A method for interference mitigation with fast parameter search

Abstract

This invention discloses a fast parameter search-based interference suppression method, comprising: performing a Fourier transform along the range dimension on an SLC image containing LFM interference to obtain a range-frequency domain-azimuth-time domain representation matrix; determining the maximum energy accumulation pulse of the SLC image based on the representation matrix; performing FRFT transforms on two rotation angles to obtain FRFT results for the two rotation angles and determining the optimal rotation angle; performing FRFT transforms on each pulse of the SLC image at the optimal rotation angle, followed by outlier detection; performing an inverse fractional Fourier transform on the image matrix after outlier detection to obtain an image after one interference suppression; recalculating the optimal rotation angle on the image after preliminary interference suppression; if it is not zero, using the recalculated optimal rotation angle to perform interference suppression cyclically until the calculated optimal rotation angle is zero; when the optimal rotation angle is zero, performing interference suppression again using the optimal rotation angle to obtain the final interference-free SLC image.

Description

Technical Field

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

[0002] Spaceborne Synthetic Aperture Radar (SAR) plays a crucial role in both military and civilian applications due to its all-weather, high-resolution characteristics. In recent years, however, the number of jamming incidents on spaceborne SAR imagery has been increasing, degrading image quality and further hindering subsequent image interpretation. Among these, Linear Frequency Modulation (LFM) jamming, a type of broadband jamming, serves to suppress areas or create deceptive interference in imagery.

[0003] Currently, the main methods for suppressing broadband interference can be categorized into parametric, semi-parametric, and non-parametric methods. Parametric methods estimate interference parameters by establishing an interference signal model to suppress interference, but their ability to estimate broadband interference signal parameters is limited. Semi-parametric methods require a large amount of computation, making it difficult to achieve efficient interference suppression given the massive amounts of data from spaceborne SAR. Non-parametric methods for LFM interference typically employ time-frequency domain notch filtering, but the selection of energy thresholds lacks prior information and is prone to causing interference residue or severe loss of useful signals. Summary of the Invention

[0004] The purpose of this invention is to provide a fast parameter search method for interference suppression, which can eliminate the interference artifacts caused by multi-component linear frequency modulated broadband interference to SAR image data, thereby quickly and effectively suppressing SLC images with multi-component LFM interference.

[0005] To achieve the above objectives, the present invention employs the following technical solution:

[0006] An interference suppression method based on fast parameter search includes:

[0007] The synthetic aperture radar (SLC) image containing LFM interference is subjected to a Fourier transform along the range dimension to obtain a representation matrix in the range-frequency domain-azimuth-time domain; the maximum energy accumulation pulse of the SLC image is determined based on the representation matrix.

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

[0009] Based on the FRFT results of the two rotation angles, the optimal rotation angle is determined;

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

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

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

[0013] Further, the step of performing a Fourier transform along the range dimension on the synthetic aperture radar (SLC) image containing LFM interference to obtain a range-frequency domain-azimuth-time domain representation matrix; and determining the maximum energy accumulation pulse of the SLC image based on the representation matrix, includes:

[0014] With size (N) a N r A synthetic aperture radar (SLC) image X(t,η) with LFM interference is subjected to a Fourier transform along the range dimension, thereby transforming each row of data in the image to the frequency domain to obtain a range-frequency domain-azimuth-time domain representation matrix X(f,η). The modulo operation of each row of this matrix is ​​then performed to accumulate the energy of each pulse in the SLC image X(t,η). The pulse X(t) with the maximum energy accumulation is used for parameter extraction; where N... a N represents the number of rows in the SLC image matrix. r Let t be the column number of the SLC image matrix, t be the fast time of the range dimension, η be the slow time of the azimuth dimension, and f be the range frequency.

