A two-stage ISAR imaging method supporting domain-weighted two-dimensional compressive sensing reconstruction

Abstract

The application provides a two-stage ISAR imaging method of domain-weighted two-dimensional compressed sensing reconstruction, which comprises the following steps: step one: constructing a radar imaging model; the radar imaging model adopts a classical turntable model; step two: constructing a signal support domain based on an FFT imaging result; a detection threshold T is set according to the mean value of all pixel points in the imaging result of the FFT method h The set obtained after removing the points exceeding the threshold and discrete points is recorded as a signal support domain, and a weighting function is obtained; step three: constructing a compressed sensing imaging model; including: constructing a sparse aperture model of echo signals and constructing a sparse reconstruction model; step four: implementing radar image reconstruction by using a compressed sensing algorithm with a weighting constraint. The application improves the accuracy of sparse aperture image reconstruction for a target with a stable flight attitude, can greatly reduce the number of observation pulses, thereby improving the number of simultaneously monitored targets and the utilization rate of radar resources.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of radar signal processing, and relates to a sparse-aperture imaging processing method for inverse synthetic aperture radar (ISAR), in particular to a two-stage ISAR imaging method based on support-domain weighted two-dimensional compressive sensing reconstruction.

BACKGROUND

[0002] The compressed sensing (CS) theory proves that the signal with sparsity in a certain signal domain can be accurately reconstructed with high probability by using the data observed with a sampling rate lower than the Nyquist sampling theorem (see the literature: “D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory, vol. 52, no. 4, pp. 1289-1306, 2006.” Donoho's paper: Compressed sensing). The high-frequency region of the two-dimensional imaging result can be equivalent to a limited 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 exactly meets the requirement of the 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 restricted isometry property for random matrices). Therefore, the CS method can be used to solve the image reconstruction problem under the condition of sparse aperture. There are various classical algorithms based on CS that can be used to solve the sparse aperture imaging problem. Among them, the Orthogonal Matching Pursuit (OMP) algorithm applies the iterative strategy of greedy optimization, has the advantages of small calculation amount and high reconstruction efficiency, and is widely used in the field of radar signal processing and imaging (see the literature “J. A. Tropp, A. C. Gilbert, “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 traditional OMP algorithm includes the whole imaging area. However, according to the sparse characteristics of the target scattering points, the solution space is much larger than the area of the real scattering points. When solving the short aperture imaging problem, Zhang Lei proposed to introduce the imaging result based on the FFT method into the OMP reconstruction algorithm as prior information, which improved the reconstruction effect under the condition of low signal-to-noise ratio (SNR) (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 thesis: Resolution enhancement for inversed synthetic aperture radar imaging under low SNR via improved compressive sensing). On this basis, Cheng Kai improved the weighted function designed according to the imaging result based on the FFT method (see the patent: Yang Shuyuan, Jiao Li Cheng, Cheng Kai, etc. ISAR imaging method based on weighted L1 optimization and visual significant attention, patent acceptance number: 2014102400723).

[0004] For the sparse aperture imaging problem of the target with stable flight attitude, the present application designs a two-stage ISAR imaging method of support domain weighted two-dimensional compressive sensing reconstruction, which improves the image reconstruction quality under low sparsity.

SUMMARY

[0005] The present application aims at the problems of the prior art and designs a two-stage ISAR imaging method of support domain weighted two-dimensional compressive sensing reconstruction. The specific content is as follows: based on the principle of compressive sensing, a two-stage ISAR imaging method is proposed for the sparse aperture imaging problem. In the first stage, the imaging result of the complete aperture is used to extract the image support domain and construct a weighted function. In the second stage, the prior information is used to weight the compressive sensing reconstruction process. The present application improves the accuracy of sparse aperture image reconstruction for the target with stable flight attitude.

