Interference suppression method for rapid parameter search

Abstract

The invention discloses an interference suppression method for fast parameter search, which comprises the following steps of: performing Fourier transform on an SLC image containing LFM interference along a distance dimension to obtain a distance frequency domain-azimuth time domain representation matrix; determining the maximum energy accumulation pulse of the SLC image based on the representation matrix; two rotation angles are selected for FRFT transformation, FRFT results of the two rotation angles are obtained, and the optimal rotation angle is determined; fRFT transformation is carried out on each pulse of the SLC image at the optimal rotation angle, and then outlier detection is carried out; performing inverse fractional Fourier transform on the image matrix after outlier detection to obtain an image after primary interference suppression; recalculating the optimal rotation angle of the image after preliminary interference suppression, and if the optimal rotation angle is not zero, circularly performing interference suppression by using the recalculated optimal rotation angle until the calculated optimal rotation angle is zero; when the optimal rotation angle is zero, the optimal rotation angle is used for executing interference suppression again, and a final non-interference SLC image is obtained.

Description

Technical Field

[0001] The invention relates to the field of radar signal processing, and in particular to an interference suppression method for fast parameter search. Background Art

[0002] Spaceborne synthetic aperture radar (SAR) plays a key role in military and civilian applications with its all-weather and high-resolution characteristics. In recent years, the number of interference cases on spaceborne SAR images has increased, reducing the quality of SAR images and further hindering subsequent image interpretation applications. Among them, Linear Frequency Modulation (LFM) is a broadband interference that has a suppressive or deceptive interference effect on images.

[0003] At present, the main interference suppression methods for broadband interference are mainly divided into parametric methods, semi-parametric methods and non-parametric methods. The parametric method estimates the interference parameters by establishing an interference signal model to suppress interference, but its ability to estimate the parameters of broadband interference signals is limited. The semi-parametric method requires a large amount of calculation, and it is difficult to achieve efficient interference suppression in the face of the huge amount of data from spaceborne SAR. The non-parametric method for LFM interference is usually a time-frequency domain notch, and the energy threshold selection lacks prior information, and it is easy to cause interference residue or serious loss of useful signals. Summary of the invention

[0004] The purpose of the present invention is to provide an interference suppression method with fast parameter search to eliminate interference artifacts caused by multi-component linear frequency modulation broadband interference to SAR image data, thereby quickly achieving effective suppression of SLC images with multi-component LFM interference.

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

[0006] An interference suppression method for fast parameter search, comprising:

[0007] Performing Fourier transformation on the synthetic aperture radar SLC image containing LFM interference along the range dimension to obtain a characterization matrix of the range frequency domain and the azimuth time domain; determining the maximum energy accumulation pulse of the SLC image based on the characterization matrix;

[0008] For the maximum energy accumulation pulse, two rotation angles are selected for FRFT transformation to obtain FRFT results of the two rotation angles;

[0009] Determining an optimal rotation angle based on the FRFT results of the two rotation angles;

[0010] Perform FRFT transformation on each pulse of the SLC image at the optimal rotation angle, and then perform outlier detection;

[0011] Perform inverse fractional Fourier transform on the image matrix after outlier detection to obtain an image after primary interference suppression;

[0012] The optimal rotation angle of the image after preliminary interference suppression is recalculated. If it is not zero, the recalculated optimal rotation angle is used to perform interference suppression repeatedly until the calculated optimal rotation angle is zero. When the optimal rotation angle is zero, interference suppression is performed again using the optimal rotation angle to obtain the final interference-free SLC image.

[0013] Furthermore, the synthetic aperture radar SLC image containing LFM interference is subjected to Fourier transformation along the range dimension to obtain a characterization matrix of the range frequency domain-azimuth time domain; and the maximum energy accumulation pulse of the SLC image is determined based on the characterization matrix, including:

[0014] The size is (N a ,N r ) The synthetic aperture radar SLC image X(t,η) containing LFM interference is Fourier transformed along the range dimension, so that each row of image data is transformed into the frequency domain to obtain the range frequency domain-azimuth time domain representation matrix X(f,η), and each row of the matrix data is accumulated along the column to obtain the energy accumulation of each pulse of the SLC image X(t,η), and the pulse with the maximum energy accumulation X(t) is used for parameter extraction; where N a is the number of rows of the SLC image matrix, N r is the number of columns of the SLC image matrix, t is the fast time in the range dimension, η is the slow time in the azimuth dimension, and f is the range frequency.

