A multi-basis SAR imaging method based on spectrum correction

Abstract

The application discloses a multi-base SAR imaging method based on spectrum correction. Firstly, a multi-base SAR system echo model is constructed, reasons for non-ideal wave number spectrum distribution are analyzed, a wave number spectrum correction problem is constructed, a windowing correction is performed on the non-ideal wave number spectrum to improve imaging performance, the wave number spectrum correction problem is converted into a constrained multi-objective optimization problem, finally, a multi-objective particle swarm optimization algorithm is adopted to perform optimization and solving, and high-quality imaging is realized when the wave number spectrum distribution is irregular. The method of the application corrects the wave number spectrum by using an optimized parallelogram window. By reasonably correcting the wave number spectrum, data loss can be reduced while maintaining high resolution, thereby improving imaging performance. The method overcomes the problem of non-ideal spatial spectrum distribution caused by the special configuration of the multi-base SAR and the problem of imaging quality decline caused thereby, and ensures that high-quality SAR imaging results can be obtained even under complex conditions.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of radar imaging, and particularly relates to a multi-base SAR imaging method based on spectrum correction. BACKGROUND

[0002] As a new radar system, multi-base SAR can observe targets from multiple angles and obtain high-resolution imaging results in a short time. Compared with existing single-base SAR and double-base SAR, the working mode of multi-base SAR is more flexible, has higher concealment and safety, and has important application potential in the fields of cooperative target positioning, anti-interference, etc. However, in actual application, due to different configurations of multi-base SAR, the distribution of wave number spectrum may be different. When the initial spatial position and initial velocity vector between platforms differ too much, the distribution of wave number spectrum may become undesirable, thereby affecting the image quality. Therefore, it is of great significance to study the realization of high-quality imaging under the condition of undesirable wave number spectrum distribution.

[0003] The echo data of multi-static SAR can be accumulated by coherent or incoherent fusion. Non-coherent multi-static SAR ignores the complexity of the relative positions between multiple stations, which can improve the signal-to-noise ratio of the image, but cannot substantially improve the resolution. The imaging quality of coherent multi-static SAR is closely related to the distribution of the wave number spectrum. The document“D. Mao, Y. Zhang, J. Pei, W. Huo, Y. Zhang, Y. Huang, and J. Yang, 'Forward-looking geometric configuration optimization design for spaceborne-airborne multistatic synthetic aperture radar', IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, vol. 14, pp. 8033-8047, 2021” proposes a coherent multi-static SAR configuration design method, which evaluates the distribution of the wave number spectrum to reflect the performance of the spatial configuration, and obtains good imaging results. The document“F. Xu et al., 'Spatial Configuration Design for Multistatic Airborne SAR Based on Multiple Objective Particle Swarm Optimization', in IEEE Transactions on Geoscience and Remote Sensing, vol. 61, pp. 1-17, 2023, Art no. 5219917” proposes a configuration design method based on wave number spectrum generation, which can improve the spatial resolution of multi-static SAR. The above two methods are to optimize the distribution of the wave number spectrum to improve the spatial resolution of multi-static SAR. However, in practical applications, when the configuration is fixed, the wave number spectrum with an undesirable distribution may lead to a decline in imaging quality, thereby affecting the entire imaging result. SUMMARY

[0004] To solve the above technical problems, the present application proposes a multi-static SAR imaging method based on spectrum correction, which converts the wave number spectrum correction problem into a constrained multi-objective optimization problem, solving the problem of low imaging quality caused by the undesirable distribution of the wave number spectrum due to the (general) system configuration.

[0005] The technical scheme adopted by the present application is as follows: a multi-static SAR imaging method based on spectrum correction, the specific steps are as follows:

[0006] Step one, echo modeling of multi-baseline SAR system;

[0007] According to the geometric model of multi-baseline SAR system, a Cartesian coordinate system is established with O as the origin. The starting positions of the transmitter and the nth receiver are (x T ,y T ,z T ) and (x Rn ,y Rn ,z Rn ); P represents an arbitrary point target in the imaging scene, whose coordinates are (x p ,y p ,0), and α T ,α Rn represent the pitch angles of the transmitter and the nth receiver; θ T ,θ Rn represent the azimuth angles of the transmitter and the nth receiver.