[0006] In order to achieve the above purpose, the technical scheme adopted by the present application is as follows:

[0007] Step one: constructing a radar imaging model;

[0008] Step two: constructing a signal support domain based on the FFT imaging result;

[0009] Step three: build the compressed sensing imaging model;

[0010] Step four: realize radar image reconstruction by using the weighted constraint compressed sensing algorithm;

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

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

[0013] The specific process of step three is as follows:

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

[0015] The two-dimensional image reconstruction algorithm based on the weighted compressed sensing algorithm in step four is called 2D-OMP reconstruction algorithm, and the specific process is as follows:

[0016] Input: valid aperture data S', sensing matrix Φ, weighting matrix W, and noise tolerance ε;

[0017] Output: target sparse reconstruction result

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

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

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

[0021] Step 4.4: record that the maximum 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 sensing matrix Φ in the qth cell array, denoted as Λ l {q}=Λ l-1 {q}∪Φ col-p , where Φ col-p represents the pth column of the sensing matrix Φ.

[0022] Step 4.5: Calculate the least square solution 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, where represents the updated element in the matrix obtained according to the cell array l index.

[0024] Step 4.7: R l = R l-1 , and 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 > epsilon is true, return to step 4.2; otherwise, end the loop and output the target sparse reconstruction result

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

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

[0028] Second, when the two-stage ISAR imaging method is applied to the monitoring of space targets, the number of observation pulses can be greatly reduced, thereby improving the number of simultaneously monitored targets and the utilization rate of radar resources. BRIEF DESCRIPTION OF DRAWINGS

[0029] Figure 1 is a general flowchart of echo signal processing.

[0030] Figure 2 is a schematic diagram of a radar imaging model.

[0031] Figure 3 is a schematic diagram of a simulation target model.

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

[0033] Figure 5 The signal support domain is constructed.

[0034] Figure 6 The imaging results under different parameter conditions are compared.

DETAILED DESCRIPTION

[0035] The purpose of the present application is to improve the image reconstruction effect under the condition of sparse aperture. A two-stage ISAR imaging method of support domain weighted two-dimensional compressive sensing reconstruction is proposed, Figure 1 The overall flowchart of echo signal processing is shown.

[0036] The specific steps and effects of the method are as follows: Figures 1-6 The specific steps and effects of the method are as follows:

[0037] Step 1: Constructing a radar imaging model

[0038] The radar imaging model adopts a classic turntable model, and the scene setting is as shown in the figure. Figure 2 A rectangular coordinate system x-O-y is established with the target centroid O as the origin, and the distance between the radar and the target centroid is R0. It is assumed that the target translation has been accurately compensated, and the target motion is converted into rotation around the target centroid with an angular velocity ω.

[0039] It is assumed that the transmitted signal is a linear frequency modulation signal, which is represented as:

[0040]

[0041] Where j represents the imaginary unit, f0 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, and satisfies 0≤m<M, M is the total number of imaging observations. is the total time, which satisfies 0≤t≤T A , where T A = MT d is the total imaging observation time.

[0042] Suppose the imaging target is composed of N T scattering points, for the i-th scattering point P(x i , y i ), it is assumed that the equivalent rotation of the target within a pulse repetition interval can be ignored, and the distance between the radar and the target at time t m is:

[0043] R i (t m) = R0 + y i cos(ωt m )+x i sin(ωt m ) (2)

[0044] Since the target rotates a small angle during the imaging observation, the above equation can be written as:

[0045] R i (t m ) = R0 + y i +x i ωt m (3)

[0046] The target echo can be expressed as:

[0047]

[0048] where A i is the echo amplitude, and c is the electromagnetic wave propagation rate.

[0049] Assuming that the radar sampling rate is f s , the number of sampling points within a single pulse is N = f s T. After receiving the target signal echo at time t m , distance Dechirp processing and inverse Fourier transform are performed to obtain a one-dimensional range image sequence of the target. 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 denoted as an MxN matrix S.

[0050] S = [s0, s1, …, s M-1 ] T (5)

[0052] where s m is an Nx1 range image sequence.

[0053] According to the ISAR imaging principle, a discrete Fourier transform (DFT) is performed on the envelope-aligned slow-time sequence to obtain a two-dimensional image of the target, i.e.

[0054] S 2D = ξS (6)

[0056]

[0057] where ξ is an MxM DFT transform matrix, and W M = exp(-j2π / M);

[0058] Step two: constructing the weighting function based on the FFT imaging result

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

[0060] The mean value of all pixel points is calculated, denoted as E,

[0061] The detection threshold is denoted as T h , and the calculation method is as follows:

[0062]

[0063] Wherein, σ is a proportional coefficient, σ > 0.

