Two-stage ISAR (Inverse Synthetic Aperture Radar) imaging method for supporting domain weighted two-dimensional compressed sensing reconstruction

Abstract

The invention provides a two-stage ISAR (inverse synthetic aperture radar) imaging method for domain weighted two-dimensional compressed sensing reconstruction. The two-stage ISAR imaging method comprises the following steps: step 1, constructing a radar imaging model; the radar imaging model adopts a classic turntable model; 2, constructing a signal support domain based on an FFT imaging result; setting a detection threshold Th according to a mean value of all pixel points in an imaging result of the FFT method, and marking a set obtained by removing discrete points from points exceeding the threshold as a signal support domain to obtain a weighting function; 3, constructing a compressed sensing imaging model; comprising the following steps: constructing a sparse aperture model of an echo signal and constructing a sparse reconstruction model; and step 4, radar image reconstruction is realized by using a weighted constrained compressed sensing algorithm. According to the method, the sparse aperture image reconstruction accuracy is improved for targets with stable flight attitudes, and the number of observation pulses can be greatly reduced, so that the number of targets monitored at the same time is improved, and the utilization rate of radar resources is improved.

Description

[Technical field]

[0001] The invention belongs to the field of radar signal processing, and relates to an inverse synthetic aperture radar (ISAR) sparse aperture imaging processing method, and specifically relates to a two-stage ISAR imaging method of support domain weighted two-dimensional compressed sensing reconstruction. [Background technology]

[0002] Compressed sensing (CS) theory proves that for signals with sparseness in a certain signal domain, data observed at a sampling rate lower than the Nyquist sampling theorem can be accurately reconstructed with a high probability (see the literature: "DL Donoho, "Compressed sensing," IEEE Trans. Inf. Theor. vol. 52, no. 4, pp. 1289-1306, 2006." Donoho's paper: Compressed sensing). The two-dimensional imaging result in the high-frequency region can be equivalent to a finite number of strong scattering points within a distance unit (see the literature "S. Zhang, "Introduction," in Sparse Bayesian ISAR imaging technique. Beijing, China: Science Press, 2020, pp. 11-12." Zhang Shuanghui's book: Sparse Bayesian ISAR imaging method), which just meets the requirements of CS theory for signal sparsity (see the literature "R. Baraniuk, M. Davenport, R. DeVore, M. Wakin, "A simple proof of the restricted isometry property for random matrices," Constr. Approx., vol. 28, no. 3, pp. 253-263, 2008" Baraniuk's paper: A simple proof of the isometry constraint of random matrices). Therefore, the CS method can be used to solve the image reconstruction problem under sparse aperture conditions. There are many classic CS-based algorithms that can be used to solve the sparse aperture imaging problem. Among them, the orthogonal matching pursuit (OMP) algorithm uses a greedy optimization iterative strategy, which has the advantages of small computational complexity and high reconstruction efficiency. It is widely used in the field of radar signal processing and imaging (see the literature "JATropp, ACGilbert, "Signal recovery from random measurements via orthogonal matching pursuit," IEEE Trans. Inform. Theory, vol. 53, no. 12, pp. 4655-4666, 2007." Tropp's paper: Signal recovery from random measurements via orthogonal matching pursuit).

[0003] The solution space of the traditional OMP algorithm iterative optimization includes the entire imaging area. However, according to the sparse characteristics of the target scattering points, such a solution space is much larger than the area of ​​the actual scattering points. When solving the short-aperture imaging problem, Zhang Lei proposed to introduce the imaging results based on the FFT method as prior information into the OMP reconstruction algorithm, which improved the reconstruction effect under low signal-to-noise ratio (SNR) conditions (see the literature: "L. Zhang, M. Xing, Qiu C., Li J., Sheng J., Li Y., Bao Z., "Resolution enhancement for inversed synthetic aperture radar imaging under low SNR via improved compressive sensing," IEEE Trans. Geo Remote Sens., vol. 48, no. 10, pp. 3824-3838, 2010." Zhang Lei's paper: Resolution enhancement of inversed synthetic aperture radar imaging under low SNR via improved compressive sensing). On this basis, Cheng Kai improved the weighting function designed according to the imaging results based on the FFT method (see patent: Yang Shuyuan, Jiao Licheng, Cheng Kai, etc. ISAR imaging method based on weighted L1 optimization and visual saliency attention, patent acceptance number: 2014102400723).