[0008] The transmitter transmits a linear frequency modulation signal. For the nth receiver, the echo signal of the target point P is pulse compressed and coherently processed with the echo data of the reference target O located at the origin, and the expression is as follows:

[0009]

[0010] Where f, τ represent the distance frequency domain variable and the azimuth time variable respectively, A, T a ,c,T r ,K r ,f c represent the signal amplitude, synthetic aperture time, electromagnetic wave velocity, pulse width, frequency modulation slope and carrier frequency of the transmitted signal respectively, and R nP (τ) and R nO (τ) represent the distance history and of the target point P and the reference point O to the transmitter and the nth receiver respectively.

[0011] According to the far field approximation, the approximate expression of the distance history difference between the target point P and O is as follows:

[0012]

[0013] According to formula (1) and formula (2), the signal is mapped from the distance frequency domain azimuth time domain to the wave number domain through variable transformation, and the expression is as follows:

[0014] s n (k x ,k y )=A n ·exp[j(x p k x +y p k y )] (3)

[0015] where k x ,k y are two spatial frequency variables in the wave-number domain, which vary with the frequency of the transmitted signal and the relative position between the platforms, A n = A rect(τ / T a ) rect(f / k r T r ) represents the signal envelope. k x ,k y The expression is as follows:

[0016]

[0017] Step two, modeling the wave-number spectrum correction problem;

[0018] The wave-number spectrum formed by each receiver is approximately a parallelogram. When the velocity and initial position between the platforms differ greatly, the wave-number spectrum distribution is not ideal. Then the wave-number spectrum is corrected as follows:

[0019] By adding a window and only retaining the wave-number spectrum data within the window, while removing the undesirable distribution part, the wave-number spectrum is more in line with the imaging requirements.

[0020] The shape of the window is defined as a parallelogram, and P c represents the coordinates of the four vertices and the center of the parallelogram window; θ w represents the angle between the two sides of the parallelogram window; B'1(w), B'2(w) represent the height of the parallelogram window, which is proportional to the projection bandwidth of the corrected wave-number spectrum.

[0021] From the properties of the parallelogram, the shape and position of the window are determined by defining the coordinates of the center point P c and two adjacent points P1, P2. The construction parameters of the window are represented by the vector w, and the expression is as follows:

[0022] w = (k xc ,k yc ,k x1 ,k y1 ,k x2 ,k y2 ) (5)

[0023] where k xc ,k yc ,k x1 ,k y1 ,k x2 ,k y2 represent the coordinates of P c , P1, P2 in the wave-number domain.

[0024] Step three, the wave number spectrum correction problem is converted into a constrained multi-objective optimization problem.

[0025] The angle range of the window is limited and the relationship between B'1(w) and B'2(w) is adjusted, the angle of the window is constrained between 4π / 9 and 5π / 9, and the ratio of the larger value to the smaller value in B'1(w), B'2(w) is less than 1.5.

[0026] Then the wave number spectrum correction problem is converted into a constrained multi-objective problem, and the expression is as follows:

[0027]

[0028] Wherein, r1(w), r2(w) represent the projection bandwidth after wave number spectrum correction, η(w) represents the data quantity after wave number spectrum correction, S mWS (w), S W (w) represent the area of the corrected wave number spectrum and the area of the window, ψ represents the search space of w, k xc ,k x1 ,k x2 ∈[k xmin ,k xmax ], k yc ,k y1 ,k y2 ∈[k ymin ,k ymax ], k xmin ,k xmax ,k ymin ,k ymax represents the range boundary of the wave number domain in the k x ,k y direction.

[0029] Step four, solving the constrained multi-objective problem and high-quality imaging.

[0030] The multi-objective particle swarm optimization algorithm (MOPSO) is cited to solve the constrained multi-objective problem obtained in step three.

[0031] Firstly, the wave number spectrum correction problem is initialized, including: radar system parameters, platform initial position and velocity, vector w; and the particle swarm in MOPSO is initialized, including particle number M, maximum iteration number I max , inertia weight w.

[0032] Wherein, the radar system parameters include: signal carrier frequency, signal bandwidth, synthetic aperture time, pulse repetition time and pulse repetition frequency.

[0033] Then the objective function formula (6) of the particle is calculated and a pareto solution set is formed, before the iteration is terminated, the position and speed of the particle are updated, and the fitness of the particle is calculated, and the pareto optimal solution set is updated.

