A method for suppressing inter-satellite interference based on low-rank recovery of sub-band spectrum

Abstract

The present invention discloses an inter-satellite interference suppression method based on sub-band spectrum low-rank recovery, comprising: performing FFT on a single-view complex image along a distance dimension; calculating the kurtosis of sampling points in each distance dimension to determine whether there is interference at the sampling point; dividing a maximum interference-free sub-band spectrum from the center into two interference-free sub-band spectra, and dividing a representation matrix into multiple sub-band spectra, and then performing IFFT along the distance dimension to obtain a corresponding time domain image; straightening and splicing the time domain image of the sub-band spectrum with interference and the time domain images of the two interference-free sub-band spectra, constructing a data set matrix and solving to obtain an interference-free data set, and then reconstructing them into a sub-band spectrum time domain image, thereby obtaining an interference-free time domain image obtained after the sub-band spectrum with interference is reconstructed; replacing the corresponding interference-free sub-band spectrum in the representation matrix with the sub-band spectrum after performing FFT on the interference-free time domain image along the distance dimension; performing IFFT on the replaced representation matrix along the distance dimension to obtain a suppressed single-view complex image.

Description

Technical Field

[0001] The present invention relates to the field of radar signal processing, and in particular to an inter-satellite interference suppression method based on sub-band spectrum low-rank recovery. Background Art

[0002] Intersatellite interference (IS) is a special type of ground-scattered interference, originating from satellite-based platforms operating in the same band. When time, space, and frequency synchronization are achieved, the victim satellite will receive the ground-scattered signal from the interfering satellite. Because the parameters of the signals transmitted by other satellite-based platforms in the same band are similar to those of the victim satellite's return signal, IIS manifests as weak, broadband interference, making it difficult to remove.

[0003] Traditional methods based on principal component analysis (PCA) or robust PCA are difficult to remove due to the weak energy of intersatellite interference. While methods based on subband spectral cancellation can suppress intersatellite interference to a certain extent, their essence is to cancel out interfering images with and without resolution loss, resulting in some loss of high-frequency details. Summary of the Invention

[0004] The purpose of the present invention is to provide an inter-satellite interference suppression method based on sub-band spectrum low-rank recovery. By utilizing the range spectrum sub-band division and replacing the incoherent subtraction step of the sub-band spectrum cancellation method with a low-rank representation (LRR), the inter-satellite interference can be suppressed while protecting the high-frequency details of the image.

[0005] In order to achieve the above tasks, the present invention adopts the following technical solutions:

[0006] A method for suppressing inter-satellite interference based on sub-band spectrum low-rank recovery, comprising:

[0007] Perform Fourier transform on the single-view complex image along the range dimension to obtain the image representation matrix in the range frequency domain and azimuth time domain;

[0008] Calculating the kurtosis of each distance dimension sampling point in the representation matrix, and judging whether the distance dimension sampling point has interference based on the relationship between the kurtosis and the threshold; determining the maximum interference-free subband spectrum corresponding to all interference-free distance dimension sampling points;

[0009] Dividing the maximum non-interference sub-band spectrum into two non-interference sub-band spectra from the center, and dividing the portion of the characterization matrix other than the two non-interference sub-band spectra into multiple sub-band spectra;

[0010] Performing inverse Fourier transform on the multiple sub-band spectra and the two non-interference sub-band spectra along the distance dimension to obtain corresponding time domain images;

[0011] For the time domain images of the multiple sub-band spectra, determine whether there is interference at the distance sampling point within the frequency band of each time domain image. If no interference exists, no processing is performed; otherwise, it is considered that the corresponding sub-band spectrum has interference; the time domain image of the sub-band spectrum with interference and the time domain images of the two non-interference sub-band spectra are straightened and spliced ​​to construct a data set matrix;

[0012] The dataset matrix itself is used as a dictionary to perform low-rank approximation and obtain the spliced ​​interference-free dataset;

[0013] Performing the inverse operations of straightening and splicing on the interference-free data set to reconstruct it into a sub-band spectrum time domain image, thereby obtaining an interference-free time domain image obtained by reconstructing the sub-band spectrum with interference;

[0014] Sub-band spectra obtained by Fourier transforming the interference-free time domain image along the distance dimension are used to replace the corresponding sub-band spectra with interference in the representation matrix;

[0015] An inverse Fourier transform is performed on the replaced representation matrix along the distance dimension to obtain the suppressed single-view complex image.

