Synthetic aperture radar radio frequency interference suppression method based on two-stage processing

Abstract

The invention discloses a synthetic aperture radar radio frequency interference suppression method based on two-stage processing, and the method comprises the steps: obtaining SAR single-view complex image data containing an interference signal, carrying out the fast Fourier transform of the SAR single-view complex image data along a distance dimension, and obtaining a distance frequency domain-azimuth time domain two-dimensional distance spectrum; based on a wavelet decomposition algorithm and a quartile distance method, preliminarily extracting a frequency spectrum component of an interference signal in the two-dimensional distance frequency spectrum to obtain a first interference signal distance frequency spectrum; based on a fast generalized singular value threshold low-rank sparse decomposition algorithm, separating the frequency spectrum component of the echo signal from the first interference signal distance frequency spectrum by using the low-rank characteristic of the interference signal to obtain a second interference signal distance frequency spectrum; and based on the two-dimensional distance spectrum and the second interference signal distance spectrum, obtaining an SAR single-view complex image after interference suppression. According to the method, the double bottlenecks that the notch threshold is difficult to select and the low-rank condition is difficult to meet in the traditional SAR radio frequency interference suppression are solved.

Description

Technical Field

[0001] The present invention belongs to the technical field of radar signal processing, and in particular relates to a synthetic aperture radar radio frequency interference suppression method based on two-stage processing. Background Art

[0002] Synthetic Aperture Radar (SAR) boasts all-day, all-weather capabilities, penetrating cloud, rain, and fog. Countries around the world are scrambling to develop their own SAR equipment and systems. Generations of satellites carrying SAR have been launched, leading to a congestion in the electromagnetic spectrum. Coupled with increasingly complex electromagnetic environments, SARs are susceptible to receiving radio frequency interference signals from other equipment during their missions. These interference signals cause the resulting SAR images to appear as bright, periodic streaks and bright spots, blurring and distorting the image, severely impacting SAR's application.

[0003] Due to the frequent occurrence of interference in synthetic aperture radar systems, a number of research results have emerged in recent years. Among them, He Yinguang proposed an interference suppression algorithm based on generalized S transform time-frequency filtering in the paper "GST Time-Frequency Filtering SAR Radio Frequency Interference Suppression Algorithm" (Xi'an Institute of Space Radio Technology, 2021). By using the paired sample T test to detect and mark the echo data with interference, the marked echo data is then transformed into the generalized S transform domain, and subspace filtering is performed on the data within the time window one by one to achieve interference suppression. However, in this method, the thresholds such as the confidence level of the T test and the number of interference subspaces need to be manually defined, and the method is highly dependent on the threshold. In the paper "A RFI Mitigation Approach for Spaceborne SAR Using Homologous Interference Knowledge at Coastal Regions" (IEEE Transactions on Geoscience and Remote Sensing, 2025), Xuezhi Chen et al. proposed an interference self-cancellation (ISC) method that leverages knowledge of homologous interference (HI) in coastal regions. This method alleviates the over-contraction problem of the classic nuclear norm minimization algorithm by extracting singular value estimates from a reference HI region and adding them as templates to the low-rank model. However, this method is computationally expensive, comparable to the classic low-rank sparse decomposition method, and its computational complexity is high, and the low-rank condition is difficult to meet.

[0004] Therefore, it is necessary to provide an improved technical solution to address the deficiencies in the above-mentioned prior art. Summary of the Invention

[0005] The present application provides a synthetic aperture radar radio frequency interference suppression method based on two-stage processing, which aims to solve the problem of how to alleviate the threshold selection difficulty of the notch method and promote the achievement of the low-rank condition required by the low-rank sparse decomposition method. The present application provides a synthetic aperture radar radio frequency interference suppression method based on two-stage processing, which includes: Step 1: Obtain the SAR single-view complex image data containing the interference signal, perform fast Fourier transform on the SAR single-view complex image data along the distance dimension to obtain a two-dimensional range spectrum in the range frequency domain-azimuth time domain; Step 2: Based on the wavelet decomposition algorithm and the quartile distance method, the spectral components of the interference signal in the two-dimensional range spectrum are preliminarily extracted to obtain a first interference signal range spectrum; Step 3: Based on the fast generalized singular value threshold low-rank sparse decomposition algorithm, the spectral components of the echo signal in the first interference signal range spectrum are separated from the first interference signal range spectrum by utilizing the low-rank characteristics of the interference signal to obtain a second interference signal range spectrum, and the spectral components of the echo signal in the second interference signal range spectrum are lower than those in the first interference signal range spectrum; Step 4: Based on the two-dimensional range spectrum and the second interference signal range spectrum, a SAR single-view complex image after interference suppression is obtained.

