processes or methods.

Claims

1. A SAR interference self-cancellation method based on weak background prior, characterized in that, Includes the following steps: The detection of co-originating interference signals with weak background in the region to be suppressed of the SAR echo signal is used as the prior interference signal. Using the SAR echo signal being equal to the decomposed low-rank component matrix and sparse component matrix as constraints, an optimization model is constructed to minimize the difference in rank between the target to be suppressed and the prior interference signal, and a sparse regularization term is set in the optimization model. By using the augmented Lagrange multiplier method, the optimization model is transformed into an unconstrained problem to obtain a new optimization model; Using the similarity matrix of the prior interference signal as an auxiliary variable, the alternating direction multiplier method is used to substitute the auxiliary variable into the update relationship of each variable in the new optimization model, and establish the iterative update expression of the new optimization model related to the auxiliary variable. The iterative update expression is calculated using a soft threshold operator to obtain the closed-form solution of the low-rank component matrix of the SAR echo signal. The SAR echo signal after interference is obtained by subtracting the closed-form solution of the low-rank component matrix from the SAR echo signal.

2. The method according to claim 1, characterized in that, The optimization model is as follows: st X=R+S, Where Dif(R,R') represents the difference in rank between the target to be suppressed and the prior interference signal, λRe(S) is the sparse regularization term, X is the original signal matrix, R represents the low-rank component matrix, R' represents the prior interference signal, S represents the sparse matrix of the useful signal, and λ is the hyperparameter of the model.

3. The method according to claim 1, characterized in that, The optimization model is transformed into an unconstrained problem using the augmented Lagrange multiplier method, including: The extreme values ​​of the optimization model under constraints are obtained by using the Lagrange function. The constraints are then combined with the optimization objective to be solved using the Lagrange parameters to form a new unconstrained optimization model.

4. The method according to claim 1, characterized in that, The expression for the soft threshold operator is: Where x is the variable to be solved, and ε is the preset threshold.

5. The method according to claim 1, characterized in that, After obtaining the interference-free SAR echo signal, the following is also included: The SAR echo signal after interference elimination is evaluated using evaluation indicators to determine the total energy loss and interference suppression accuracy of the SAR echo signal after interference elimination.

6. The method according to claim 5, characterized in that, The evaluation index includes the interference energy suppression ratio, which is used to evaluate the total energy loss. The calculation method is as follows: Where, x m,n For SAR echo signal, s m,n is the sparse component matrix after matrix decomposition, where m and n represent the matrix dimensions; The evaluation metric includes the singular value loss ratio (SVR), which evaluates the accuracy of interference suppression. A smaller SVR indicates higher interference suppression accuracy. The calculation method is as follows: Where, σ i Denotes the singular values ​​of the low-rank component matrix after decomposition. represents the singular value of the prior interference signal, and abs(·) is the absolute value operator.

Images