[0016] Furthermore, the single-view complex image is subjected to Fourier transform along the range dimension to obtain a representation matrix of the image in the range frequency domain and the azimuth time domain, which is expressed as:

[0017]

[0018] The representation matrix represents the single-view complex image SLC, τ is the fast time of the distance dimension, t is the slow time of the azimuth dimension, e is a natural constant, j is an imaginary unit, f is the distance frequency, The number of sampling points in the orientation dimension of the matrix is ​​N a , the number of sampling points in the distance dimension is N r , Represents complex space.

[0019] Furthermore, the calculating of the kurtosis of each distance dimension sampling point in the characterization matrix and judging whether there is interference at the distance dimension sampling point based on the relationship between the kurtosis and a threshold value includes:

[0020] Calculate N in the representation matrix X(f,t) respectively r distance dimension sampling points f i The kurtosis K i :

[0021]

[0022] Among them, Re[·] represents the real part of the complex number, μ i Represents the i-th distance dimension sampling point f i The mean ofi Indicates the i-th distance frequency point f i The standard deviation of

[0023] If K i is greater than the threshold, then the distance dimension sampling point f i There is interference; if it is less than or equal to the threshold, there is no interference at the distance dimension sampling point.

[0024] Furthermore, the maximum interference-free subband spectrum corresponding to all interference-free distance dimension sampling points is determined, including:

[0025] Count the maximum spectrum width occupied by all interference-free distance dimension sampling points. The frequency band where the maximum spectrum width is located is considered to be the maximum interference-free sub-band spectrum X CLEAR (f, t), the corresponding distance dimension sampling points N B .

[0026] Furthermore, the dividing the maximum non-interference sub-band spectrum into two non-interference sub-band spectra from the center, and dividing the portion of the characterization matrix other than the two non-interference sub-band spectra into multiple sub-band spectra, includes:

[0027] X CLEAR (f,t)=[X CLEAR1 (f,t),X CLEAR2 (f,t)]

[0028] Where each interference-free subband spectrum X CLEAR1 (f,t),X CLEAR2 (f, t) is the number of sampling points in the azimuth dimension, N a , the number of sampling points in the distance dimension is Matrix of

[0029] According to the number of sampling points in the distance dimension Divide the representation matrix X(f,t) into N+2 sub-band spectra, that is, 2 interference-free sub-band spectra X CLEAR1 (f,t),X CLEAR2 (f, t) and other N sub-band spectra to be processed are expressed as:

[0030] X(f,t)=[X1(f,t),...,X j-1 (f,t),X CLEAR1 (f,t),X CLEAR2 (f,t),X j (f,t),...,X N (f,t)]

[0031] Among them, 1<j≤N and The subband spectrum to be processed X1(f,t) and X N The number of sampling points in the azimuth dimension of (f, t) is Na , the number of sampling points in the distance dimension is The other N-2 subbands X2(f,t),...X N-1 The number of sampling points in the azimuth dimension of (f, t) is N a , the number of sampling points in the distance dimension is

[0032] Furthermore, performing inverse Fourier transform on the multiple sub-band spectra and the two non-interference sub-band spectra along the distance dimension to obtain corresponding time domain images includes:

[0033] The number of sampling points for the distance dimension is The N sub-band spectra X2(f,t),…,X CLEAR1 (f,t),X CLEAR2 (f,t),...,X N-1 (f, t) performs inverse Fourier transform along the distance dimension to obtain the sub-band spectrum time domain image X2(τ, t),...,X N-1 (τ, t) and interference-free subband spectrum time domain image X CLEAR1 (τ,t),X CLEAR2 (τ,t).

[0034] Furthermore, for the time domain images of the multiple sub-band spectra, it is determined whether there is interference at the distance sampling point within the frequency band of each time domain image. If no interference exists, no processing is performed; otherwise, it is considered that the corresponding sub-band spectrum has interference; the time domain image of the sub-band spectrum with interference and the time domain images of the two non-interference sub-band spectra are straightened and spliced ​​to construct a data set matrix, including:

[0035] For the sub-band spectrum time domain image X to be processed j (τ, t), where j = 2, ...., N-1; the relationship between the kurtosis and the threshold is used to determine whether there is interference at the distance dimension sampling point within the frequency band. If there is no interference, no processing is performed, otherwise it is considered that X j The subband spectrum X corresponding to (τ, t) j (f, t) has interference; at this time, X j (τ, t) and two interference-free sub-band spectral time domain images X CLEAR1 (τ,t),X CLEAR2 (τ, t) are straightened into one dimension and then spliced ​​to obtain the data set matrix X.