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

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

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

[0018] Further, based on the FRFT results of the two rotation angles, the optimal rotation angle is determined, including:

[0019] Amplitude normalization is performed on X1(u) and X2(u) after FRFT transformation, and a threshold Thr is selected based on energy intensity.i :

[0020]

[0021] Thr i For X i The intensity threshold of (u) is selected, x k For X i The k-th element in (u), n i For X i The number of elements in (u), i = 1, 2;

[0022] Calculate the projection lengths L1 and L2 of X1(u) and X2(u) onto the FRFT domain: for L i Statistically, x satisfies k ≥Thr i x k The quantity K, with K as L i ;

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

[0024]

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

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

[0027]

[0028] Furthermore, each pulse of the SLC image is subjected to FRFT transformation at the optimal rotation angle, followed by outlier detection, including:

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

[0030] Thr1 = μ X +3σ X

[0031] Where, μ X For X θ The mean, σ X For X θ The standard deviation of (u); using the detection threshold Thr1, find all outliers and set them to zero to obtain L. θ (u):

[0032]

[0033] When Xθ The value x in (u) i If the value is not less than the detection threshold Thr1, replace it with 0; otherwise, keep the original value; the image matrix after removing interference for outlier detection is denoted as L. θ (u).

[0034] Furthermore, an inverse fractional Fourier transform is performed on the image matrix after outlier detection to obtain an image after first-order interference suppression, including:

[0035]

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

[0037] A terminal device includes a processor, a memory, and a computer program stored in the memory; when the processor is executed by a computer, it implements the interference suppression method for fast parameter search.

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

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

[0040] This invention utilizes a SAR interference suppression method based on fast FRFT parameter search to suppress interference in SLC images containing broadband LFM interference. Only two FRFT operations are performed during parameter selection, effectively avoiding the slow parameter search problem of traditional FRFT methods due to the large amount of SAR data. Furthermore, by employing an outlier detection-based interference suppression method, this invention effectively avoids interference from residual identical LFM components after suppression, resulting in significantly improved image quality with minimal loss of useful signal. Attached Figure Description

[0041] Figure 1 This is a flowchart of a method according to one embodiment of the present invention;

[0042] Figure 2 This is a map showing the cumulative power spectrum distance in the SLC image.

[0043] Figure 3 This is the time-frequency diagram of the pulse containing the interference.

[0044] Figure 4 (a) is the projection of FRFT in the u-domain with a rotation angle of α1, and (b) is the projection of FRFT in the u-domain with a rotation angle of α2.

[0045] Figure 5 The time-frequency plot after FRFT at the optimal order;

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

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

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

[0049] To address the aforementioned problems, this invention provides a SAR image interference suppression method based on rapid FRFT parameter search. According to the projection of the interference components into different spaces in the fractional Fourier domain, the optimal order is quickly searched using two FRFTs. At the optimal order, outlier detection is used to filter the interference pulses. Referring to the accompanying drawings, the specific implementation of this invention is as follows:

[0050] Step 1, with a size of (N) a N r The synthetic aperture radar (SLC) image X(t,η) with LFM interference is subjected to a Fourier transform along the range dimension, thereby transforming each row of data in the image to the frequency domain to obtain the range-frequency domain-azimuth-time domain representation matrix X(f,η). The modulus of each row of data in this matrix is ​​accumulated along the column to obtain the energy accumulation of each pulse (i.e., each row of data) of the SLC image X(t,η). The pulse X(t) with the maximum energy accumulation is used for parameter extraction.

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

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

[0053]

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

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

[0056]

[0057] Thr i For X i The intensity threshold of (u) is selected, x k For X i The k-th element in (u), n i For X i The number of elements in (u).

[0058] The projection lengths L1 and L2 of X1(u) and X2(u) in the FRFT domain are calculated as follows:

[0059] For L i Statistically, x satisfies k ≥Thr i x k The quantity K, with 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 on the FRFT domain. Using geometric relationships, we can obtain:

[0061]

[0062] Where θ is the optimal rotation angle of the LFM interference signal in the FRFT, that is, the FRFT domain projection length L of the LFM interference signal at this rotation angle θ. θ Shortest; calculate the optimal rotation angle θ:

[0063]

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

[0065] Thr1 = μ X +3σ X (5)

[0066] Where, x i For X θ The value in (u), For X θ The mean of X, where n is X θ The length of (u), For X θ The standard deviation of (u); using the detection threshold Thr1, find all outliers and set them to zero to obtain L. θ (u).