[0015] Furthermore, for the maximum energy accumulation pulse, two rotation angles are selected for FRFT transformation to obtain FRFT results of the two rotation angles, including:

[0016] For the maximum energy accumulation pulse X(t), two rotation angles α1 and α2 are selected for FRFT transformation to obtain the FRFT results X1(u) and X2(u) of the pulse X(t) at two different rotation angles α1 and α2.

[0017] Furthermore, α1 and α2 satisfy: α1+α2=π; the selection range of the angle α1 is (5°, 85°).

[0018] Further, based on the FRFT results of the two rotation angles, determining the optimal rotation angle includes:

[0019] Normalize the amplitude of X1(u) and X2(u) after FRFT transformation and select the threshold Thr by energy intensityi :

[0020]

[0021] Among them, Thr i For X i (u) intensity selection threshold, x k For X i The kth element in (u), n i For X i (u) The number of elements in, i = 1, 2;

[0022] Calculate the projection lengths L1 and L2 of X1(u) and X2(u) in the FRFT domain: i , statistics satisfy x k ≥Thr i x k The number K, K as L i ;

[0023] Calculate the projection lengths L1 and L2 on the FRFT domain:

[0024]

[0025] Where, θ is the optimal rotation angle of the LFM interference signal in the FRFT domain; L θ is the projection length of the FRFT transformation result corresponding to the optimal rotation angle in the FRFT domain;

[0026] The optimal rotation angle θ is calculated using the following formula:

[0027]

[0028] Furthermore, FRFT transformation is performed on each pulse of the SLC image at the optimal rotation angle, and then outlier detection is performed, including:

[0029] The detection threshold Thr1 can be expressed as:

[0030] Thr1=μ X +3σ X

[0031] Among them, μ X For X θ The mean value, σ X For X θ (u) standard deviation; use the detection threshold Thr1 to find all outliers and set them to zero to get L θ (u):

[0032]

[0033] When Xθ The value x in (u) i When it is not less than the detection threshold Thr1, its value is replaced by 0; otherwise, the original value is retained; the image matrix after outlier detection and interference removal is recorded as L θ (u).

[0034] Furthermore, the image matrix after outlier detection is subjected to an inverse fractional Fourier transform to obtain an image after primary interference suppression, including:

[0035]

[0036] Among them, θ is the optimal rotation angle, and u represents the image matrix L after removing interference θ (u) Sampling point in the FRFT domain, e is a natural constant, j is an imaginary unit, and t is the fast time in the distance dimension.

[0037] 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 interference suppression method of the fast parameter search is implemented.

[0038] A computer-readable storage medium stores a computer program; when the computer program is executed by a processor, the interference suppression method for fast parameter search is implemented.

[0039] Compared with the prior art, the present invention has the following technical features:

[0040] The present invention utilizes a SAR interference suppression method based on fast FRFT parameter search to achieve interference suppression of SAR SLC images containing LFM broadband interference. Only two FRFTs are performed when selecting FRFT parameters, effectively avoiding the problem that the traditional FRFT method is slow when performing parameter search due to the large amount of SAR data. At the same time, the present invention can effectively avoid the interference of the same LFM component remaining after suppression by using an interference suppression method using outlier detection, and the image quality is greatly improved after interference suppression, and the loss of useful signals is very small. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 is a flow chart of a method in one embodiment of the present invention;

[0042] Figure 2 It is the distance accumulation result diagram of the power spectrum of the SLC image distance dimension;

[0043] Figure 3 It is the time-frequency diagram of the pulse where the interference occurs;

[0044] Figure 4 (a) is the projection diagram of FRFT in u domain when the rotation angle is α1, (b) is the projection diagram of FRFT in u domain when the rotation angle is α2;

[0045] Figure 5 It is the time-frequency diagram after FRFT at the optimal order;

[0046] Figure 6 (a) is the FRFT domain result diagram before interference suppression, and (b) is the FRFT domain result diagram after interference suppression;

[0047] Figure 7 (a) is the SLC image before interference suppression, and (b) is the SLC image after interference suppression. DETAILED DESCRIPTION

[0048] Fractional Fourier Transform (FRFT) can find the sparse domain of LFM signal and effectively suppress LFM interference after transforming the domain; however, searching for FRFT rotation angle requires a lot of computing time, and it is difficult to search for the optimal parameters for multi-component LFM interference. The notch method based on energy difference is difficult to suppress weak energy interference.