[0006] In an embodiment of the present application, step 2 includes: Step 2.1: Perform wavelet decomposition on the two-dimensional range spectrum to obtain wavelet coefficients of each order, wherein, ; ; Step 2.2: Based on the quartile distance method, identify and mark the wavelet coefficients exceeding the threshold, and perform wavelet reconstruction on the wavelet coefficients exceeding the threshold to obtain the first interference signal range spectrum.

[0007] In an embodiment of the present application, the expression of the wavelet coefficient is:

[0008] wherein, is the wavelet coefficient, is the wavelet domain, is the azimuth time axis, is the wavelet decomposition operator, is the two-dimensional range spectrum, is the range spectrum axis, is the absolute value operation, is the azimuth time axis is the first sampling point.

[0009] ​In one embodiment of the present invention, performing wavelet reconstruction on wavelet coefficients exceeding a threshold to obtain a first interference signal range spectrum includes: Calculate the phase of the two-dimensional range spectrum; Performing wavelet reconstruction on the wavelet coefficients exceeding the threshold to obtain the amplitude of the first interference signal range spectrum; A first interference signal range spectrum is obtained based on the phase of the two-dimensional range spectrum and the amplitude of the first interference signal range spectrum.

[0010] In one embodiment of the present invention, the amplitude of the first interference signal distance spectrum is expressed as:

[0011] in, is the amplitude of the first interference signal distance spectrum, is the orientation time axis, is the distance spectrum axis, is the wavelet reconstruction operator, is the wavelet coefficient exceeding the threshold, is the wavelet domain, is the absolute value operation, Position time axis Previous sampling points; the expression of the first interference signal distance spectrum is:

[0012] in, is the first interference signal distance spectrum, is the dot multiplication operation, is the phase of the two-dimensional range spectrum, Is an imaginary unit.

[0013] In one embodiment of the present invention, step 3 includes: Step 3.1: Based on the first interference signal distance spectrum, construct a first model of the fast generalized singular value threshold low-rank sparse decomposition algorithm, and convert the first model into an augmented Lagrangian function; Step 3.2: Construct a generalized singular value threshold operator; Step 3.3: Based on the generalized singular value threshold operator and the random projection singular value decomposition algorithm, the low-rank characteristics of the interference signal are utilized to iteratively solve the augmented Lagrangian function. After each iterative solution, a low-rank matrix of the first interference signal distance spectrum is obtained. The low-rank matrix is ​​a matrix containing the interference signal. Step 3.4: When the number of iterations is equal to or greater than the iteration threshold, the iteration is stopped, and the low-rank matrix solved by the last iteration is determined as the second interference signal range spectrum.

[0014] In an embodiment of the present application, the expression of the first model is: wherein the constraint condition of the first model is , is a first interference signal range spectrum, is a low-rank matrix, is a sparse matrix, the sparse matrix is a matrix containing echo signals, is the number of singular values, represents the singular value, is a non-convex surrogate function, is an operator for obtaining all singular values of a matrix, is a hyperparameter, is the L1 norm of the sparse matrix ; The expression of the augmented Lagrangian function is:

[0015] wherein, is an augmented Lagrangian function, is a hyperparameter, is a Lagrange multiplier, is an inner product operation, is and the difference norm.

[0016] In an embodiment of the present application, step 4 comprises: Step 4.1: subtracting the second range spectrum from the two-dimensional range spectrum to obtain an interference-suppressed range spectrum; Step 4.2: performing fast inverse Fourier transform on the interference-suppressed range spectrum along the range dimension to obtain an interference-suppressed SAR single-view complex image.

[0017] Another aspect of the present application provides a storage medium, wherein the storage medium stores a computer program, and the computer program is used to execute the steps of the synthetic aperture radar radio frequency interference suppression method based on the two-stage processing in any one of the above embodiments.

[0018] Compared with the prior art, the present application has the following beneficial effects: The embodiment of the present application provides a two-stage processing synthetic aperture radar radio frequency interference suppression method, first, a wavelet decomposition algorithm is used, a spectrum component of an interference signal is preliminarily extracted through quartile distance-based outlier detection, a first interference signal range spectrum is obtained, then, based on the low-rank characteristics of the interference signal, a fast generalized singular value threshold low-rank sparse decomposition algorithm is combined, spectrum components of echo signals are separated from the first interference signal range spectrum, a second interference signal range spectrum with lower spectrum components is obtained, that is, a relatively pure interference signal range spectrum is obtained, since the second interference signal range spectrum is obtained based on the first interference signal range spectrum, the sensitivity of threshold selection in the wavelet decomposition algorithm process can be reduced, that is, the two-stage processing method enhances the robustness of threshold selection; in addition, the wavelet decomposition algorithm is used to preliminarily extract the spectrum component of the interference signal, the proportion of the echo signal in the range spectrum is reduced, so that the preliminarily extracted interference signal is more in line with the low-rank characteristics, so that when the fast generalized singular value threshold low-rank sparse decomposition algorithm is combined to separate the spectrum components of the echo signals from the first interference signal range spectrum, the input data, that is, the first interference signal range spectrum, already has a good low-rank condition, so that the complexity of calculation can be reduced, and the efficiency of radio frequency interference and radar echo separation can be improved.