[0036] Furthermore, the straightening operation is to take each column of data in the image matrix as a unit and reconnect the units in order according to the column order to form a new one-dimensional matrix; the splicing operation is to reconnect the stretched X j (τ,t) as the first column, the stretched X CLEAR1 (τ,t),X CLEAR2(τ, t) as the second and third columns to form the data set matrix X.

[0037] Furthermore, the low-rank approximation solution is performed using the dataset matrix itself as a dictionary to obtain a spliced ​​interference-free dataset, including:

[0038] The ADMM algorithm is used to solve the interference-free data set; the problem to be solved is expressed as:

[0039]

[0040] in, is a low-rank matrix, represents the noise matrix, λ represents the Lagrange multiplier, ‖·|| * represents the nuclear norm, ||·|| 2，1 Indicates L 2，1 norm.

[0041] Furthermore, the interference-free data set is subjected to an inverse operation of straightening and splicing to reconstruct the interference-free data set into a sub-band spectrum time domain image, thereby obtaining an interference-free time domain image obtained by reconstructing the sub-band spectrum with interference, including:

[0042] The interference-free dataset XZ is straightened and spliced ​​inversely and reconstructed into three sub-band spectral time domain images [L j (τ,t),L CLEAR1 (τ,t),L CLEAR2 (τ, t)], thus obtaining the sub-band spectrum X with interference j The interference-free time domain image L obtained after (τ,t) is reconstructed j (τ,t); at the same time, for L j (τ, t) performs Fourier transform along the distance dimension to obtain the subband spectrum L j (f, t), replace the corresponding sub-band spectrum with interference X j (f,t).

[0043] A terminal device includes a processor, a memory, and a computer program stored in the memory; when the processor is executed by a computer, the inter-satellite interference suppression method based on sub-band spectrum low-rank recovery is implemented.

[0044] A computer-readable storage medium stores a computer program; when the computer program is executed by a processor, the inter-satellite interference suppression method based on sub-band spectrum low-rank recovery is implemented.

[0045] Compared with the prior art, the present invention has the following technical features:

[0046] This method innovatively exploits the fact that intersatellite interference (ISI) does not cover the entire frequency band to construct a model that satisfies low-rank recovery requirements. By using a low-rank representation of the subband spectrum, it effectively avoids the loss of high-frequency detail caused by traditional subband spectrum cancellation methods. Furthermore, this method can effectively remove broadband ISI from single-look complex images (SLCs), significantly improving image quality. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 It is a flow chart of an embodiment of the present invention;

[0048] Figure 2 (a) is the original interference image in the embodiment of the present invention; (b) is the time domain image with interference sub-band spectrum after sub-band spectrum division of (a); (c) is the time domain image without interference sub-band spectrum after sub-band spectrum division of (a); (d) is the inter-satellite interference suppression result of traditional sub-band spectrum cancellation; (e) is the result after inter-satellite interference suppression in the embodiment. DETAILED DESCRIPTION

[0049] Referring to the accompanying drawings, the present invention provides an inter-satellite interference suppression method based on low-rank recovery of sub-band spectra. This method is based on the characteristics of inter-satellite interference that do not have full-band coverage and the fact that the satellite models in the same band are known. Therefore, the interference-free sub-band is determined according to the signal parameters; then, the range spectrum is divided into equal intervals according to the number of points occupied by the interference-free sub-band spectrum bandwidth. At the same time, the interference-free sub-band spectrum is used as a dictionary to make a low-rank representation of the interfered sub-band spectrum to reconstruct an interference-free sub-band image with loss of high-frequency details; finally, through sub-band spectrum reconstruction, the original image without interference and loss of high-frequency details can be obtained.

[0050] The technical solution of the present invention comprises the following steps:

[0051] Step 1: Perform Fourier transform on the single-view complex image SLC along the range dimension to obtain the image representation matrix in the range frequency domain-azimuth time domain

[0052]

[0053] in represents the single-view complex image SLC, τ is the fast time of the distance dimension, t is the slow time of the azimuth dimension, e is a natural constant, j is an imaginary unit, f is the distance frequency, The number of sampling points in the orientation dimension of the matrix is ​​N a , the number of sampling points in the distance dimension is N r , The SLC image has two dimensions, where the azimuth dimension is consistent with the tangential velocity of the aircraft or satellite, and the range dimension is consistent with the radial velocity of the aircraft or satellite.

[0054] Step 2: Calculate the N in the representation matrix X(f,t) respectively. r distance dimension sampling points f i The kurtosis K i , the kurtosis of a single frequency point is calculated by the following formula:

[0055]

[0056] Among them, Re[·] represents the real part of the complex number, μ i Represents the i-th distance dimension sampling point f i The mean of i Indicates the i-th distance frequency point f i The standard deviation of .