[0034] Finally, the optimized correction result is selected from the optimal solution set. By reasonably correcting the wave number spectrum, the data loss is reduced while maintaining high resolution, and the imaging performance is improved. Based on the corrected wave number spectrum, the polar coordinate multi-base SAR imaging algorithm is used to obtain the high-quality imaging result after optimization and correction.

[0035] The method of the present application first constructs a multi-base SAR system echo model, analyzes the reasons for the undesirable distribution of the wave number spectrum, constructs a wave number spectrum correction problem, and performs window correction on the undesirable wave number spectrum to improve the imaging performance. The wave number spectrum correction problem is converted into a constrained multi-objective optimization problem, and finally a multi-objective particle swarm optimization algorithm is used for optimization and solution. The present application realizes high-quality imaging when the wave number spectrum distribution is irregular. The method of the present application uses the optimized parallelogram window to correct the wave number spectrum. By reasonably correcting the wave number spectrum, the data loss can be reduced while maintaining high resolution, thereby improving the imaging performance. The present application overcomes the problem of undesirable spatial spectrum distribution caused by the special configuration of multi-base SAR and the resulting decline in imaging quality, and ensures that high-quality SAR imaging results can be obtained even under complex conditions. BRIEF DESCRIPTION OF DRAWINGS

[0036] Figure 1 The flowchart of the multi-base SAR imaging method based on spectrum correction of the present application.

[0037] Figure 2 The geometric configuration diagram of the multi-base SAR system in the embodiment of the present application.

[0038] Figure 3 The wave number spectrum diagram under the "one transmission and two reception" configuration in the embodiment of the present application.

[0039] Figure 4 The wave number spectrum diagram after windowing under the "one transmission and two reception" configuration in the embodiment of the present application.

[0040] Figure 5 The wave number spectrum and imaging result obtained by the original configuration and the wave number spectrum and imaging result of the two sets of correction windows under the "one transmission and four reception" configuration in the embodiment of the present application. DETAILED DESCRIPTION

[0041] The present application uses simulation experiments to demonstrate the effectiveness of the proposed method. All steps and conclusions of the present application are verified on the Matlab2023 simulation platform. The method of the present application will be further described in conjunction with the drawings and embodiments.

[0042] As Figure 1 shown, a spectrum correction-based multi-base SAR imaging method flow chart of the present application, the specific steps are as follows:

[0043] Step one, multi-base SAR echo modeling;

[0044] First, as Figure 2 shown, the multi-base SAR system geometry modeling is adopted, and the radar simulation parameters shown in Table 1 are selected.

[0045] Table 1

[0046]

[0047] This embodiment takes a multi-base SAR system composed of one transmitter and four receivers as an example, and establishes a Cartesian coordinate system with O as the origin. The starting positions and speeds of the transmitter and the four receiving stations are shown in Table 1; P represents an arbitrary point target in the imaging scene, whose coordinates are (x p ,y p ,0), α T ,α Rn represent the pitch angles of the transmitter and the nth receiver; θ T ,θ Rn represent the azimuth angles of the transmitter and the nth receiver.

[0048] The transmitter transmits a linear frequency modulation signal, and for the nth (n∈[1,2,3,4]) receiver, the echo signal of the target point P is expressed as follows after pulse compression and coherent processing with the echo data of the reference target O located at the origin:

[0049]

[0050] Where f,τ represent the distance frequency domain variable and the azimuth time variable respectively, A represents the amplitude of the echo signal, T a =1s represents the synthetic aperture time, c=3×10 8 m / s represents the electromagnetic wave speed, T r =2.5μs represents the pulse width, K r =7.2×10 13 Hz / s represents the frequency modulation slope, f c =9.6GHz represents the carrier frequency of the transmitted signal, R nP (τ) and R nO (τ) represent the distance history and of the target point P and the reference point O to the transmitter and the nth receiver, respectively.