[0004] Aiming at the sparse aperture imaging problem of targets with stable flight attitude, the present invention designs a two-stage ISAR imaging method based on support domain weighted two-dimensional compressed sensing reconstruction to improve the image reconstruction quality under low sparsity. [Summary of the invention]

[0005] The purpose of the present invention is to design a two-stage ISAR imaging method of support domain weighted two-dimensional compressed sensing reconstruction in view of the problems of the prior art. The specific contents are as follows: Based on the principle of compressed sensing, a two-stage ISAR imaging method is proposed for the problem of sparse aperture imaging. In the first stage, the image support domain is extracted and a weighting function is constructed using the imaging results of the complete aperture. In the second stage, this prior information is used to weight the compressed sensing reconstruction process. This method improves the accuracy of sparse aperture image reconstruction for the goal of stable flight posture.

[0006] In order to achieve the above object, the technical solution adopted by the present invention is as follows:

[0007] Step 1: Build a radar imaging model;

[0008] Step 2: Construct the signal support domain based on the FFT imaging results;

[0009] Step 3: Construct a compressed sensing imaging model;

[0010] Step 4: Reconstruct radar image using weighted constrained compressed sensing algorithm;

[0011] The specific process of step 2 is as follows:

[0012] The detection threshold T is set according to the mean value of all pixels in the imaging result of the FFT method. h , the set obtained after removing the discrete points from the points that pass the threshold is recorded as the signal support domain, and the weighting function is obtained.

[0013] The specific process described in step 3 is as follows:

[0014] Based on the principle of compressed sensing, the perception matrix Φ = PΨ is constructed, where Ψ = ξ -1 is a sparse transformation basis, and P is a sparse measurement matrix.

[0015] The two-dimensional image reconstruction is realized by using a weighted compressed sensing algorithm as described in step 4, which is hereinafter referred to as a 2D-OMP reconstruction algorithm. The specific process is as follows:

[0016] Input: effective aperture data S′, perception matrix Φ, weighting matrix W, noise tolerance ε;

[0017] Output: target sparse reconstruction result

[0018] Step 4.1: The loop count is recorded as l and the residual matrix is ​​recorded as R l , the selected basis vectors in the perception matrix Φ are stored in the cell array Λ l Initialization: l = 0, R l =S′,

[0019] Step 4.2: Let l = l + 1;

[0020] Step 4.3: Calculate the weighted projection matrix G, G = W⊙P, where P = abs[(Φ H R l-1 )],() H represents the conjugate transpose of the matrix, and ⊙ represents the Hadamard product.

[0021] Step 4.4: Note that the largest element in G is located in the pth row and qth column of matrix G. Update the cell array and store the pth column of the sensor matrix Φ into the qth cell array, denoted as Λ l {q}=Λ l-1 {q}∪Φ col-p , where Φ col-p represents the p-th column of the perception matrix Φ.

[0022] Step 4.5: Compute the least squares solution Γ l =[(Λ l {q}) H Λ l {q}] -1 (Λ l {q}) H S′ col-q , where S′ col-q represents the qth column of S′.

[0023] Step 4.6: Update the signal to be reconstructed. in, Represents the cell array Λ l Index the updated element in the matrix.

[0024] Step 4.7: R l =R l-1 , then update the qth column of the residual matrix, R l-col-q =S′ col-q -Λ l {q}Γ l ;

[0025] Step 4.8: If || R l || F >ε holds true, return to step 4.2; otherwise, end the loop and output the target sparse reconstruction result

[0026] The beneficial effects of the present invention mainly include:

[0027] First, echo signal reconstruction is realized based on the principle of compressed sensing. The proposed support domain weighted constraint reduces the size of the solution space in the iterative optimization process and can improve the accuracy of target reconstruction under low sparsity conditions.