[0049] In view of the above problems, the present invention provides a SAR image interference suppression method based on fast FRFT parameter search. According to the projection of the interference component in different spaces of the fractional Fourier domain, the optimal order is quickly searched through two FRFTs, and the interference pulse is filtered by outlier detection at the optimal order. Referring to the attached drawings, the present invention is specifically implemented as follows:

[0050] Step 1: Set the size (N a ,N r )The synthetic aperture radar SLC image X(t,η) containing LFM interference is Fourier transformed along the range dimension, so that each row of image data is transformed into the frequency domain to obtain the range-frequency domain-azimuth-time domain representation matrix X(f,η). Each row of the matrix data is accumulated along the column modulus to obtain the energy accumulation of each pulse (i.e., each row of data) of the SLC image X(t,η), and the pulse X(t) with the maximum energy accumulation is taken for parameter extraction.

[0051] Where N a is the number of rows of the SLC image matrix, N r is the number of columns of the SLC image matrix, t is the fast time in the range dimension, η is the slow time in the azimuth dimension, and f is the range frequency.

[0052] Step 2: For the pulse X(t) obtained in step 1, select two rotation angles α1 and α2 for FRFT, where α1 and α2 satisfy: α1+α2=π; the selection range of angle α1 is (5°, 85°), and the FRFT results X1(u) and X2(u) of the pulse X(t) at two different rotation angles are obtained; the calculation formula of FRFT is as follows:

[0053]

[0054] Among them, K p (t,u) is the kernel function of FRFT, u represents the one-dimensional signal X(t) in the FRFT domain X p (u), e is a natural constant, j is an imaginary unit, and i = 1, 2.

[0055] Step 3: Normalize the amplitude of X1(u) and X2(u) after FRFT obtained in step 2 and select the threshold Thr by energy intensity. i :

[0056]

[0057] Among them, Thr i For X i (u) intensity selection threshold, x k For X i The kth element in (u), n i For X i The number of elements in (u).

[0058] Calculate the projection lengths L1 and L2 of X1(u) and X2(u) in the FRFT domain using the following calculation method:

[0059] For L i , statistics satisfy x k ≥Thr i x k The number K, K as L i For example, for L1, after calculating the threshold Thr1, count the number of element values ​​in X1(u) that are greater than Thr1, and use this number as L1.

[0060] Calculate the projection lengths L1 and L2 in the FRFT domain and use the geometric relationship to get:

[0061]

[0062] Among them, θ is the optimal rotation angle of the LFM interference signal in FRFT, that is, the FRFT domain projection length L corresponding to the LFM interference signal at the rotation angle θ θ Shortest; calculate the optimal rotation angle θ:

[0063]

[0064] Step 4: Perform FRFT transformation on each pulse of the SLC image at the optimal rotation angle θ θ (u), and then perform outlier detection. The detection threshold Thr1 can be expressed as:

[0065] Thr1=μ X +3σ X (5)

[0066] Among them, x i For X θ The value in (u), For X θ The mean of θ The length of (u), For X θ (u) standard deviation; use the detection threshold Thr1 to find all outliers and set them to zero to get L θ (u).

[0067]

[0068] That is, when X θ The value x in (u) i When it is not less than the detection threshold Thr1, its value is replaced by 0; otherwise, the original value is retained; the image matrix after outlier detection and interference removal is recorded as L θ (u).

[0069] Step 5: L obtained in step 4 θ (u) Perform an inverse fractional Fourier transform, that is, perform FRFT with a rotation angle corresponding to -θ, and obtain the image L(t) after interference suppression:

[0070]

[0071] Step 6: Re-execute steps 2 and 3 on the interference suppressed image L(t) and calculate the optimal rotation angle θ again. 1 ;

[0072] Step 7, if θ 1 = 0, then use θ 1 Perform interference suppression again according to steps 4 and 5 to obtain the final interference-free SLC image;

[0073] Step 8, if θ 1 ≠0 indicates that there is another component of LFM interference, let θ = θ 1 Return to execute steps 4 to 6 until the optimal rotation angle is calculated to be 0, and then use the method of step 7 to obtain the final interference-free SLC image.

