Inter-satellite interference suppression method based on sub-band spectrum low-rank recovery

Abstract

The invention discloses an inter-satellite interference suppression method based on sub-band spectrum low-rank recovery. The inter-satellite interference suppression method comprises the following steps: performing FFT (Fast Fourier Transform) on a single-view complex image along a distance dimension; calculating kurtosis of sampling points in each distance dimension, and judging whether interference exists in the sampling points or not; dividing the maximum interference-free sub-band spectrum into two interference-free sub-band spectrums from the center, dividing the representation matrix into a plurality of sub-band spectrums, and then executing IFFT along a distance dimension to obtain a corresponding time domain image; the time domain image of the sub-band spectrum with interference and the time domain images of the two non-interference sub-band spectrums are straightened and spliced, a data set matrix is constructed and solved to obtain a non-interference data set, then the non-interference data set is reconstructed into a sub-band spectrum time domain image, and therefore the non-interference time domain image obtained after the sub-band spectrum with interference is reconstructed is obtained; replacing the corresponding sub-band spectrum with interference in the representation matrix with the sub-band spectrum after FFT is executed on the non-interference time domain image along the distance dimension; and performing IFFT (Inverse Fast Fourier Transform) 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 a special type of ground-scattering interference, and its interference source comes from satellite platforms operating in the same band. When time, space and frequency synchronization are met, the interfered satellite will receive the ground-scattered signal from the interfering satellite. Since the signal parameters transmitted by other satellite platforms in the same band are similar to the echo signal parameters of the interfered satellite, at this time, the intersatellite interference will be characterized as broadband interference with weak energy and difficult to remove.

[0003] Traditional methods based on principal component analysis or robust principal component analysis are difficult to remove due to the weak energy of intersatellite interference. Although the method based on sub-band spectrum cancellation can suppress intersatellite interference to a certain extent, its essence is to use the cancellation between the interference image without resolution loss and the interference image with resolution loss, and there will still be 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, which utilizes the range spectrum sub-band division and replaces the incoherent subtraction step of the sub-band spectrum cancellation method with a low-rank representation (LRR), thereby achieving the purpose of suppressing inter-satellite interference 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 distance dimension to obtain the image representation matrix in the distance frequency domain and azimuth time domain;

[0008] Calculate the kurtosis of each distance dimension sampling point in the characterization matrix, and determine whether there is interference at the distance dimension sampling point based on the relationship between the kurtosis and the threshold; determine the maximum non-interference sub-band spectrum corresponding to all non-interference 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 part of the characterization matrix except the two non-interference sub-band spectra into a plurality of 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 there is no interference, do not process it, otherwise it is considered that the corresponding sub-band spectrum has interference; straighten and splice the time domain image of the sub-band spectrum with interference and the time domain images of the two sub-band spectra without interference to construct a data set matrix;

[0012] The dataset matrix itself is used as a dictionary to perform low-rank approximation and obtain a concatenated, interference-free dataset.

[0013] Performing 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 after the sub-band spectrum with interference is reconstructed;

[0014] The sub-band spectrum after Fourier transformation along the distance dimension of the interference-free time domain image is replaced with the corresponding sub-band spectrum with interference in the representation matrix;

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

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

[0017]

[0018] The representation matrix represents the single-view complex image SLC, τ is the fast time in the distance dimension, t is the slow time in the azimuth dimension, e is a natural constant, j is an imaginary unit, f is the distance frequency, The number of sampling points of 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 calculation characterizes the kurtosis of each distance dimension sampling point in the matrix, and determines whether there is interference at the distance dimension sampling point according to the relationship between the kurtosis and the threshold value; including:

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

[0021]

[0022] Where Re[·] represents the real part of a complex number, μ i Represents the i-th distance dimension sampling point f i The mean value, σi 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] Further, 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 non-interference distance dimension sampling points. The frequency band where the maximum spectrum width is located is considered to be the maximum non-interference sub-band spectrum X CLEAR (f, t), the corresponding distance dimension sampling point number N B .