[0028] Second, when the designed two-stage ISAR imaging method is applied to the monitoring of space targets, it can greatly reduce the number of observation pulses, thereby increasing the number of targets monitored simultaneously and improving the utilization of radar resources.

Brief Description of the Drawings

[0029] Figure 1 This is the overall flow chart of echo signal processing.

[0030] Figure 2 Schematic diagram of radar imaging model.

[0031] Figure 3 Schematic diagram of the simulation target model.

[0032] Figure 4 This is the imaging result of the full-aperture data FFT method.

[0033] Figure 5 It is the signal support domain.

[0034] Figure 6 Comparison of imaging results under different parameter conditions. [Specific implementation method]

[0035] The purpose of the present invention is to improve the image reconstruction effect under sparse aperture conditions. A two-stage ISAR imaging method based on support domain weighted two-dimensional compressed sensing reconstruction is proposed. Figure 1 This is the overall flow chart of echo signal processing.

[0036] The following is combined with Figure 1-6 , the method proposed by the present invention is further described, and the specific steps and effects are as follows:

[0037] Step 1: Build a radar imaging model

[0038] The radar imaging model adopts the classic turntable model, and the scene settings are as follows: Figure 2 As shown. The rectangular coordinate system xOy is established with the target mass center O as the origin, and the distance between the radar and the target mass center is R 0 Assuming that the target translation has been accurately compensated, the target motion is converted into a rotation around the target center of mass with an angular velocity ω.

[0039] Assume that the transmitted signal is a linear frequency modulation signal, which can be expressed as:

[0040]

[0041] Where j represents the imaginary unit, f 0 is the signal carrier frequency, k is the frequency modulation slope, is the fast time variable, T is the pulse width, and the signal bandwidth is B = kT. m =mT d is the slow time variable, where T d is the pulse repetition interval, m is the pulse number, satisfying 0≤m<M, and M is the total number of pulses for imaging observation. is the full time, satisfying 0≤t≤T A , where T A =MT d is the total imaging observation time.

[0042] Assume that the imaging target is N T scattering points, for the i-th scattering point P(x i ,y i ), assuming that its equivalent rotation within a pulse repetition interval can be ignored, at t m The distance from the radar at the moment is:

[0043] Ri (t m )=R 0 +y i cos(ωt m )+x i sin(ωt m ) (2)

[0044] Since the target rotation angle is small during the imaging observation, the above formula can be written as:

[0045] R i (t m )=R 0 +y i +x i ωt m (3)

[0046] The target echo can be expressed as:

[0047]

[0048] Among them, A i is the echo amplitude, and c is the electromagnetic wave propagation velocity.

[0049] Assume the radar sampling rate is f s , then the number of sampling points in a single pulse is N = f s T. Receive t m After the target signal echoes at the instant, the one-dimensional range image sequence of the target is obtained by performing range Dechirp processing and inverse Fourier transform. After obtaining the slow time-range image sequence of the target, envelope alignment and phase correction are performed, and the processed range image sequence is recorded as an M×N matrix S.

[0050] S=[s 0 ,s 1 ,…,s M-1 ] T (5)

[0052] Among them, s m is an N×1 range image sequence.

[0053] According to the ISAR imaging principle, the two-dimensional image of the target can be obtained by performing discrete Fourier transform (DFT) on the slow time sequence after envelope alignment, that is,

[0054] S 2D =ξS (6)

[0056]

[0057] Where ξ is the M×M DFT transformation matrix, W M =exp(-j2π / M);

[0058] Step 2: Construct a weighting function based on FFT imaging results

[0059] The method of extracting the signal support domain from the target image and constructing the weighting function is as follows:

[0060] Calculate the mean of all pixels, denoted as E,

[0061] The detection threshold is denoted as T h , calculated as follows:

[0062]

[0063] Among them, σ is the proportionality coefficient, σ>0.

[0064] M×M mask matrix Ω 0 It is expressed as:

[0065]

[0066] The morphological method is used to remove discrete points and finally the signal support domain Ω is obtained.