[0074] Example:

[0075] Step 1, the synthetic aperture radar SLC image with size (13584,68686) is as follows Figure 7 As shown in (a), the IW1 subband image containing LFM broadband interference is Fourier transformed along the distance dimension, where Na is the number of rows of the SLC image matrix, N r is the number of columns of the SLC image matrix, t and η represent fast time and slow time respectively. Each row of image data is transformed into the frequency domain to obtain the representation matrix X(f,η) of the range frequency domain-azimuth time domain. Each row of the matrix data is accumulated along the column modulus to obtain the energy accumulation of each pulse, as shown in Figure 2 As shown, the pulse with maximum energy is selected as the parameter extraction. In this embodiment, the interference is in the 1251th pulse.

[0076] Step 2: For the one-dimensional pulse X(t) obtained in step 1, its time-frequency diagram is as follows: Figure 3 As shown, it can be seen that the interference is linear frequency modulation broadband interference. Two rotation angles α1 and α2 symmetric about π are selected for FRFT. The angle selection range is (10°, 80°). The FRFTX1(u) and X2(u) of the pulse at two different angles are obtained. The calculation formula of FRFT is as follows:

[0077]

[0078] Among them, K p (t,u) is the kernel function of FRFT, u represents the one-dimensional signal X(t) in the FRFT domain X p In this embodiment, α1 = 0.1π / 2, α1 = 1.9π / 2.

[0079] Step 3: Normalize the amplitude of X1(u) and X2(u) after the pulse FRFT obtained in step 2 and select the threshold Thr to calculate the projection lengths L1 and L2 in the u domain, as shown in Figure 4 As shown, using geometric relationships, we can get

[0080]

[0081] Among them, θ is the optimal rotation angle of the LFM interference signal in FRFT, L θ is the u-domain projection length corresponding to θ. The optimal rotation angle θ is calculated, and in this embodiment, the optimal rotation angle is 0.1918.

[0082]

[0083] Step 4: for each pulse of the SLC image obtained in step 3 Corresponding order FRFT transformation is performed under X θ (u), and then outlier detection is performed by amplitude. The detection threshold Thr1 can be expressed as:

[0084] Thr1=μ X +3σ X (5)

[0085] Among them, x i For X θ The value in (u), For X θ The mean of θ Length, For X θ The standard deviation of (u). Use the detection threshold Thr to find all outliers and set them to zero to get L θ (u); The results of this embodiment in the FRFT domain before and after the outliers are set to zero are as follows Figure 6 shown.

[0086]

[0087] Step 5: Remove the interference from the L obtained in step 4 θ (u) Perform an inverse fractional Fourier transform, that is, perform FRFT with a rotation angle corresponding to -θ to obtain the maximum energy pulse X(t) obtained in step 1, and obtain the image L(t) after interference suppression.

[0088]

[0089] Step 6: Calculate the optimal rotation angle θ again through step 3 for the image L(t) after the first interference suppression 1 If θ 1 = 0, then use the optimal angle obtained in step 3 to perform interference suppression operations in steps 4 and 5 on each pulse one by one to obtain the interference-free SLC image L(t,η); if θ 1 ≠0, there is another component of LFM interference, let θ=θ 1 Perform steps 4 and 5 until the optimal rotation angle calculated in step 3 is 0. Use the optimal angle obtained in step 3 to perform interference suppression operations in steps 4 and 5 on each pulse one by one to obtain an interference-free SLC image L(t,η), as shown in Figure 7 as shown in (b).

[0090] For multi-component LFM interference with different modulation rates, the optimal parameters will be selected according to the energy in each FRFT parameter search. The first parameter estimation will estimate the rotation angle corresponding to the LFM interference with stronger energy, and the subsequent iteration will estimate the LFM interference parameters with weaker energy. Therefore, this method can suppress multi-component LFM interference.

[0091] 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. An interference suppression method for fast parameter search, characterized in that: include: The synthetic aperture radar SLC image containing LFM interference is Fourier transformed along the range dimension to obtain the representation matrix of range frequency domain and azimuth time domain. Determining a maximum energy accumulation pulse of the SLC image based on the characterization matrix; For the maximum energy accumulation pulse, two rotation angles are selected for FRFT transformation to obtain FRFT results of the two rotation angles; Determining an optimal rotation angle based on the FRFT results of the two rotation angles; Perform FRFT transformation on each pulse of the SLC image at the optimal rotation angle, and then perform outlier detection; Perform inverse fractional Fourier transform on the image matrix after outlier detection to obtain an image after primary interference suppression; The optimal rotation angle of the image after preliminary interference suppression is recalculated. If it is not zero, the recalculated optimal rotation angle is used to perform interference suppression repeatedly until the calculated optimal rotation angle is zero. When the optimal rotation angle is zero, interference suppression is performed again using the optimal rotation angle to obtain the final interference-free SLC image.