[0019] The present application will be further described in detail below with reference to the accompanying drawings and embodiments. BRIEF DESCRIPTION OF DRAWINGS

[0020] Figure 1 FIG. 1 is a flowchart of a two-stage processing synthetic aperture radar radio frequency interference suppression method provided by the embodiment of the present application; Figure 2 (a) is a SAR single-view complex image containing an interference signal provided by the embodiment of the present application; Figure 2 (b) Figure 2 (g) is a SAR single-view complex image after interference suppression obtained by using a frequency domain notch method (FNF), a principal component analysis method (PCA), a robust principal component analysis method (RPCA), a wavelet domain notch method (WNF), a generalized singular value threshold low-rank sparse decomposition method (GSVT-LRSD) and the present method (WNF-GSVT-LRSD) respectively under different interference to signal ratios (ISRs) provided by the embodiment of the present application; Figure 3 FIG. 4 is an RMSE index curve diagram of SAR images before and after interference suppression of the WNF method and the present method under the condition of ISR=0dB provided by the embodiment of the present application; Figure 4 FIG. 5 is an RMSE index curve diagram of SAR images before and after interference suppression of the WNF method and the present method under the condition of ISR=10dB provided by the embodiment of the present application; Figure 5 A distance spectrum contrast chart before and after processing by the WNF method is provided for an embodiment of the present application. DETAILED DESCRIPTION

[0021] In order to further illustrate the technical means and effects taken by the present application to achieve the predetermined object, a two-stage processing-based synthetic aperture radar radio frequency interference suppression method according to the present application is described in detail below in combination with the drawings and specific embodiments.

[0022] The foregoing and other technical contents, features and effects of the present application can be clearly presented in the detailed description of the specific embodiments below in combination with the drawings. Through the description of the specific embodiments, the technical means and effects taken by the present application to achieve the predetermined object can be understood more deeply and specifically. However, the accompanying drawings are provided for reference and illustration only, and are not intended to limit the technical solutions of the present application.

[0023] It should be noted that, in this document, relational terms such as first and second and the like can only be used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply that these entities or operations exist in any such actual relationship or order. Moreover, the terms "comprising", "including" or any other variant thereof are intended to cover non-exclusive inclusion, so that a process, method, article or apparatus that includes a list of elements does not necessarily include only those elements in the list, but can include other elements not expressly listed or included. Without more limitations, the element defined by the sentence "comprising a" does not exclude the presence of additional identical elements in the process, method, article or apparatus including the element.

[0024] The present application aims to solve the problem of how to alleviate the difficulty of threshold selection in the trap wave method while promoting the achievement of the low-rank condition required by the low-rank sparse decomposition method. The present application provides a two-stage processing-based synthetic aperture radar radio frequency interference suppression method, please refer to Figure 1 The method comprises the following steps: Step 1: Obtain SAR single-view complex image data containing interference signals, and perform fast Fourier transform on the SAR single-view complex image data along the distance dimension to obtain a two-dimensional distance spectrum in the distance frequency domain and the azimuth time domain.

[0025] The SAR single-view complex image data refers to the image data after imaging the echo data collected by the SAR system, but before multi-view processing. Each sampling point contains electromagnetic wave information reflected from the corresponding ground area, and usually exists in the form of complex number, including amplitude and phase information.

[0026] The SAR single-view complex image data containing interference signals refers to each sampling point in the SAR single-view complex image data containing not only echo signals reflected by ground objects but also various interference signals (such as narrowband interference and wideband interference) from the outside world.

[0027] In SAR imaging, the "range dimension" refers to the data dimension along the distance direction between the radar and the target. Since SAR determines the distance by measuring the time difference between the transmitted pulse and the received echo, the data along the range dimension is actually time series data.

[0028] In the embodiment of the present application, the expression of the two-dimensional range spectrum is as follows:

[0029] wherein, is a two-dimensional range spectrum, is a range spectrum axis, is an azimuth time axis, is a range time axis, is SAR single-view complex image data containing interference signals, , is the total number of pixels of the range time axis, is the total number of pixels of the azimuth time axis, is a complex domain.

[0030] Step 2: Based on the wavelet decomposition algorithm and the interquartile range method, the spectral components of the interference signals in the two-dimensional range spectrum are preliminarily extracted to obtain a first interference signal range spectrum.

[0031] The interquartile range (IQR) method is a statistical technique for identifying outliers in a data set. It measures the dispersion of data based on the quartiles of the data set and defines which data points can be considered as outliers. The IQR is usually defined as the difference between the third quartile ( ) and the first quartile ( ), that is, .