[0051] According to the far field approximation, the distance history difference between the target point P and O is approximately expressed as follows:

[0052]

[0053] According to formula (7) and formula (8), the signal is mapped from the range frequency domain azimuth time domain to the wave number domain by variable transformation, and the expression is as follows:

[0054] s n (k x ,k y )=A n ·exp[j(x p k x +y p k y )] (9)

[0055] Wherein, k x ,k y It represents two spatial frequency variables in the wave number domain, which will change with the frequency of the transmitted signal and the relative position between the platform, A n =A·rect(τ / T a )·rect(f / k r T r ) represents the signal envelope. kx,ky expression is as follows:

[0056]

[0057] Step two, wave number spectrum correction problem modeling;

[0058] Due to the difference of the configuration of multi-base SAR, the distribution of wave number spectrum will also be different. This embodiment adopts one transmitting and two receiving wave number spectrum, as shown in Figure 3 , analyzes the influence of wave number spectrum distribution on imaging quality.

[0059] The wave number spectrum formed by each receiver is approximately a parallelogram, Figure 3 , f, τ represent the range frequency domain variable and azimuth time domain variable respectively; B1, B2 represent the projection bandwidth of wave number spectrum in the two directions respectively; θ1, θ2 represent the included angle of two parallelograms respectively; k xmin ,k xmax ,k ymin ,k ymax It represents the range boundary of wave number domain in k x ,k y Direction.

[0060] Under different wavenumber spectral distributions, the shape and size of the wavenumber spectrum are closely related to imaging quality. The included angle of the wavenumber spectrum parallelogram is affected by the platform velocity, which determines the included angle between the two resolution directions of the reconstructed PSF. If the included angle deviates too much from π / 2, it will cause coupling between the two sidelobes of the reconstructed PSF, thereby reducing imaging quality. In addition, if the spatial differences between platforms are too large, resulting in large differences in elevation and azimuth angles, the MuSAR wavenumber spectrum may exhibit a discontinuous distribution, leading to data loss, which will also seriously affect imaging quality, or even prevent imaging altogether.

[0061] In summary, when the speed and initial position of the platforms differ significantly, the wavenumber spectrum distribution will be suboptimal, leading to a decrease in imaging quality. In this case, wavenumber spectrum correction processing is required to improve imaging performance.

[0062] Specifically, by adding a window and retaining only the wavenumber spectrum data within the window while removing undesirable distributions, the wavenumber spectrum can be made more suitable for imaging requirements, thereby improving imaging performance.

[0063] right Figure 3 The wavenumber spectrum after windowing is as follows Figure 4 As shown, where P1, P2, P3, P4, P c Represents the coordinates of the four vertices and the center of the parallelogram window; θ w B'1(w) and B'2(w) represent the angle between the two sides of the parallelogram window; B'1(w) and B'2(w) represent the height of the parallelogram window, which is proportional to the projection bandwidth of the corrected wavenumber spectrum.

[0064] Since the wavenumber spectrum is approximately parallelogram-shaped, to ensure that the windowed wavenumber spectrum meets the high-quality imaging requirements of the analysis, the window shape is defined as a parallelogram. This is achieved by defining the center point P of the window. c The shape and position of the window can be determined by the coordinates of two adjacent points P1 and P2. The construction parameters of the window can be represented by the vector w, as shown in the following expression:

[0065] w=(k xc ,k yc ,k x1 ,k y1 ,k x2 ,k y2 (11)

[0066] Where, k xc ,k yc ,k x1 ,k y1 ,k x2 ,k y2 P represents c The coordinates of P1 and P2 in the wavenumber domain.

[0067] Step three, the wave number spectrum correction problem is converted into a constrained multi-objective optimization problem;

[0068] In order to correct the wave number spectrum, the following two key ideas are followed:

[0069] First, it is necessary to ensure that the resolution of the result is still high after the wave number spectrum is corrected. Since there is an inverse relationship between resolution and projection bandwidth, the correction operation may cause the resolution to decrease. Therefore, it is necessary to try to make the corrected wave number spectrum still have a large projection bandwidth, so as to minimize the loss of resolution.

[0070] Secondly, it is necessary to reduce the data missing between the corrected wave number spectra. This means that it is necessary to ensure that the ratio between the wave number spectrum data in the window and the total data contained in the window is high. In this way, the integrity and continuity of the imaging can be improved, and the imaging can be further improved.