[0026] Further, the dividing the maximum non-interference sub-band spectrum into two non-interference sub-band spectra from the center, and dividing the part of the characterization matrix except the two non-interference sub-band spectra into a plurality of 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, which is N a , the number of sampling points in the distance dimension is Matrix of

[0029] Sampling points according to distance dimension Divide the representation matrix X(f, t) into N+2 sub-band spectra, i.e., 2 interference-free sub-band spectra X CLEAR1 (f,t),X CLEAR2 (f, t) and other N sub-band spectra to be processed, expressed as:

[0030] X(f,t)=[X 1 (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 Subband spectrum to be processed X 1 (f, t) and X NThe number of sampling points in the azimuth dimension of (f, t) is N a , the number of sampling points in the distance dimension is Other N-2 subbands X 2 (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] Further, 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, including:

[0033] The number of sampling points for the distance dimension is The N sub-band spectrum X 2 (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 X to be processed 2 (τ,t),...,X N-1 (τ, t) and the interference-free subband spectrum time domain image X CLEAR1 (τ,t),X CLEAR2 (τ,t).

[0034] Further, 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 there is no interference, 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 spectra without interference 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 in 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 concatenated 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 order of columns 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, forming the data set matrix X.

[0037] Furthermore, the low-rank approximation solution is performed using the data set matrix itself as a dictionary to obtain a spliced ​​interference-free data set, 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] Further, the interference-free data set is subjected to inverse operations of straightening and splicing to be reconstructed 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, 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 subband 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 subband spectrum with interference X j (f,t).

[0043] A terminal device comprises 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] The present invention innovatively utilizes the characteristic of intersatellite interference not covering the entire frequency band, constructs a model that satisfies low-rank recovery, and effectively avoids the high-frequency detail loss problem caused by the traditional sub-band spectrum cancellation method by performing low-rank representation on the sub-band spectrum. At the same time, the present invention can effectively remove broadband intersatellite interference on a single complex image (SLC), and significantly improve image quality. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 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. The method is based on the characteristics of inter-satellite interference that non-full-band coverage exists and 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 bandwidth of the interference-free sub-band spectrum. At the same time, the interference-free sub-band spectrum is used as a dictionary, and the interfered sub-band spectrum can be represented by a low rank 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 distance dimension to obtain the image representation matrix in the distance frequency domain and azimuth time domain:

[0052]

[0053] in represents the single-view complex image SLC, τ is the fast time in the distance dimension, t is the slow time in the azimuth dimension, e is a natural constant, j is an imaginary unit, f is the distance frequency, The number of sampling points of 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, wherein the azimuth dimension is consistent with the tangential velocity direction of the aircraft and satellite movement, and the distance dimension is consistent with the radial velocity direction of the aircraft and satellite movement.

[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] Where Re[·] represents the real part of a complex number, μ i Represents the i-th distance dimension sampling point f i The mean value, σ 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 point number 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 N in the azimuth dimension. 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, i.e., 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)=[X 1 (f,t),...,X j-1(f,t),X CLEAR1 (f,t),X CLEAR2 (f,t),X j (f,t),...,X N (f,t)]

[0064] Among them, 1<j≤N and Subband spectrum to be processed X 1 (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 Other N-2 subbands X 2 (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 spectrum X 2 (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 X to be processed 2 (τ,t),...,X N-1 (τ, t) and the 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 in 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) 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: taking each column of data in the image matrix as a unit, reconnecting the units in sequence according to the order of the columns 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 data set X obtained in step 7 as a dictionary to perform low-rank approximation solution to obtain a concatenated interference-free data set 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 data set 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 the augmented Lagrangian function:

[0080]

[0081] where tr[·] means taking 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 ) represents taking ρμ k and max u The minimum number between 0 and ρ, 0<ρ<1 is a constant, max u It is a positive number that is set first.

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

[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 XCLEAR1 (τ,t),X CLEAR2 (τ, t) reconstructs the image; thus obtaining the subband 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 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, performing 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)=[X 1 (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 transformed along the distance 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 distance dimension FFT and sub-band spectrum division on the interfered image, and then obtain the corresponding sub-band spectrum time domain image through distance dimension IFFT. Select a data set consisting of 1 interfered sub-band spectrum time domain image and 2 non-interference sub-band spectrum time domain images to perform the LRR algorithm to obtain 3 sub-band spectrum low-rank images after interference suppression. Then, perform distance dimension 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 domain-azimuth time domain map of the non-interference SLC image is obtained. Finally, perform range dimension IFFT on the range frequency domain-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 distance frequency domain-azimuth time domain

[0108]

[0109] Where τ is the distance fast time, η is the azimuth slow time, and f is the distance 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] Here, Re[·] represents the real part of a complex number. i Indicates the i-th distance frequency point f i The mean value, σ i Indicates the i-th distance frequency point f i The standard deviation of .