[0032] wherein, is the third quartile, indicating that 75% of the wavelet coefficients are less than this value, is the first quartile, indicating that 25% of the wavelet coefficients are less than this value, then the upper bound and the lower bound of the outliers can be represented as follows:

[0033]

[0034] wherein, For the threshold factor, it can be adjusted according to the required confidence level, for example, in an embodiment of the present application, .

[0035] In some embodiments, step 2 comprises: Step 2.1: performing wavelet decomposition on the two-dimensional range spectrum to obtain wavelet coefficients of each order, wherein, . .

[0036] Specifically, the two-dimensional range spectrum is subjected to wavelet decomposition of order at each azimuth time point, and the expression of the wavelet coefficients obtained by the wavelet decomposition at each azimuth time point is:

[0037] wherein, is a wavelet coefficient, is a wavelet domain, is an azimuth time axis, is a wavelet decomposition operator, is an absolute value operation, is the th sampling point on the azimuth time axis .

[0038] It should be noted that before the absolute value operation, the phase of the two-dimensional range spectrum is calculated and retained in order to facilitate subsequent calculation of the first interference signal range spectrum.

[0039] Step 2.2: identifying and marking the wavelet coefficients that exceed the threshold value based on the interquartile range method, and performing wavelet reconstruction on the wavelet coefficients that exceed the threshold value to obtain the first interference signal range spectrum.

[0040] In an embodiment of the present application, the wavelet coefficients that exceed the upper threshold value are marked as outliers and retained, and the wavelet coefficients that are lower than the lower threshold value are set to zero in order to facilitate wavelet reconstruction on only the retained wavelet coefficients to obtain the first interference signal range spectrum.

[0041] It should be noted that the echo signal usually exhibits a relatively smooth and low-frequency part, and the corresponding wavelet coefficients are relatively small. Setting these smaller wavelet coefficients to zero aims to remove the influence of the echo signal and only retain the larger wavelet coefficients that may represent the interference signal.

[0042] Specifically, the wavelet coefficients that exceed the threshold value can be expressed as follows:

[0043] in, are the wavelet coefficients exceeding the threshold.

[0044] In some embodiments, performing wavelet reconstruction on the wavelet coefficients exceeding the threshold to obtain the first interference signal range spectrum specifically includes: Wavelet coefficients exceeding the threshold are reconstructed to obtain the amplitude of the first interference signal range spectrum, and the first interference signal range spectrum is obtained based on the phase of the two-dimensional range spectrum and the amplitude of the first interference signal range spectrum.

[0045] Specifically, the expression for the amplitude of the first interference signal distance spectrum is:

[0046] in, is the amplitude of the first interference signal distance spectrum, is the wavelet reconstruction operator, are the wavelet coefficients exceeding the threshold.

[0047] The expression of the first interference signal distance spectrum is:

[0048] in, is the first interference signal distance spectrum, is the dot multiplication operation, is the phase of the two-dimensional range spectrum, Is an imaginary unit.

[0049] It should be noted that after the above steps 1 and 2, the RF interference signal and the SAR echo signal are initially separated, which reduces the rank of the range spectrum and promotes the achievement of the low-rank condition to a certain extent.

[0050] Step 3: Based on the Fast Generalized Singular Value Thresholding - Low Rank Sparse Decomposition (FGSVT-LRSD) algorithm, the low-rank characteristics of the interference signal are utilized to separate the spectral components of the echo signal in the first interference signal range spectrum from the first interference signal range spectrum to obtain the second interference signal range spectrum.

[0051] The spectrum component of the echo signal in the second interference signal distance spectrum is lower than the spectrum component of the echo signal in the first interference signal distance spectrum.

[0052] In some embodiments, step 3 includes: Step 3.1: Based on the first interference signal distance spectrum, a first model of a fast generalized singular value threshold low-rank sparse decomposition algorithm is constructed, and the first model is converted into an augmented Lagrange function.

[0053] Specifically, the expression of the first model is:

[0054] The constraint condition of the first model is , is the first interference signal distance spectrum, is a low-rank matrix, is a sparse matrix, and the sparse matrix is a matrix containing echo signals, is the number of singular values, represents the singular value, is a non-convex proxy function, is an operator for obtaining all singular values of a matrix, is a hyperparameter, is the L1 norm of the sparse matrix .

[0055] The expression of the augmented Lagrange function is:

[0056] wherein, is the augmented Lagrange function, is a hyperparameter, is a Lagrange multiplier, is an inner product operation, is the norm of the difference between and .

[0057] Step 3.2: Construct a generalized singular value threshold operator.

[0058] It should be noted that since the function gradient of any non-convex proxy function is convex, in order to solve the non-convex low-rank minimization problem, a generalized singular value threshold operator needs to be constructed for the FGSVT-LRSD algorithm.