[0071] In addition, in order to further optimize the imaging effect, the angle range of the window can also be limited and the relationship between B'1(w) and B'2(w) can be adjusted. The angle of the window is constrained between 4π / 9 and 5π / 9, and the ratio of the larger value to the smaller value in B'1(w), B'2(w) is less than 1.5. In this way, not only can the reconstructed PSF be ensured to be as orthogonal as possible, but also the two-dimensional resolution can be more balanced.

[0072] In summary, the wave number spectrum correction problem is converted into a constrained multi-objective problem, and the expression is as follows:

[0073]

[0074] where r1(w), r2(w) represent the projection bandwidth after the wave number spectrum is corrected, η(w) represents the data amount after the wave number spectrum is corrected, S mWS (w), S W (w) represent the area of the corrected wave number spectrum and the area of the window, ψ represents the search space of w, k xc ,k x1 ,k x2 ∈[k xmin ,k xmax ], k yc ,k y1 ,k y2 ∈[k ymin ,k ymax ].

[0075] Step four, solving the multi-objective constrained optimization problem and high-quality imaging;

[0076] The multi-objective particle swarm optimization algorithm (MOPSO) is used to solve the constrained multi-objective problem.

[0077] First, initialize the wave number spectrum correction problem, including radar system parameters, platform initial position and velocity, as shown in Table 1, and vector w; and initialize the particle swarm in MOPSO, including particle number M = 120, maximum iteration number I = 100, and inertia weight w = 0.5. max

[0078] The radar system parameters include signal carrier frequency, signal bandwidth, synthetic aperture time, pulse repetition time, and pulse repetition frequency.

[0079] Then, the objective function formula (12) of the particle is calculated, and a pareto solution set is formed. Before the iteration is terminated, the position and velocity of the particle are updated, the fitness of the particle is calculated, and the pareto optimal solution set is updated.

[0080] Finally, the optimized correction result is selected from the optimal solution set. By reasonably correcting the wave number spectrum, the data loss is reduced while maintaining high resolution, and the imaging performance is improved.

[0081] Two sets of optimized correction window results are obtained by MOPSO, as shown in Table 2, and the objective functions under the two sets of results are calculated.

[0082] Table 2

[0083] Correction window P c (k xc ,k yc )]]> [P1(k x1 ,k y1 )]]> [P2(k x2 ,k y2 )]]> [r1(w)] [r2(w)] η(w) w1 (205.4,319.7) (204.3,326.6) (212.4,319.9) 0.1082 0.0948 0.4018 w2 (205.9,319.7) (212.4,322.3) (203.4,326.2) 0.1020 0.1015 0.3906

[0084] Based on the corrected wave number spectrum, the polar coordinate multi-base SAR imaging algorithm is used to obtain the optimized and corrected high-quality imaging result.

[0085] In this embodiment, as shown in Figure 5 , the imaging result of the original configuration on the target point P(0, 0) is shown, and the imaging result after correction using the two sets of correction windows is shown. Figure 5 (a) and (d) are the wave number spectrum and the reconstructed PSF under the original configuration parameters. It can be seen that due to the large gap between the wave number spectrums, the main lobe of the reconstructed PSF is split and the sidelobe is high, and the imaging effect is poor. Figure 5 (b) and (e) are the wave number spectrum and the reconstructed PSF after w1 correction; Figure 5 (c) and (f) are the wave number spectrum and the reconstructed PSF after w2 correction. From Figure 5 (e) and Figure 5 (f), it can be seen that the reconstructed PSF obtained by the corrected wave number spectrum has good focusing effect.

[0086] ​Table 3 lists the performance indicators of the reconstructed PSF obtained from the original wave number spectrum, the wave number spectrum after the correction of w1 and w2, including the resolution in the range direction and the azimuth direction, PSLR and ISLR. It can be seen that after the correction, the resolution in the range direction is reduced from 0.24 m to 0.4 m, and the resolution in the azimuth direction is reduced from 0.27 m to 0.3 m. Although the resolution is reduced, the PSLR and ISLR in the range direction and the azimuth direction are improved. This shows that the corrected result improves the imaging quality at the cost of a certain resolution.