[0064] The mask matrix Ω0 of MxM is represented 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), the atom in the mth row and the nth column of the matrix S 2D Corresponds to the high-resolution range image corresponding to the mth azimuth and the nth distance unit. In the present application, the weighting matrix W constrains the solution space in the form of Hadamard product, so the atom in the weighting matrix is one-to-one corresponding to the atom in S 2D . The atom in the mth row and the nth column of the weighting matrix is represented as:

[0068] W(m,n)=α·Ω(m,n)+ζ (10)

[0069] Wherein, α is a proportional coefficient, α > 0. ζ represents a small amount, ζ > 0.

[0070] The weighting function makes it possible to preferentially reconstruct the scattering points in the signal support domain when using the OMP optimization algorithm to iteratively solve, and also reduces the reconstruction of false scattering points caused by noise signals or sidelobe signals of strong scattering points.

[0071] Step three: constructing a compressed sensing imaging model

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

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

[0074] The sparse aperture model lacks some azimuth data compared to the complete aperture echo, 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 the 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 sensing 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 denotes the matrix conjugate transpose, and ⊙ denotes the Hadamard product.

[0094] Step 4.4: Let the largest element in G be located in the p-th row and the q-th column of the matrix. Update the cell array Λ l {q} = Λ l-1 {q} ∪ Φ col-p , where Φ col-p denotes the p-th column of the sensing 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 denotes the q-th column of S'.

[0096] Step 4.6: Update the signal to be reconstructed, where denotes the updated element in the matrix according to the cell array Λ l index.

[0097] Step 4.7: R l = R l-1 , and then update the q-th 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 is true, return to Step 4.2; otherwise, end the loop and output the target sparse reconstruction result

[0099] Thus, the entire process of radar image compressed sensing reconstruction based on signal support domain weighted constraint is completed.

[0100]

Simulation experiment

[0101] Experimental scenario and radar parameter setting: The present invention sets a satellite model as the imaging target, such as Figure 3 As shown in Figure 1. The radar transmit pulse sweep frequency range 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 of the full aperture based on the FFT method are shown in Figure 1. Figure 4 As shown. The signal support domain extracted on this basis 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 this invention are shown as follows: Figure 6 The simulation results show that when the azimuth aperture data sparsity is reduced to 10% and the signal-to-noise ratio is 10dB, the proposed method can still achieve 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 of domain-weighted two-dimensional compressive sensing reconstruction, characterized in that, Comprising the following steps: Step one: constructing a radar imaging model; the radar imaging model adopts a classic turntable model, a scene is set to establish a rectangular coordinate system x-O-y 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 movement is converted into rotation around the target mass center with an angular velocity ω; Step two: Construct the signal support domain based on the FFT imaging result; set the detection threshold T according to the mean value of all pixel points in the imaging result of the FFT method h The set obtained after removing the discrete points of the points exceeding the threshold is denoted as the signal support domain, and a weighting function is obtained; Step three: constructing a compressed sensing imaging model; comprising: constructing a sparse aperture model of echo signals and constructing a sparse reconstruction model; Step four: implementing radar image reconstruction using a weighted constraint compressed sensing algorithm; in step four, a two-dimensional image reconstruction algorithm using a weighted compressed sensing algorithm is implemented, hereinafter referred to as 2D-OMP reconstruction algorithm, and the specific process is as follows: Input: effective aperture data S', sensing matrix Φ, weighting matrix W, and noise tolerance ε; Output: Target sparse reconstruction result Step 4.1: Cycle count is denoted by / , residual matrix is denoted by R l ; selected basis vectors in the perception matrix Φ are stored in the cell array Λ l ; initialization: / = 0, R l = S', Step 4.2: let l = l + 1; Step 4.3: Compute the weighted projection matrix G, G = W ® P, where P = abs[(Φ H R l-1 )],() H denotes matrix conjugate transpose, ® denotes Hadamard product; Step 4.4: The maximum 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 sensing matrix Φ into the qth cell array, denoted as Λ l {q} = Λ l-1 {q}∪Φ col-p wherein, Φ col-p denotes the pth column of the sensing matrix Φ; Step 4.5: Compute least squares solution Γ l = [(Λ l {q}) H Λ l {q}] -1 (Λ l {q}) H S′ col-q where S′ col-q denotes the qthcolumn of S′; Step 4.6: update the signal to be reconstructed, wherein, represents the matrix obtained from the array of cells Λ l the element in the matrix that is updated according to the index. Step 4.7: R l = R l-1 Then update the qth column of the residual matrix, R l-col-q = S' col-q - A l {q}Γ l ; Step 4.8: If ||R l || F >ε holds, go to Step 4.2; otherwise end the loop and output the target sparse reconstruction result 2. The two-stage ISAR imaging method of domain-weighted two-dimensional compressed sensing reconstruction according to claim 1, in step one, the transmitted signal is a linear frequency modulation signal, denoted as: wherein j denotes the imaginary unit, f0is 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; 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 is the total time satisfying 0≤t≤T A , where T A = MT d is the total imaging observation time.