[0059] The expression of the initially constructed generalized singular value threshold operator is:

[0060]

[0061] wherein, is the initially constructed generalized singular value threshold operator, Indicates calculation The operation of the corresponding variable value when taking the minimum value, For the The sparse matrix after iterations is For the The Lagrange multiplier after iterations is, For the Hyperparameters after iterations.

[0062] In the embodiment of the present invention, the above formula can be converted into:

[0063] in, represents diagonal operation, is a matrix Singular Value Decomposition (SVD) of is the transposed matrix of the right singular vectors, is a left singular vector.

[0064] matrix The singular values ​​of , then the above formula can be converted to solve the following problem:

[0065]

[0066] in, is the generalized singular value threshold operator, Indicates calculation The operation of the corresponding variable value when taking the minimum value, is a matrix No. Singular values.

[0067] Step 3.3: Based on the generalized singular value threshold operator and the random projection singular value decomposition algorithm, the low-rank characteristics of the interference signal are utilized to iteratively solve the augmented Lagrangian function. After each iterative solution, a low-rank matrix of the first interference signal distance spectrum is obtained. The low-rank matrix is ​​a matrix containing the interference signal.

[0068] It should be noted that the solution to the above problem is or local extreme point Since the SVD operation is the most complex step in the above formula, the random projection singular value decomposition (RSVD) is considered to replace the SVD to reduce the operation time. According to the Johnson-Lindenstraus lemma, the random projection maps the data in the high-dimensional space to the low-dimensional space by constructing a randomly generated projection matrix, and preserves the relative distance between the data points as much as possible while reducing the dimension. Therefore, the non-full rank SVD operation can be realized by random projection, which reduces the dimension of the matrix involved in the operation while approximating the SVD operation.

[0069] Specifically, let the input matrix of the RSVD operation be matrix , , the number of singular values of matrix is , and . First, a Gaussian random matrix is constructed, and then the matrix multiplication operation is performed, and the orthogonal basis of is obtained by QR decomposition. Then, a low-dimensional matrix is constructed, and the matrix is decomposed by SVD to obtain . The orthogonal basis of is used to update the left singular vector , and the final result is obtained. As can be seen, the RSVD operation reduces the computational complexity from to . Since the narrowband radio frequency interference has the low rank characteristic, , the acceleration of the algorithm is realized.

[0070] wherein is the left singular vector of matrix after singular value decomposition, is the diagonal matrix of matrix after singular value decomposition, is the right singular vector of matrix after singular value decomposition, , and are the matrices obtained by taking the first K rows of , and matrices, respectively.

[0071] Specifically, in each iteration, the low-rank matrix is updated as follows:

[0072] wherein the low-rank matrix after the first iteration, the low-rank matrix after the second iteration, the low-rank matrix after the third iteration, the low-rank matrix after the fourth iteration, the low-rank matrix after the fifth iteration, the low-rank matrix after the sixth iteration, the low-rank matrix after the seventh iteration, the low-rank matrix after the eighth iteration, the low-rank matrix after the ninth iteration, the low-rank matrix after the tenth iteration, the Lagrange multiplier after the first iteration, the Lagrange multiplier after the second iteration, the Lagrange multiplier after the third iteration, the Lagrange multiplier after the fourth iteration.

[0073] wherein, and are calculated. In each iteration, the rank of the low-rank matrix needs to be calculated to be substituted into the RSVD operation of the next iteration, i.e. after the update of the low-rank matrix is completed, the sparse matrix is updated as follows:

[0074] wherein, , the sparse matrix after the first iteration, the sparse matrix after the second iteration, , is a sign function.

[0075] Finally, the updated and are obtained as follows:

[0076]

[0077] wherein, the Lagrange multiplier after the first iteration, the Lagrange multiplier after the second iteration, the hyper-parameter after the first iteration, the hyper-parameter after the second iteration, is a hyper-parameter and .

[0078] Step 3.4: stop the iteration in the case that the number of iterations is equal to or greater than the iteration threshold, and determine the low-rank matrix solved in the last iteration as the second interference signal range spectrum.

[0079] It can be understood that in the case that the above algorithm gradually reaches the convergence condition, i.e. in the case that the number of iterations is equal to or greater than the iteration threshold, it is indicated that the first interference signal range spectrum​ Further separation of the spectral components of the jamming signal and the echo signal spectral components, i.e. in this case, the iteration can be stopped, and the low-rank matrix solved in the last iteration is determined as the second jamming signal range spectrum.

[0080] Step 4: Based on the two-dimensional range spectrum and the second jamming signal range spectrum, a SAR single-view complex image after interference suppression is obtained.

[0081] In some embodiments, step 4 comprises: Step 4.1: Subtract the second range spectrum from the two-dimensional range spectrum to obtain a range spectrum after interference suppression.