[0067] From formula (6), we can see that the matrix S 2D The atoms in the mth row and nth column in the mth direction represent the high-resolution range image corresponding to the nth distance unit in the mth direction. In the present invention, the weighting matrix W constrains the solution space in the form of Hadamard product, so the atoms in the weighting matrix and S 2D The atoms in the weight matrix are one-to-one corresponding to each other. The atoms in the mth row and nth column are represented as:

[0068] W(m,n)=α·Ω(m,n)+ζ (10)

[0069] Among them, α is the proportionality coefficient, α>0. ζ represents a very small quantity, ζ>0.

[0070] The weighting function allows the scattering points in the signal support domain to be reconstructed first when the OMP optimization algorithm is used for iterative solution, while also reducing the reconstruction of erroneous scattering points caused by noise signals or sidelobe signals of strong scattering points.

[0071] Step 3: Build a compressed sensing imaging model

[0072] According to the theory of compressed sensing, sparse signals can be accurately reconstructed using sampling signals below the Nyquist sampling rate. According to the theory of electromagnetic scattering, the target imaging result in the high-frequency region can be equivalent to a set of finite strong scattering points, which naturally satisfies the sparsity constraint of the compressed sensing theory. The sparse aperture model and sparse reconstruction model are constructed below.

[0073] Step 3.1: Construct a sparse aperture model of the echo signal

[0074] Compared with the complete aperture echo, the sparse aperture model lacks some azimuth data, which is discontinuous in the slow time domain. The sparsely distributed effective aperture data S′ can be represented as a discrete sampling of the matrix S:

[0075] S′=PS (11)

[0076]

[0077] Where P is a Q×M dimensional measurement matrix.

[0078] Step 3.2: Build a sparse reconstruction model

[0079] The sparse reconstruction model can be expressed as:

[0080] S′=PS=PΨS 2D =ΦS 2D (13)

[0081] Where Ψ=ξ -1 is the sparse transformation basis, Φ is the perception matrix, Φ=PΨ.

[0082] The reconstruction result of ISAR image is recorded as It can be obtained by solving the following underdetermined system of equations:

[0083]

[0084] The sparse reconstruction result of the target can be obtained by solving the following sparse optimization problem:

[0085]

[0086] Among them, ||·|| F represents the Frobenius norm of the matrix, and ε is the noise tolerance. Under the assumption of Gaussian white noise, the estimation of the pure noise pixel amplitude of the FFT imaging result of stage 1 can be used as the noise tolerance ε.

[0087] Step 4: Reconstruct radar image using weighted constrained compressed sensing algorithm

[0088] The specific process of the weighted 2D-OMP reconstruction algorithm is as follows:

[0089] Input: effective aperture data S′, perception matrix Φ, weighting matrix W, noise tolerance ε

[0090] Output: target sparse reconstruction result

[0091] Step 4.1: The loop count is recorded as l and the residual matrix is ​​recorded as R l , the selected basis vectors in the perception matrix Φ are stored in the cell array Λ l Initialization: l = 0, R l =S′,

[0092] Step 4.2: Let l = l + 1;

[0093] Step 4.3: Solve P = abs[(Φ H R l-1 )], G = W⊙P, where () H represents the conjugate transpose of the matrix, and ⊙ represents the Hadamard product.

[0094] Step 4.4: Note that the largest element in G is located in the pth row and qth column of the matrix. Update the cell array Λ l {q}=Λ l-1 {q}∪Φ col-p , where Φ col-p represents the p-th column of the perception matrix Φ.

[0095] Step 4.5: Γ l =[(Λ l {q}) H Λ l {q}] -1 (Λ l {q}) H S′ col-q , where S′ col-q represents the qth column of S′.

[0096] Step 4.6: Update the signal to be reconstructed. in Represents the cell array Λ l Index the updated element in the matrix.

[0097] Step 4.7: R l =R l-1 , then update the qth column of the residual matrix, R l-col-q =S′ col-q -Λ l {q}Γ l

[0098] Step 4.8: If || R l || F >ε holds true, return to step 4.2; otherwise, end the loop and output the target sparse reconstruction result

[0099] This completes the entire process of radar image compressed sensing reconstruction based on signal support domain weighted constraints.