3. The two-stage ISAR imaging method of claim 2, wherein: Let the imaging target be composed of N T scattering points, for the i-th scattering point P(x i ,y i ), let its equivalent rotation amount in a pulse repetition interval be negligible, and the distance between it and the radar at time t m be: R i (t m )=R0+y i cos(ωt m )+x i sin(ωt m )。 4. The two-stage ISAR imaging method of claim 3, wherein: The target echo is denoted as: where A i is the echo amplitude, c is the electromagnetic wave propagation rate.

5. The two-stage ISAR imaging method of claim 4, wherein The radar sampling rate is f s The number of sampling points within a single pulse is N = f s T; the target signal echo is received at t m The one-dimensional range image sequence of the target is obtained after the distance Dechirp processing and the inverse Fourier transform. After obtaining the target slow-time-range image sequence, envelope alignment and phase correction are performed, and the processed range image sequence is denoted as an M×N matrix S; S = [s0, s1,..., s M-1 ] T where s m is a sequence of range images of size N x 1; According to the ISAR imaging principle, the slow-time sequence after envelope alignment is subjected to discrete Fourier transform to obtain a two-dimensional image of the target, i.e., S 2D = ξS.

6. The two-stage ISAR imaging method of claim 5, wherein: In step two, the mean value of all pixel points is calculated, denoted as E, The detection threshold is denoted as T h , and the calculation is as follows: Where σ is a proportional coefficient, σ > 0; The M×N mask matrix Ω0 is denoted as: The morphological method is used to remove discrete points, and finally the signal support domain Ω0 is obtained.

7. The two-stage ISAR imaging method of claim 6, wherein: Matrix S 2D The atom in the mth row and nth column of the matrix S represents the high-resolution range profile corresponding to the nth range cell of the mth azimuth direction. The weight matrix W constrains the solution space in a Hadamard product fashion, so that atoms in the weight matrix are one-to-one corresponding to atoms in S 2D The atom in the mth row and nth column in the weight matrix is denoted as: W(m,n)=α·Ω0(m,n)+ζ Where α is a proportional coefficient, α > 0; ζ represents a very small amount, ζ > 0.

8. The two-stage ISAR imaging method of domain-weighted two-dimensional compressed sensing reconstruction according to claim 1, in step three, a sparse aperture model of echo signals is constructed: The sparse distribution of effective aperture data S' is denoted as a discrete sampling of matrix S: S' = PS wherein P is a Q×M measurement matrix.

9. The two-stage ISAR imaging method of domain-weighted two-dimensional compressed sensing reconstruction according to claim 8, in step three, a sparse reconstruction model is constructed: The sparse reconstruction model is denoted as: S' = PS = P Ψ S 2D = ΦS 2D wherein, Ψ = ξ -1 Ψ is a sparse transform basis, and Φ is a perceptual matrix, Φ = PΨ. The reconstruction result of ISAR image is denoted as The underdetermined equations are solved to obtain 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 noise tolerance ε is estimated by estimating the amplitude of the pure noise pixel in the FFT imaging result.

Images