[0082] Specifically, the second jamming signal range spectrum is , and the range spectrum after interference suppression is .

[0083] Step 4.2: Perform fast inverse Fourier transform on the range spectrum after interference suppression along the range dimension to obtain a SAR single-view complex image after interference suppression.

[0084] Specifically, the expression of the SAR single-view complex image after interference suppression is:

[0085] wherein, is the SAR single-view complex image after interference suppression.

[0086] In summary, the embodiment of the present application provides a two-stage processing synthetic aperture radar radio frequency interference suppression method, which firstly utilizes a wavelet decomposition algorithm to preliminarily extract spectral components of a jamming signal based on quartile distance outlier detection to obtain a first jamming signal range spectrum, and then separates spectral components of an echo signal from the first jamming signal range spectrum based on a low-rank feature of the jamming signal and in combination with a fast generalized singular value threshold low-rank sparse decomposition algorithm to obtain a second jamming signal range spectrum with lower spectral components, i.e. a relatively pure jamming signal range spectrum. Since the second jamming signal range spectrum is obtained based on the first jamming signal range spectrum, the sensitivity to threshold selection in the wavelet decomposition algorithm process can be reduced, i.e. the two-stage processing method enhances the robustness to threshold selection. In addition, the present application preliminarily extracts spectral components of the jamming signal through the wavelet decomposition algorithm, reduces the proportion of the echo signal in the range spectrum, and makes the preliminarily extracted jamming signal more in line with the low-rank feature, so that when the spectral components of the echo signal are separated from the first jamming signal range spectrum in combination with the fast generalized singular value threshold low-rank sparse decomposition algorithm, the input data, i.e. the first jamming signal range spectrum, already has a good low-rank condition, thereby reducing the complexity of the calculation and improving the efficiency of the separation of the radio frequency interference and the radar echo.

[0087] It should be noted that the conventional radio frequency interference suppression usually selects one of the non-parametric method, the parametric method or the semi-parametric method, and each method has its advantages and disadvantages, and needs to be optimized according to the SAR scene or the interference type, and therefore the robustness is poor. However, the method combines the wavelet domain notch filtering method in the non-parametric method and the generalized singular value threshold low-rank sparse decomposition method in the semi-parametric method, and realizes more excellent and more robust interference suppression performance.

[0088] Next, using the C-band GF-3 satellite measured SAR data, the simulated narrowband radio frequency interference is superimposed, and the interference suppression experiment is carried out to verify the superiority of the method. Specifically, the minimum mean square error (RMSE) between the SAR complex images before and after the application of different interference suppression methods can be compared to measure the suppression effect of different interference suppression methods. It should be noted that the smaller the RMSE, the better the interference suppression effect, that is, the echo signal is more effectively protected.

[0089] The calculation formula of RMSE is as follows:

[0090] Exemplarily, as shown in FIG. 1, wherein Figure 2 (a) is a SAR single-view complex image containing interference signals provided by an embodiment of the present application, Figure 2 (b) is a SAR single-view complex image containing interference signals provided by an embodiment of the present application, Figure 2 (c) is a SAR single-view complex image containing interference signals provided by an embodiment of the present application, Figure 2 (g) is a SAR single-view complex image after interference suppression obtained by using the frequency domain notch method (FNF), the principal component analysis method (PCA), the robust principal component analysis method (RPCA), the wavelet domain notch method (WNF), the generalized singular value threshold low-rank sparse decomposition method (GSVT-LRSD) and the method (WNF-GSVT-LRSD) under different interference to signal ratios (ISRs) provided by an embodiment of the present application. From Figure 2 (b) is a SAR single-view complex image after interference suppression obtained by using the frequency domain notch method (FNF), the principal component analysis method (PCA), the robust principal component analysis method (RPCA), the wavelet domain notch method (WNF), the generalized singular value threshold low-rank sparse decomposition method (GSVT-LRSD) and the method (WNF-GSVT-LRSD) under different interference to signal ratios (ISRs) provided by an embodiment of the present application. From Figure 2 (g) can be seen that the SAR single-view complex image after interference suppression obtained by using the method has higher clarity.

[0091] In order to further evaluate the interference suppression performance of the method, the RMSE is used for quantitative evaluation of the interference suppression effect, and the RMSE between the SAR single-view complex images obtained by using each of the above methods after interference suppression and the original SAR image without interference under different interference to signal ratios (ISRs) is shown in Table 1 as follows: Table 1

[0092] From the comparison in Table 1 above, it can be seen that the RMSE difference between the SAR single-view complex image obtained after interference suppression by this method and the original SAR image without interference is the smallest, that is, the interference suppression performance of this method is the best.

[0093] In addition, in order to verify the superiority of the two-stage processing framework proposed by this method, in an embodiment of the present invention, a comparative experiment on the interference suppression performance of the WNF method and this method under different thresholds was carried out, and the change in the rank of the distance spectrum before and after WNF was analyzed to prove that this method can alleviate the problem of difficult threshold selection of notch-type methods and achieve low-rank conditions.