2. The interference suppression method for fast parameter search according to claim 1, characterized in that: The synthetic aperture radar SLC image containing LFM interference is subjected to Fourier transformation along the range dimension to obtain a representation matrix of the range frequency domain-azimuth time domain; Determining the maximum energy accumulation pulse of the SLC image based on the characterization matrix includes: The size is (N a ,N r ) The synthetic aperture radar SLC image X(t,η) containing LFM interference is Fourier transformed along the range dimension, so that each row of image data is transformed into the frequency domain to obtain the range frequency domain-azimuth time domain representation matrix X(f,η), and each row of the matrix data is accumulated along the column to obtain the energy accumulation of each pulse of the SLC image X(t,η), and the pulse with the maximum energy accumulation X(t) is used for parameter extraction; where N a is the number of rows of the SLC image matrix, N r is the number of columns of the SLC image matrix, t is the fast time in the range dimension, η is the slow time in the azimuth dimension, and f is the range frequency.

3. The interference suppression method for fast parameter search according to claim 1, characterized in that: The method of selecting two rotation angles for FRFT transformation for the maximum energy accumulation pulse to obtain FRFT results of the two rotation angles includes: For the maximum energy accumulation pulse X(t), two rotation angles α1 and α2 are selected for FRFT transformation to obtain the FRFT results X1(u) and X2(u) of the pulse X(t) at two different rotation angles α1 and α2.

4. The interference suppression method for fast parameter search according to claim 3, characterized in that: α1 and α2 satisfy: α1+α2=π; the selection range of the angle α1 is (5°, 85°).

5. The interference suppression method for fast parameter search according to claim 1, characterized in that: Determining an optimal rotation angle based on the FRFT results of the two rotation angles includes: Normalize the amplitude of X1(u) and X2(u) after FRFT transformation and select the threshold Thr by energy intensity i : Among them, Thr i For X i (u) intensity selection threshold, x k For X i The kth element in (u), n i For X i (u) The number of elements in, i = 1, 2; Calculate the projection lengths L1 and L2 of X1(u) and X2(u) in the FRFT domain: i , statistics satisfy x k ≥Thr i x k The number K, K as L i ; Calculate the projection lengths L1 and L2 on the FRFT domain: Where, θ is the optimal rotation angle of the LFM interference signal in the FRFT domain; L θ is the projection length of the FRFT transformation result corresponding to the optimal rotation angle in the FRFT domain; The optimal rotation angle θ is calculated using the following formula:

6. The interference suppression method for fast parameter search according to claim 1, characterized in that: Perform FRFT transformation on each pulse of the SLC image at the optimal rotation angle, and then perform outlier detection, including: The detection threshold Thr1 can be expressed as: Thr1=μ X +3s X Among them, μ X For X θ The mean value, σ X For X θ (u) standard deviation; use the detection threshold Thr1 to find all outliers and set them to zero to get L θ (u): When X θ The value x in (u) i When it is not less than the detection threshold Thr1, its value is replaced by 0; otherwise, the original value is retained; the image matrix after outlier detection and interference removal is recorded as L θ (u).

7. The interference suppression method for fast parameter search according to claim 1, characterized in that: Perform an inverse fractional Fourier transform on the image matrix after outlier detection to obtain an image after primary interference suppression, including: Among them, θ is the optimal rotation angle, and u represents the image matrix L after removing interference θ (u) Sampling point in the FRFT domain, e is a natural constant, j is an imaginary unit, and t is the fast time in the distance dimension.

8. A terminal device comprising a processor, a memory and a computer program stored in the memory; characterized in that: When the processor is executed by a computer, the interference suppression method for fast parameter search according to any one of claims 1 to 7 is implemented.

9. A computer-readable storage medium, wherein a computer program is stored in the medium; characterized in that: When the computer program is executed by a processor, the interference suppression method for fast parameter search according to any one of claims 1 to 7 is implemented.

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