[0057] Step 3, according to the kurtosis K i The relationship with the threshold is used to determine the distance dimension sampling point f i Is there any interference?

[0058] If the kurtosis K i is greater than the threshold 3, indicating that the distance dimension sampling point f i There is interference; if it is less than or equal to the threshold 3, it means that there is no interference at the distance dimension sampling point; finally, the maximum spectrum width occupied by all interference-free distance dimension sampling points is counted, and the frequency band where the maximum spectrum width is located is considered to be the maximum interference-free sub-band spectrum X CLEAR (f, t), the corresponding distance dimension sampling points N B .

[0059] Step 4: Divide the maximum interference-free sub-band spectrum into two interference-free sub-band spectra from the center, namely:

[0060] X CLEAR (f,t)=[X CLEAR1 (f,t),X CLEAR2 (f,t)]

[0061] Each interference-free subband spectrum is the azimuth dimension with N sampling points. a , the number of sampling points in the distance dimension is The matrix of .

[0062] Step 5: Sampling points according to distance dimension Divide the representation matrix X(f,t) into N+2 sub-band spectra, that is, 2 interference-free sub-band spectra X CLEAR1 (f,t),X CLEAR2 (f, t) and other N sub-band spectra to be processed; the process can be expressed as:

[0063] X(f,t)=[X1(f,t),...,X j-1 (f,t),XCLEAR1 (f,t),X CLEAR2 (f,t),X j (f,t),...,X N (f,t)]

[0064] Among them, 1<j≤N and The subband spectrum to be processed X1(f,t) and X N The number of sampling points in the azimuth dimension of (f, t) is N a , the number of sampling points in the distance dimension is The other N-2 subbands X2(f,t),...X N-1 The number of sampling points in the azimuth dimension of (f, t) is N a , the number of sampling points in the distance dimension is

[0065] Step 6: The number of sampling points in the distance dimension in step 5 is The N sub-band spectra X2(f,t),...,X CLEAR1 (f,t),X CLEAR2 (f,t),...,X N-1 (f, t) performs inverse Fourier transform along the distance dimension to obtain the sub-band spectrum time domain image X2(τ, t),...,X N-1 (τ, t) and interference-free subband spectrum time domain image X CLEAR1 (τ,t),X CLEAR2 (τ,t).

[0066] Step 7: Take the sub-band spectrum time domain image X to be processed in step 6 j (τ, t), where j = 2, ...., N-1; according to the method in step 3, determine whether there is interference at the distance dimension sampling point within the frequency band. If there is no interference, no processing is performed. Otherwise, it is considered that X j (τ, t) corresponds to the subband spectrum X in the representation matrix X(f, t) after division j (f, t) has interference, then X j (τ, t) and two interference-free sub-band spectral time domain images X CLEAR1 (τ,t),X CLEAR2 (τ, t) are straightened into one dimension and then spliced ​​to obtain the data set matrix Since the sub-band spectral time domain image becomes a one-dimensional vector after the straightening operation, the dataset matrix formed after splicing is a two-dimensional matrix.

[0067] The straightening operation is to take each column of data in the image matrix as a unit and reconnect the units in order according to the column order to form a new one-dimensional matrix. The specific expression is as follows:

[0068]

[0069]

[0070] The splicing operation is to stretch the X j (τ,t) as the first column, the stretched X CLEAR1 (τ,t),X CLEAR2 (τ, t) as the second and third columns to form the data set matrix X; the specific expression is as follows:

[0071]

[0072] Step 8: Select the dataset X obtained in step 7 as the dictionary to perform low-rank approximation to obtain the concatenated interference-free dataset XZ.

[0073] The ADMM algorithm can be used to quickly solve the optimization problem:

[0074]

[0075] in, is a low-rank matrix, represents the noise matrix, λ represents the Lagrange multiplier, ||·|| * represents the nuclear norm, ||·|| 2，1 Indicates L 2，1 norm, ||·|| F represents the F-norm.

[0076] This problem can be solved by performing k iterations of the ADMM algorithm, and the concatenated interference-free dataset XZ can be obtained, where the parameter superscript k represents the parameter at the kth iteration; specifically, it can be expressed as:

[0077] 1) The optimization target Z is replaced by the process variable J:

[0078]

[0079] 2) Construct augmented Lagrangian function:

[0080]

[0081] Where tr[·] represents the trace of the matrix, represents the Lagrange multiplier, and μ represents the penalty parameter.