[0094] In the WNF method, the threshold value is controlled by the threshold factor Therefore, in the embodiment of the present invention, the interference suppression performance comparison experiment between the WNF method and the present method under different threshold factors is conducted to verify the robustness of the present method to the threshold selection. Figure 3 and Figure 4 As shown, when When ISR=0dB and ISR=10dB are compared (where Figure 3 is the RMSE indicator curve when ISR=0dB, Figure 4 is the RMSE index curve under the condition of ISR=10dB), the RMSE of the SAR image before and after interference suppression using only the WNF method and the method based on two-stage processing (i.e., WNF-GSVT-LRSD in the figure) can be obtained from the RMSE index curve. When only the WNF method is used for interference suppression, the RMSE decreases with The change is large, that is, the threshold selection has a great influence on the interference suppression result. However, after using this method to suppress interference, the RMSE is almost unchanged. This proves that the interference suppression performance of this method is robust to the selection of the notch threshold.

[0095] Likewise, Figure 5 As shown in the figure, the experiment compares the rank of the range spectrum before and after the WNF method when ISR=-10dB. In the measured data, if the interference signal energy is low, due to the presence of the ground echo signal, the range spectrum containing the interference signal does not necessarily meet the low rank condition, such as Figure 5 As shown in Figure 2, before the WNF method is processed, the rank is 956. After the WNF method is processed, the echo signal and the interference signal are initially separated. That is, the first interference signal distance spectrum only has the energy of the interference signal and a small amount of the echo signal. Figure 5 As shown, Rank=10 at this time, that is, the rank of the distance spectrum of the first interference signal is greatly reduced, which is closer to the ideal low-rank condition, which is beneficial to the application of the subsequent FGSVT-LRSD algorithm to a certain extent.

[0096] The experimental results above demonstrate that the method provided by the present invention has superior interference suppression performance compared to existing interference suppression methods. Compared to traditional interference suppression methods, the method provided by the present invention utilizes both the strength and low-rank characteristics of radio frequency interference, alleviating the difficulty of threshold selection in notch-based methods. It also facilitates the achievement of the low-rank conditions required by low-rank sparse decomposition methods, achieving precise separation of narrowband radio frequency interference and radar echoes.

[0097] In the several embodiments provided herein, it should be understood that the apparatus and method disclosed herein can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative. For example, the module division is merely a logical functional division. In actual implementation, other division methods may be used. For example, multiple modules or components may be combined or integrated into another system, or some features may be ignored or not implemented.

[0098] In addition, the functional modules in various embodiments of the present invention may be integrated into a single processing module, each module may exist physically separately, or two or more modules may be integrated into a single module. The aforementioned integrated modules may be implemented in the form of hardware or hardware plus software functional modules.

[0099] Yet another embodiment of the present invention provides a storage medium storing a computer program for executing the steps of the synthetic aperture radar radio frequency interference suppression method based on two-stage processing described in the above embodiment.

[0100] Another aspect of the present invention provides an electronic device comprising a memory and a processor, wherein the memory stores a computer program, and when the processor calls the computer program in the memory, it implements the steps of the synthetic aperture radar radio frequency interference suppression method based on two-stage processing as described in the above embodiment. Specifically, the above-mentioned integrated module implemented in the form of a software function module can be stored in a computer-readable storage medium. The above-mentioned software function module is stored in a storage medium and includes a number of instructions for causing an electronic device (which can be a personal computer, server, or network device, etc.) or a processor to perform some of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes various media that can store program code, such as a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk.

[0101] The above is further detailed description of the present application in combination with specific preferred embodiments, and cannot be deemed as limitation of the specific implementation of the present application to these descriptions. For those skilled in the art to which the present application belongs, without departing from the concept of the present application, a number of simple deductions or substitutions can be made, and all should be deemed as falling within the protection scope of the present application.

Claims

1. A method for suppressing radio frequency interference of synthetic aperture radar based on two-stage processing, characterized in that: include: Step 1: Acquire SAR single-view complex image data containing an interference signal, perform fast Fourier transform on the SAR single-view complex image data along the range dimension, and obtain a two-dimensional range spectrum in the range frequency domain and azimuth time domain; Step 2: Based on the wavelet decomposition algorithm and the interquartile range method, preliminarily extract the spectral components of the interference signal in the two-dimensional range spectrum to obtain a first interference signal range spectrum; Step 3: Based on the fast generalized singular value threshold low-rank sparse decomposition algorithm, the low-rank feature of the interference signal is utilized to separate the spectral component of the echo signal in the first interference signal distance spectrum from the first interference signal distance spectrum to obtain a second interference signal distance spectrum, where the spectral component of the echo signal in the second interference signal distance spectrum is lower than the spectral component of the echo signal in the first interference signal distance spectrum; Step 4: Obtain an interference-suppressed SAR single-view complex image based on the two-dimensional range spectrum and the second interference signal range spectrum.