[0067]

[0068] That is, when X θ The value x in (u) i If the value is not less than the detection threshold Thr1, replace it with 0; otherwise, keep the original value; the image matrix after removing interference for outlier detection is denoted as L. θ (u).

[0069] Step 5, take the L obtained in step 4 θ (u) Perform an inverse fractional Fourier transform, i.e., perform an FRFT corresponding to the rotation angle of -θ, to obtain the image L(t) after one round of interference suppression:

[0070]

[0071] Step 6: Repeat steps 2 and 3 for the interference-suppressed image L(t) to recalculate the optimal rotation angle θ. 1 ;

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

[0073] Step 8, if θ 1 If ≠0, it indicates the existence of another LFM interference component. Let θ = θ 1 Return to steps 4 to 6 until the optimal rotation angle is calculated to be 0, and then obtain the final interference-free SLC image using the method in step 7.

[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 sub-band image containing LFM broadband interference is subjected to a Fourier transform along the range dimension, where Na N represents the number of rows in the SLC image matrix. r Let be the number of columns in the SLC image matrix, and t and η represent fast and slow time, respectively. Transforming each row of data in the image to the frequency domain yields a range-frequency-azimuth-time domain representation matrix X(f,η). Accumulating the data along the columns of each row of this matrix, we obtain the energy accumulation for each pulse, as shown below. Figure 2 As shown, the pulse with the maximum energy is selected as the parameter extraction choice. In this embodiment, the interference is at the 1251st pulse.

[0076] Step 2, the time-frequency diagram of the one-dimensional pulse X(t) obtained in Step 1 is as follows: Figure 3 As shown, the interference is a linear frequency modulated broadband interference. Two rotation angles α1 and α2, symmetrical about π, are selected for FRFT, with the angle range being (10°, 80°). This yields the FRFT values ​​X1(u) and X2(u) of the pulse at two different angles. The FRFT calculation formula is as follows:

[0077]

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

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

[0080]

[0081] Where θ is the optimal rotation angle of the LFM interference signal in the FRFT, L θ Let θ be the projection length of the u-domain. 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 Perform FRFT transformation X θ (u), and then outlier detection is performed through amplitude. The detection threshold Thr1 can be expressed as:

[0084] Thr1 = μ X +3σ X (5)

[0085] Where, x i For X θ The value in (u), For X θ The mean of X, where n is X θ Length, For X θ The standard deviation of (u). All outliers are found using the detection threshold Thr, and then set to zero to obtain L. θ (u); The results in the FRFT domain before and after setting outliers to zero in this embodiment are as follows: Figure 6 As shown.

[0086]

[0087] Step 5, remove the interference from the L obtained in step 4. θ (u) Perform inverse fractional Fourier transform, i.e., perform FRFT corresponding to the rotation angle of -θ, to obtain the maximum energy pulse X(t) obtained in step 1 and the image L(t) after interference suppression.

[0088]

[0089] Step 6: Calculate the optimal rotation angle θ again for the image L(t) after the first interference suppression, using the method described in Step 3. 1 If θ 1 If θ = 0, then the interference suppression operations of steps 4 and 5 are performed pulse by pulse using the optimal angle obtained in step 3 to obtain the interference-free SLC image L(t,η); if θ 1 If ≠0, then there exists another component, LFM interference. Let θ = θ 1 Perform steps 4 and 5 until the optimal rotation angle calculated in step 3 is 0. Using the optimal angle obtained in step 3, perform the interference suppression operations of steps 4 and 5 pulse by pulse for each pulse to obtain the interference-free SLC image L(t,η). Figure 7 As shown in (b).

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

[0091] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.