[0082] 3) Keep other variables unchanged and update J:

[0083]

[0084] 4) Keep other variables unchanged and update Z:

[0085]

[0086] where X H Represents the conjugate transposed matrix of X.

[0087] 5) Keep other variables unchanged and update E:

[0088]

[0089] 6) Update the Lagrange multiplier:

[0090]

[0091] 7) Update the penalty parameter μ:

[0092] μ k+1 =min(ρμ k ,max u )

[0093] Where min(ρμ k ,max u ) means taking ρμ k and max u The minimum number between 0<ρ<1 is a constant, max u It is a positive number that is set first.

[0094] 8) Check the convergence conditions; the algorithm stops iterating when the maximum number of iterations is reached or the following stopping conditions are met.

[0095] ‖X-XZ k+1 -E k+1 ‖ ∞ <εand‖Z k+1 -J k+1 ‖ ∞ <ε

[0096] Where ε>0 represents the error coefficient.

[0097] Step 9: Perform the inverse operations of straightening and splicing described in step 7 on the interference-free dataset XZ obtained in step 8 to reconstruct it into three sub-band spectral time domain images [L j (τ,t),L CLEAR1 (τ,t),L CLEAR2 (τ,t)], where L CLEAR1 (τ,t),L CLEAR2 (τ,t) is the interference-free subband spectrum time domain image X CLEAR1 (τ,t),X CLEAR2 (τ, t) reconstructs the image; thus obtaining the sub-band spectrum X with interference j The interference-free time domain image L obtained after (τ,t) is reconstructedj (τ,t); at the same time, for L j (τ, t) performs Fourier transform along the distance dimension to obtain the subband spectrum L j (f, t), replace the corresponding interfered subband spectrum X in step 5 j (f,t).

[0098] The inverse operations of straightening and splicing can be specifically expressed as follows:

[0099]

[0100]

[0101]

[0102] Step 10: perform steps 7 to 9 on the remaining sub-band spectral time domain images to be processed in step 6; that is, for the sub-band spectral time domain image X to be processed j (τ, t), if it is determined that there is no interference, no replacement operation is performed; if there is interference, a reconstruction process is required to determine the corresponding reconstructed subband spectrum L j (τ, t), and replace the corresponding sub-band spectrum with interference in the representation matrix X(f, t) after the sub-band spectrum is divided in step 5. The process can be expressed as:

[0103] L(f,t)=[X1(f,t),...,L j-1 (f,t),X CLEAR1 (f,t),X CLEAR2 (f,t),L j (f,t),...,X N (f,t)]

[0104] Finally, the spectrum L(f, t) is inversely Fourier transformed along the range dimension to obtain the suppressed single-view complex image L(τ, t).

[0105] See attached Figure 1 , a flow chart of an embodiment of the present invention; first, perform range-dimensional FFT and sub-band spectrum division on the interfered image, and then obtain the corresponding sub-band spectrum time domain image through range-dimensional IFFT. A data set consisting of one interfered sub-band spectrum time domain image and two non-interferenced sub-band spectrum time domain images is selected to perform the LRR algorithm to obtain three sub-band spectrum low-rank images after interference suppression. Then, perform range-dimensional FFT on the sub-band spectrum image without interference after suppression to replace the original sub-band spectrum region with interference. After executing N-2 times in sequence, the range-frequency-azimuth-time domain map of the non-interference SLC image is obtained. Finally, perform range-dimensional IFFT on the range-frequency-azimuth-time domain map to obtain the SLC image after interference suppression.

[0106] Example:

[0107] Step 1: Image the SLC Perform Fourier transform along the distance dimension to obtain the image representation matrix in the range frequency domain-azimuth time domain

[0108]

[0109] Where τ is the range fast time, η is the azimuth slow time, and f is the range frequency, The number of sampling points in the orientation dimension of the representation matrix is ​​1500, and the number of sampling points in the distance dimension is 24912.

[0110] Step 2: Calculate the 24912 distance frequency sampling points in X(f,t) respectively The kurtosis K i , the kurtosis of a single frequency point is calculated by the following formula:

[0111]

[0112] Where Re[·] represents the real part of a complex number. i Indicates the i-th distance frequency point f i The mean of i Indicates the i-th distance frequency point f i The standard deviation of .

[0113] Step 3, according to the kurtosis K i Is it greater than 3 to determine the frequency f i Is there interference? If it is greater than 3, it means that there is interference at this frequency point. If it is less than or equal to 3, it means that there is no interference at this frequency point. Finally, all the interference-free frequencies and the maximum spectrum width occupied by the interference-free frequencies are counted. The frequency band where the latter is located is considered to be the maximum interference-free sub-band spectrum X CLEAR (f, t), the corresponding number of sampling points is 8192.