[0113] Step 3: According to the kurtosis K i Whether it is greater than 3 to determine the frequency point f i Is there interference? If it is greater than 3, it means that there is interference at the frequency point. If it is less than or equal to 3, it means that there is no interference at the frequency point. Finally, all 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 subband spectrum into two clean subbands 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 azimuth dimension and 4096 sampling points in the distance dimension.

[0117] Step 5: According to the number of sampling points 4096, the representation matrix X(f,t) is divided into 8 sub-band spectra, namely 2 clean sub-bands X CLEAR1 (f,t),X CLEAR2 (f, t) and the other 6 sub-bands to be processed. The process can be expressed as:

[0118] X(f,t)=[X 1 (f,t),X CLEAR (f,t),X 2 (f,t),X 3 (f,t),X 4 (f,t),X 5 (f,t),X 6 (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 sample 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 image X to be processed 2 (τ,t),X 3 (τ,t),X 4 (τ,t),X 5 (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 sub-band spectrum time domain image X to be processed in step 6 2 (τ, t), determine the frequency point f within its frequency band according to step 3 i There is interference. X 2(τ, t) will be combined with the two non-interfering sub-band spectral 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 data set 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 to obtain the concatenated interference-free data set XZ, 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 ) represents 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 iteration 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 operation of straightening and splicing shown in step 7 on the interference-free dataset XZ obtained in step 8 to reconstruct it into a spectral time domain image with a size of 3 sub-bands [L 2 (τ,t),L CLEAR1 (τ,t),L CLEAR2 (τ,t)]; at the same time, for L 2 (τ, t) performs Fourier transform along the distance direction to obtain the subband spectrum L 2 (f, t), replaces the original interfering sub-band spectrum time domain image X 2 (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 characterization matrix X(f, t) shown in step 5. The process can be expressed as:

[0149] L(f,t)=[X 1 (f,t),X CLEAR (f,t),L 2 (f,t),L 3 (f,t),X 4 (f,t),X5 (f,t),X 6 (f,t)]

[0150] Finally, perform inverse Fourier transform on the spectrum L(f, t) 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 the 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 embodiments of the present application, and should all be included in the protection scope 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 distance dimension to obtain the image representation matrix in the distance frequency domain and azimuth time domain; Calculate the kurtosis of each distance dimension sampling point in the representation matrix, and determine whether there is interference at the distance dimension sampling point according to 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 part of the characterization matrix except the two non-interference sub-band spectra into a plurality of 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; Straighten and splice the time domain image of the sub-band spectrum with interference and the time domain images of two sub-band spectrums without interference to construct a data set matrix; The dataset matrix itself is used as a dictionary to perform low-rank approximation and obtain a concatenated, 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 after the sub-band spectrum with interference is reconstructed; Sub-band spectra after Fourier transformation along the distance dimension of the interference-free time domain image are replaced with 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 a 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 single-view complex image is subjected to Fourier transform along the distance dimension to obtain the representation matrix of the image in the distance frequency domain-azimuth time domain, which is expressed as: The representation matrix represents the single-view complex image SLC, τ is the fast time in the distance dimension, t is the slow time in the azimuth dimension, e is a natural constant, j is an imaginary unit, f is the distance frequency, The number of sampling points of 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 the N in the representation matrix X(f,t) respectively r distance dimension sampling points f i The kurtosis K i : Where Re[·] represents the real part of a complex number, μ i Represents the i-th distance dimension sampling point f i The mean value, σ 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 non-interference distance dimension sampling points. The frequency band where the maximum spectrum width is located is considered to be the maximum non-interference sub-band spectrum X CLEAR (f, t), the corresponding distance dimension sampling point number 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 method of dividing the maximum non-interference sub-band spectrum into two non-interference sub-band spectrums from the center, and dividing the part of the characterization matrix except the two non-interference sub-band spectrums into a plurality of sub-band spectrums, comprises: 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, which is N a , the number of sampling points in the distance dimension is Matrix of According to the distance dimension, the number of sampling points Divide the representation matrix X(f, t) into N+2 sub-band spectra, i.e., 2 interference-free sub-band spectra X CLEAR1 (f,t),X CLEAR2 (f, t) and other N sub-band spectra to be processed, 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 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 subband 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 the 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 in 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 concatenated 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, forming 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 data set matrix itself as a dictionary to obtain a spliced ​​interference-free data set, 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: The interference-free data set is subjected to inverse operations 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 after the sub-band spectrum with interference is reconstructed, 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 subband 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 subband spectrum with interference X j (f,t).

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