2. The method for suppressing SAR radio frequency interference based on two-stage processing according to claim 1, characterized in that: The step 2 includes: Step 2.1: Perform the two-dimensional distance spectrum Order wavelet decomposition, get the wavelet coefficients of each order, where, ; Step 2.2: Based on the interquartile range method, identify and mark the wavelet coefficients exceeding the threshold, perform wavelet reconstruction on the wavelet coefficients exceeding the threshold, and obtain the first interference signal range spectrum.

3. The method for suppressing SAR radio frequency interference based on two-stage processing according to claim 2, characterized in that: The expression of wavelet coefficient is: in, is the wavelet coefficient, is the wavelet domain, is the orientation time axis, is the wavelet decomposition operator, is the two-dimensional distance spectrum, is the distance spectrum axis, is the absolute value operation, Position time axis Previous sampling points.

4. The method for suppressing SAR radio frequency interference based on two-stage processing according to claim 2, characterized in that: The performing wavelet reconstruction on the wavelet coefficients exceeding the threshold to obtain the first interference signal range spectrum includes: calculating the phase of the two-dimensional range spectrum; Performing wavelet reconstruction on the wavelet coefficients exceeding the threshold to obtain the amplitude of the first interference signal range spectrum; The first interference signal range spectrum is obtained based on the phase of the two-dimensional range spectrum and the amplitude of the first interference signal range spectrum.

5. The method for suppressing SAR radio frequency interference based on two-stage processing according to claim 4, characterized in that: The expression of the amplitude of the first interference signal distance spectrum is: in, is the amplitude of the first interference signal distance spectrum, is the orientation time axis, is the distance spectrum axis, is the wavelet reconstruction operator, is the wavelet coefficient exceeding the threshold, is the wavelet domain, is the absolute value operation, Position time axis Previous sampling points; The expression of the first interference signal distance spectrum is: in, is the first interference signal distance spectrum, is the dot multiplication operation, is the phase of the two-dimensional range spectrum, Is an imaginary unit.

6. The method for suppressing SAR radio frequency interference based on two-stage processing according to claim 1, characterized in that: The step 3 comprises: Step 3.1: constructing a first model of a fast generalized singular value threshold low-rank sparse decomposition algorithm based on the first interference signal distance spectrum, and converting the first model into an augmented Lagrangian function; Step 3.2: Construct a generalized singular value threshold operator; Step 3.3: Based on the generalized singular value threshold operator and the random projection singular value decomposition algorithm, the augmented Lagrangian function is iteratively solved using the low-rank characteristics of the interference signal, and a low-rank matrix of the distance spectrum of the first interference signal is obtained after each iterative solution, where the low-rank matrix is ​​a matrix containing the interference signal; Step 3.4: When the number of iterations is equal to or greater than the iteration threshold, the iteration is stopped, and the low-rank matrix solved by the last iteration is determined as the second interference signal range spectrum.

7. The method for suppressing SAR radio frequency interference based on two-stage processing according to claim 6, characterized in that: The expression of the first model is: Among them, the constraints of the first model are , is the first interference signal distance spectrum, is the low-rank matrix, is a sparse matrix, wherein the sparse matrix is ​​a matrix containing echo signals, is the number of singular values, Indicates the singular values, is a non-convex surrogate function, To obtain all the singular values ​​of a matrix, is a hyperparameter, is a sparse matrix The L1 norm of The expression of the augmented Lagrangian function is: in, is the augmented Lagrangian function, is a hyperparameter, is the Lagrange multiplier, is the inner product operation, for and Different norm.

8. The method for suppressing SAR radio frequency interference based on two-stage processing according to claim 6, characterized in that: The expression of the generalized singular value threshold operator is: in, is the generalized singular value threshold operator, Indicates calculation The operation of the corresponding variable value when taking the minimum value, is any non-convex surrogate function, is a variable, is a matrix No. singular values, For the The sparse matrix after iterations is For the The Lagrange multiplier after iterations is, For the Hyperparameters after iterations.

9. The method for suppressing SAR radio frequency interference based on two-stage processing according to claim 1, characterized in that: The step 4 comprises: Step 4.1: Subtracting the second range spectrum from the two-dimensional range spectrum to obtain an interference-suppressed range spectrum; Step 4.2: Performing a fast inverse Fourier transform on the interference-suppressed range spectrum along the range dimension to obtain the interference-suppressed SAR single-view complex image.

10. A storage medium storing a computer program, wherein: The computer program is used to execute the steps of the synthetic aperture radar radio frequency interference suppression method based on two-stage processing according to any one of claims 1 to 9.

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