[0114] Step 4: Divide the maximum interference-free sub-band spectrum into two clean sub-bands from the center, namely

[0115] X CLEAR (f,t)=[X CLEAR1 (f,t),X CLEAR2 (f,t)]

[0116] Each clean subband is a matrix with 1500 sampling points in the orientation dimension and 4096 sampling points in the distance dimension.

[0117] Step 5: Divide the representation matrix X(f,t) into 8 sub-band spectra according to the number of sampling points 4096, namely 2 clean sub-bands X CLEAR1 (f,t),XCLEAR2 (f, t) and the other 6 sub-bands to be processed, the process can be expressed as:

[0118] X(f,t)=[X1(f,t),X CLEAR (f, t), X2(f, t), X3(f, t), X4(f, t), X5(f, t), X6(f, t)] where 1<j≤6 and 0<168≤4096. Subband matrix and The number of sampling points in the azimuth dimension is 1500, and the number of sampling points in the distance dimension is 168. The other four subband matrices The number of sampling points in the orientation dimension is 1500, and the number of sampling points in the distance dimension is 4096.

[0119] Step 6: respectively perform the 6 sub-band spectra with 4096 sampling points in the distance dimension in step 5.

[0120] and Perform inverse Fourier transform along the distance dimension to obtain the sub-band spectrum time domain images to be processed X2(τ,t), X3(τ,t), X4(τ,t), X5(τ,t) and the interference-free sub-band spectrum time domain image X CLEAR1 (τ,t),X CLEAR2 (τ,t).

[0121] Step 7: Take the time domain image X2(τ,t) of the sub-band spectrum to be processed in step 6, and determine the frequency point f within its frequency band according to step 3. i There is interference. X2(τ,t) will be combined with the two non-interference sub-band spectrum time domain images X CLEAR1 (τ,t),X CLEAR2 (τ, t) is straightened and spliced ​​to obtain the data set

[0122] Step 8: Select the dataset X obtained in step 7 as the dictionary for low-rank approximation. ADMM can be used to quickly solve the optimization problem:

[0123]

[0124] in, is a low-rank matrix, represents the noise matrix, λ represents the Lagrange multiplier, ||·|| * represents the nuclear norm, ||·|| 2，1 Indicates L 2，1 norm.

[0125] This problem can be solved by performing 122 iterations of the ADMM algorithm, and the concatenated interference-free dataset XZ can be obtained, which can be specifically expressed as:

[0126] Initialize variables, λ = 0.001, μ = 0.001, ρ = 1.1, max u =10000, maximum number of iterations is 1000.

[0127] 1) The optimization target Z is replaced by J.

[0128]

[0129] 2) Construct the augmented Lagrangian function.

[0130]

[0131] Where tr[·] represents the trace of the matrix

[0132] 3) Keep other variables unchanged and update J.

[0133]

[0134] 4) Keep other variables unchanged and update Z.

[0135]

[0136] where X H Represents the conjugate transposed matrix of X.

[0137] 5) Keep other variables unchanged and update E.

[0138]

[0139] 6) Update the Lagrange multiplier.

[0140]

[0141] 7) Update the penalty parameter μ.

[0142] μ k+1 =min(ρμ k ,max u )

[0143] Where min(ρμ k ,max u ) means taking ρμ k and max u The minimum number between .

[0144] 8) Check convergence conditions. The algorithm stops iterating when the maximum number of iterations is reached or the following stop conditions are met.

[0145] ‖X-XZ k+1 -E k+1 ‖∞ <εand‖Z k+1 -J k+1 ‖ ∞ <ε

[0146] Where ε = 0.000001, which represents the error coefficient.

[0147] Step 9: Perform the inverse straightening and splicing operations of step 7 on the interference-free dataset XZ obtained in step 8 to reconstruct it into a 3-subband spectral time domain image [L2(τ,t),L CLEAR1 (τ,t),L CLEAR2 (τ, t)]; at the same time, Fourier transform is performed on L2(τ, t) along the distance direction to obtain the sub-band spectrum L2(f, t), which replaces the original interfered sub-band spectrum time domain image X2(f, t).