[0100]

Simulation experiment

[0101] Experimental scenario and radar parameter setting: The present invention sets a satellite model as an imaging target, such as Figure 3 As shown. The sweep frequency range of the radar pulse is 8 to 12 GHz, the sweep frequency interval is 0.025 GHz, the azimuth sweep angle range is -15° to 15°, the sweep angle interval is 0.075°, and the elevation angle is 30°. The radar receiver echo signal-to-noise ratio is set to 10 dB. The imaging results based on the FFT method of the full aperture are shown in Figure 4 As shown. Based on this, the signal support domain extracted is as follows Figure 5 shown.

[0102] The sparsity is set to 40%, 20% and 10% respectively, and the imaging results of the traditional OMP method and the method proposed in the present invention are shown in Figure 2. Figure 6 The simulation results show that when the azimuth aperture data sparsity is reduced to 10% and the signal-to-noise ratio is 10 dB, the method proposed in the present invention can still obtain good imaging results. In addition, compared with the traditional OMP method, the number of false points in the reconstruction results of this method is greatly reduced.

Claims

1. A two-stage ISAR imaging method based on domain-weighted two-dimensional compressed sensing reconstruction, characterized in that: The steps include: Step 1: Construct a radar imaging model; the radar imaging model adopts a classic turntable model, and the scene setting establishes a rectangular coordinate system xOy with the target mass center O as the origin, and the distance between the radar and the target mass center is R0; it is assumed that the target translation has been accurately compensated, and the target's movement is converted into a rotation around the target mass center at an angular velocity ω; Step 2: Construct the signal support domain based on the FFT imaging results; set the detection threshold T according to the mean value of all pixels in the imaging results of the FFT method h , the set obtained after removing the discrete points from the points that pass the threshold is recorded as the signal support domain, and the weighting function is obtained; Step 3: constructing a compressed sensing imaging model; including: constructing a sparse aperture model of the echo signal and constructing a sparse reconstruction model; Step 4: Use the weighted constrained compressed sensing algorithm to reconstruct the radar image.

2. According to the two-stage ISAR imaging method of domain weighted two-dimensional compressed sensing reconstruction in claim 1, in step 1, the transmission signal is a linear frequency modulation signal, which is expressed as: in, j represents the imaginary unit, f0 is the signal carrier frequency, k is the frequency modulation slope, is a fast time variable, T is the pulse width, and the signal bandwidth is B = kT; t m =mT d is the slow time variable, where T d is the pulse repetition interval, m is the pulse number, satisfying 0≤m<M, and M is the total number of pulses for imaging observation; is the full time, satisfying 0≤t≤T A , where T A =MT d is the total imaging observation time.

3. A two-stage ISAR imaging method based on domain-weighted two-dimensional compressed sensing reconstruction according to claim 2, characterized in that: N T scattering points, for the i-th scattering point P(x i ,y i ), assuming that the equivalent rotation within a pulse repetition interval can be ignored, at t m The distance from the radar at the moment is: R i (t m )=R0+y i cos(ωt m )+x i sin(ωt m )。 4. The two-stage ISAR imaging method of domain weighted two-dimensional compressed sensing reconstruction according to claim 3 is characterized by: The target echo is expressed as: Among them, A i is the echo amplitude, and c is the electromagnetic wave propagation velocity.

5. The two-stage ISAR imaging method of domain weighted two-dimensional compressed sensing reconstruction according to claim 4 is characterized in that: The radar sampling rate is f s , then the number of sampling points in a single pulse is N = f s T; received t m After the target signal echoes at the moment, the one-dimensional range image sequence of the target is obtained by performing range Dechirp processing and inverse Fourier transform. After obtaining the slow time-range image sequence of the target, envelope alignment and phase correction are performed, and the processed range image sequence is recorded as an M×N matrix S; S=[s0,s1,…,s M-1 ] T Among them, s m is an N×1 range image sequence; According to the ISAR imaging principle, the two-dimensional image of the target is obtained by performing discrete Fourier transform on the slow time sequence after envelope alignment, that is, S 2D =ξS。 6. The two-stage ISAR imaging method of domain weighted two-dimensional compressed sensing reconstruction according to claim 1, characterized in that: In step 2, the mean of all pixels is calculated, denoted as E. The detection threshold is denoted as T h , calculated as follows: Among them, σ is the proportionality coefficient, σ>0; The M×M mask matrix Ω0 is expressed as: The morphological method is used to remove discrete points and finally the signal support domain Ω is obtained.