Claims

1. A method for interference suppression through fast parameter search, characterized in that, include: By performing a Fourier transform along the range dimension on the synthetic aperture radar (SLC) image containing LFM interference, the range-frequency domain-azimuth-time domain representation matrix is ​​obtained. The maximum energy accumulation pulse of the SLC image is determined based on the characterization matrix; For the maximum energy accumulation pulse, two rotation angles are selected for FRFT transformation to obtain FRFT results for the two rotation angles; Based on the FRFT results of the two rotation angles, the optimal rotation angle is determined; For each pulse of the SLC image, perform FRFT transformation at the optimal rotation angle, and then perform outlier detection. Perform an inverse fractional Fourier transform on the image matrix after outlier detection to obtain an image after one round of interference suppression; The optimal rotation angle is recalculated for the image after initial interference suppression. If it is not zero, the interference suppression is performed cyclically using the recalculated optimal rotation angle until the calculated optimal rotation angle is zero. When the optimal rotation angle is zero, the 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 a Fourier transform along the range dimension to obtain a range-frequency domain-azimuth-time domain representation matrix. Determining the maximum energy accumulation pulse of the SLC image based on the characterization matrix includes: The size is Synthetic Aperture Radar (SLC) Imagery with LFM Jamming Performing a Fourier transform along the range dimension transforms each row of image data into the frequency domain, yielding a range-frequency-azimuth-time domain representation matrix. The SLC image is obtained by taking the modulus of each row of data in the matrix and accumulating it along the columns. The energy accumulation of each pulse is used to determine the pulse with the highest energy accumulation. Used for parameter extraction; where The row number of the SLC image matrix. The number of columns in the SLC image matrix. It is the fast time of distance dimension. It is the slow time of the orientation dimension. It refers to the distance frequency.

3. The interference suppression method for fast parameter search according to claim 1, characterized in that, For the maximum energy accumulation pulse, two rotation angles are selected for FRFT transformation to obtain FRFT results for the two rotation angles, including: For the maximum energy accumulation pulse Choose 2 rotation angles and Perform FRFT transform to obtain the pulse. At two different rotation angles and FRFT transform and .

4. The interference suppression method for fast parameter search according to claim 3, characterized in that, and satisfy: ;angle The selection range is .

5. The interference suppression method for fast parameter search according to claim 3, characterized in that, Based on the FRFT results of the two rotation angles, the optimal rotation angle is determined, including: After FRFT transformation and Amplitude normalization is performed and a threshold is selected based on energy intensity. : in for The intensity selection threshold, for The first in k One element, for The number of elements in the middle, i =1,2; calculate and Projection length in the FRFT domain and :against Statistical satisfaction of quantity K ,Will K As ; Calculate the projection length in the FRFT domain and : in, The optimal rotation angle for the LFM interference signal in the FRFT domain; The projection length of the FRFT transformation result corresponding to the optimal rotation angle onto the FRFT domain; The optimal rotation angle can be calculated using the following formula. : 。 6. The interference suppression method for fast parameter search according to claim 1, characterized in that, Each pulse of the SLC image is subjected to FRFT transformation at the optimal rotation angle, followed by outlier detection, including: Intensity selection threshold Represented as: in, for The mean, for Standard deviation; For each pulse of the SLC image at the optimal rotation angle The result of performing FRFT transformation below; Using detection thresholds Find all outliers and set them to zero. : (6) when The value in Not less than the detection threshold When the value is zero, replace it with 0; otherwise, keep the original value. The image matrix after outlier detection and interference removal is denoted as... .

7. The interference suppression method for fast parameter search according to claim 1, characterized in that, Performing an inverse fractional Fourier transform on the image matrix after outlier detection yields an image with first-order interference suppression, including: in, To achieve the optimal rotation angle, Represents the image matrix after removing interference. At the sampling points in the FRFT domain, It is a natural constant. j The imaginary unit, t Let be the fast time of 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 the computer, it implements the interference suppression method for fast parameter search according to any one of claims 1-7.

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

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