[0148] Step 10: Perform steps 7 to 9 on the remaining sub-band spectral time domain images to be processed in step 1, and replace the corresponding interfering frequency bands in the representation matrix X(f, t) shown in step 5. This process can be expressed as:

[0149] L(f,t)=[X1(f,t),X CLEAR (f,t),L2(f,t),L3(f,t),X4(f,t),X5(f,t),X6(f,t)]

[0150] Finally, the spectrum L(f, t) is inversely Fourier transformed along the distance direction to obtain the suppressed image L(τ, t), see Appendix Figure 2 ; Among them, the area within the box in (a) is inter-satellite interference; it can be seen that the interference on (a) has been completely removed in (d).

[0151] The above embodiments are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. These modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present application, and should all be included in the scope of protection of the present application.

Claims

1. A method for suppressing inter-satellite interference based on sub-band spectrum low-rank recovery, characterized in that: include: Perform Fourier transform on the single-view complex image along the range dimension to obtain the image representation matrix in the range frequency domain and azimuth time domain; Calculating the kurtosis of each distance dimension sampling point in the representation matrix, and judging whether there is interference at the distance dimension sampling point based on the relationship between the kurtosis and the threshold; Determine the maximum interference-free subband spectrum corresponding to all interference-free distance dimension sampling points; Dividing the maximum non-interference sub-band spectrum into two non-interference sub-band spectra from the center, and dividing the portion of the characterization matrix other than the two non-interference sub-band spectra into multiple sub-band spectra; Performing inverse Fourier transform on the multiple sub-band spectra and the two non-interference sub-band spectra along the distance dimension to obtain corresponding time domain images; For the time domain images of the multiple sub-band spectra, determine whether there is interference at the distance sampling point within each time domain image frequency band; if no interference exists, no processing is performed; otherwise, it is considered that the corresponding sub-band spectrum has interference; The time domain image of the sub-band spectrum with interference and the time domain images of the two sub-band spectrums without interference are straightened and spliced ​​to construct a data set matrix; The dataset matrix itself is used as a dictionary to perform low-rank approximation and obtain the spliced ​​interference-free dataset; Performing the inverse operations of straightening and splicing on the interference-free data set to reconstruct it into a sub-band spectrum time domain image, thereby obtaining an interference-free time domain image obtained by reconstructing the sub-band spectrum with interference; Sub-band spectra obtained by Fourier transforming the interference-free time domain image along the distance dimension are used to replace the corresponding sub-band spectra with interference in the representation matrix; An inverse Fourier transform is performed on the replaced representation matrix along the distance dimension to obtain the suppressed single-view complex image.

2. The inter-satellite interference suppression method based on sub-band spectrum low-rank recovery according to claim 1, characterized in that: The Fourier transform is performed on the single-view complex image along the range dimension to obtain the image representation matrix in the range frequency domain-azimuth time domain, which is expressed as: The representation matrix represents the single-view complex image SLC, τ is the fast time of the distance dimension, t is the slow time of the azimuth dimension, e is a natural constant, j is an imaginary unit, f is the distance frequency, The number of sampling points in the orientation dimension of the matrix is ​​N a , the number of sampling points in the distance dimension is N r , Represents complex space.

3. The inter-satellite interference suppression method based on sub-band spectrum low-rank recovery according to claim 1, characterized in that: The calculating of the kurtosis of each distance dimension sampling point in the characterization matrix and judging whether there is interference at the distance dimension sampling point according to the relationship between the kurtosis and the threshold value comprises: Calculate N in the representation matrix X(f,t) respectively r distance dimension sampling points f i The kurtosis K i : Among them, Re[·] represents the real part of the complex number, μ i Represents the i-th distance dimension sampling point f i The mean of i Indicates the i-th distance frequency point f i The standard deviation of If K i is greater than the threshold, then the distance dimension sampling point f i There is interference; if it is less than or equal to the threshold, there is no interference at the distance dimension sampling point.

4. The inter-satellite interference suppression method based on sub-band spectrum low-rank recovery according to claim 1, characterized in that: Determine the maximum interference-free subband spectrum corresponding to all interference-free distance dimension sampling points, including: Count the maximum spectrum width occupied by all interference-free distance dimension sampling points. The frequency band where the maximum spectrum width is located is considered to be the maximum interference-free sub-band spectrum X CLEAR (f, t), the corresponding distance dimension sampling points N B .