7. The two-stage ISAR imaging method of domain weighted two-dimensional compressed sensing reconstruction according to claim 6, characterized in that: Matrix S 2D The atom in the mth row and nth column represents the high-resolution range image corresponding to the nth distance unit in the mth azimuth direction; The weighted matrix W constrains the solution space in the form of a Hadamard product, so the atoms in the weighted matrix are 2D The atoms in are in one-to-one correspondence in position; the atoms in the mth row and nth column of the weighted matrix are represented as: W(m,n)=α·Ω(m,n)+ζ Among them, α is the proportional coefficient, α>0; ζ represents a very small quantity, ζ>0.

8. According to the two-stage ISAR imaging method of domain weighted two-dimensional compressed sensing reconstruction in claim 1, in step three, a sparse aperture model of the echo signal is constructed: The sparsely distributed effective aperture data S′ is represented as a discrete sampling of the matrix S: S′=PS in, P is a Q×M dimensional measurement matrix.

9. According to the two-stage ISAR imaging method of domain weighted two-dimensional compressed sensing reconstruction according to claim 1 or 8, in step three, a sparse reconstruction model is constructed: The sparse reconstruction model is expressed as: S′=PS=PΨS 2D =ΦS 2D in, Ψ=ξ -1 is the sparse transformation basis, Φ is the perception matrix, Φ=PΨ; The reconstruction result of ISAR image is recorded as By solving the following underdetermined system of equations: The sparse reconstruction result of the target is obtained by solving the following sparse optimization problem: Among them, ||·|| F represents the Frobenius norm of the matrix, and ε is the noise tolerance. Under the assumption of Gaussian white noise, the estimation of the pure noise pixel amplitude of the FFT imaging result of stage 1 is used as the noise tolerance ε.

10. The two-stage ISAR imaging method of domain weighted two-dimensional compressed sensing reconstruction according to claim 1, characterized in that: In step 4, a weighted compressed sensing algorithm is used to achieve two-dimensional image reconstruction, which is hereinafter referred to as the 2D-OMP reconstruction algorithm. The specific process is as follows: Input: effective aperture data S′, perception matrix Φ, weighting matrix W, noise tolerance ε; Output: target sparse reconstruction result Step 4.1: The loop count is recorded as l and the residual matrix is ​​recorded as R l , the selected basis vectors in the perception matrix Φ are stored in the cell array Λ l In; Initialization: l = 0, R l =S′, Step 4.2: Let l = l + 1; Step 4.3: Calculate the weighted projection matrix G, G = W⊙P, where P = abs[(Φ H R l-1 )],() H represents the matrix conjugate transpose, ⊙ represents the Hadamard product; Step 4.4: Note that the largest element in G is located in the pth row and qth column of the matrix G; update the cell array and store the pth column of the sensor matrix Φ into the qth cell array, denoted as Λ l {q}=Λ l-1 {q}∪Φ col-p , where Φ col-p represents the p-th column of the perception matrix Φ; Step 4.5: Compute the least squares solution Γ l =[(Λ l {q}) H Λ l {q}] -1 (Λ l {q}) H S′ col-q , where S′ col-q represents the qth column of S′; Step 4.6: Update the signal to be reconstructed. in, Represents the cell array Λ l The updated element in the matrix obtained by indexing; Step 4.7: R l =R l-1 , then update the qth column of the residual matrix, R l-col-q =S′ col-q -Λ l {q}Γ l ; Step 4.8: If || R l || F >ε holds true, return to step 4.2; otherwise, end the loop and output the target sparse reconstruction result

Images