5. The inter-satellite interference suppression method based on sub-band spectrum low-rank recovery according to claim 1, characterized in that: The step of dividing the maximum non-interference sub-band spectrum into two non-interference sub-band spectrums from the center, and dividing the portion of the characterization matrix other than the two non-interference sub-band spectrums into a plurality of sub-band spectrums includes: X CLEAR (f,t)=[X CLEAR1 (f,t),X CLEAR2 (f,t)] Where each interference-free subband spectrum X CLEAR1 (f,t),X CLEAR2 (f, t) is the number of sampling points in the azimuth dimension, N a , the number of sampling points in the distance dimension is Matrix of According to the number of sampling points in the distance dimension Divide the representation matrix X(f,t) into N+2 sub-band spectra, that is, 2 interference-free sub-band spectra X CLEAR1 (f,t),X CLEAR2 (f, t) and other N sub-band spectra to be processed are expressed as: X(f,t)=[X1(f,t),...,X j-1 (f,t),X CLEAR1 (f,t),X CLEAR2 (f,t),X j (f,t),...,X N (f,t)] Among them, 1<j≤N and The subband spectrum to be processed X1(f,t) and X N The number of sampling points in the azimuth dimension of (f, t) is N a , the number of sampling points in the distance dimension is The other N-2 subbands X2(f,t),...X N-1 The number of sampling points in the azimuth dimension of (f, t) is N a , the number of sampling points in the distance dimension is 6. The inter-satellite interference suppression method based on sub-band spectrum low-rank recovery according to claim 1, characterized in that: Performing an inverse Fourier transform on the multiple sub-band spectra and the two non-interference sub-band spectra along the distance dimension to obtain corresponding time domain images, including: The number of sampling points for the distance dimension is The N sub-band spectra X2(f,t),...,X CLEAR1 (f,t),X CLEAR2 (f,t),...,X N-1 (f, t) performs inverse Fourier transform along the distance dimension to obtain the sub-band spectrum time domain image X2(τ, t),...,X N-1 (τ, t) and interference-free subband spectrum time domain image X CLEAR1 (τ,t),X CLEAR2 (τ,t).

7. The inter-satellite interference suppression method based on sub-band spectrum low-rank recovery according to claim 1, characterized in that: For the time domain images of the multiple sub-band spectra, determine whether there is interference at the distance sampling point within each time domain image frequency band; if no interference exists, no processing is performed; otherwise, it is considered that the corresponding sub-band spectrum has interference; The time domain image of the sub-band spectrum with interference and the time domain images of the two sub-band spectrums without interference are straightened and spliced ​​to construct a data set matrix, including: For the sub-band spectrum time domain image X to be processed j (τ, t), where j = 2, ...., N-1; the relationship between the kurtosis and the threshold is used to determine whether there is interference at the distance dimension sampling point within the frequency band. If there is no interference, no processing is performed, otherwise it is considered that X j The subband spectrum X corresponding to (τ, t) j (f, t) has interference; at this time, X j (τ, t) and two interference-free sub-band spectral time domain images X CLEAR1 (τ,t),X CLEAR2 (τ, t) are straightened into one dimension and then spliced ​​to obtain the data set matrix X.

8. The inter-satellite interference suppression method based on sub-band spectrum low-rank recovery according to claim 1, characterized in that: The straightening operation is to take each column of data in the image matrix as a unit and reconnect the units in order according to the column order to form a new one-dimensional matrix; the splicing operation is to connect the stretched X j (τ,t) as the first column, the stretched X CLEAR1 (τ,t),X CLEAR2 (τ, t) as the second and third columns to form the data set matrix X.

9. The inter-satellite interference suppression method based on sub-band spectrum low-rank recovery according to claim 1, characterized in that: The low-rank approximation solution is performed using the dataset matrix itself as a dictionary to obtain a spliced ​​interference-free dataset, including: The ADMM algorithm is used to solve the interference-free data set; the problem to be solved is expressed as: in, is a low-rank matrix, represents the noise matrix, λ represents the Lagrange multiplier, ||·|| * represents the nuclear norm, ||·|| 2，1 Indicates L 2，1 norm.

10. The inter-satellite interference suppression method based on sub-band spectrum low-rank recovery according to claim 1, characterized in that: Performing the inverse operations of straightening and splicing on the interference-free data set to reconstruct it into a sub-band spectrum time domain image, thereby obtaining an interference-free time domain image obtained by reconstructing the sub-band spectrum with interference, including: The interference-free dataset XZ is straightened and spliced ​​inversely and reconstructed into three sub-band spectral time domain images [L j (τ,t),L CLEAR1 (τ,t),L CLEAR2 (τ, t)], thus obtaining the sub-band spectrum X with interference j The interference-free time domain image L obtained after (τ,t) is reconstructed j (τ,t); at the same time, for L j (τ, t) performs Fourier transform along the distance dimension to obtain the subband spectrum L j (f, t), replace the corresponding sub-band spectrum with interference X j (f,t).

Images