[0087] Table 3

[0088] Indicator Original result the result corrected by w1 the result corrected by w2 Range resolution 0.24m 0.41m 0.42m Range PSLR -11.05 dB -13.47 dB -13.61 dB Range ISLR -8.34 dB -9.91 dB -9.99 dB Azimuth resolution 0.27m 0.31m 0.30m Azimuth PSLR -14.11 dB -17.57 dB -18.69 dB Azimuth ISLR -11.12 dB -12.75 dB -13.13 dB

[0089] In summary, the method of the present application corrects the wave number spectrum by using the optimized parallelogram window. By reasonably correcting the wave number spectrum, the data loss can be reduced while maintaining high resolution, thereby improving the imaging performance. The problem of unsatisfactory spatial spectrum distribution caused by the special configuration of multi-base SAR and the resulting decline in imaging quality is overcome, and high-quality SAR imaging results can be obtained even under complex conditions.

[0090] Those skilled in the art will realize that the embodiments described herein are for the purpose of helping the reader understand the principles of the present application and should be understood as not limiting the scope of protection of the present application to such specific statements and embodiments. The present application can have various modifications and changes for those skilled in the art. Any modification, equivalent replacement, improvement, etc. within the spirit and principles of the present application should be included in the scope of protection of the claims of the present application.

Claims

1.A method for multi-baseline SAR imaging based on spectrum correction, comprising the following steps: Step 1, modeling of multi-baseline SAR system echo; According to the geometric model of multi-base SAR system, a Cartesian coordinate system is established with O as the origin; the starting positions of the transmitter and the nth receiving station are (x T ,y T ,z T ) and (x Rn ,y Rn ,z Rn ); P represents an arbitrary point target in the imaging scene, whose coordinates are (xp, yp, 0); α T , α Rn represent the pitch angles of the transmitter and the nth receiver; θ T , θ Rn represent the azimuth angles of the transmitter and the nth receiver; A transmitter transmits a linear frequency modulation signal, and for the nth receiver, the echo signal of a target point P is expressed as follows after pulse compression and coherent processing with echo data of a reference target O located at the origin: wherein f, τ represent the range and azimuth time variables, respectively, A, T a , c, T r , K r , f c represent the signal amplitude, synthetic aperture time, electromagnetic wave velocity, pulse width, frequency modulation slope, and carrier frequency of the transmitted signal, respectively, R nP (τ) and R nO (τ) represent the range histories and of the target point P and the reference point O to the transmitter and the nth receiver, respectively According to the far-field approximation, the distance history difference between the target point P and the target O is expressed as follows: According to formula (1) and formula (2), the signal is mapped from the range-frequency domain and the azimuth-time domain to the wave-number domain through variable transformation, and the expression is as follows: s n (k x ,k y )=A n ·exp[j(x p k x +y p k y )] (3) where k x ,k y denote two spatial frequency variables in the wave number domain, which vary with the frequency of the transmitted signal and the relative position between the platform and the target, A n = A rect(τ / T a ) rect(f / k r T r ) denotes the signal envelope; k x ,k y is expressed as follows: Step 2, modeling of the wave-number spectrum correction problem; The wave-number spectrum formed by each receiver is approximately a parallelogram, and when the speed and initial position of the platforms differ greatly, the wave-number spectrum distribution is not ideal, so the wave-number spectrum is corrected as follows: By adding a window and only retaining the wave-number spectrum data within the window, while removing the non-ideal distribution part, the wave-number spectrum is made to better meet the imaging requirements; The shape of the window is defined as a parallelogram, and P1, P2, P3, P4, P c represents the coordinates of the four vertices of the parallelogram window and the center; θw represents the angle between two sides of the parallelogram window; B1'(w), B2'(w) represent the height of the parallelogram window, which is proportional to the projection bandwidth of the corrected wave number spectrum; From the properties of a parallelogram, the shape and position of the window are determined by defining the center point P c of the window and the coordinates of two adjacent points P1, P2. The construction parameters of the window are represented by the vector w, which is expressed as follows: w = (k xc ,k yc ,k x1 ,k y1 ,k x2 ,k y2 ) (5) where k xc ,k yc ,k x1 ,k y1 ,k x2 ,k y2 represents P c , P1, P2 are coordinates in the wave number domain; Step 3, converting the wave-number spectrum correction problem into a constrained multi-objective optimization problem; The angle range of the window is limited and the relationship between B1'(w) and B'2(w) is adjusted, the angle of the window is constrained between 4π / 9 and 5π / 9, and the ratio of the larger value to the smaller value in B1'(w), B2'(w) is less than 1.5; Then the wave-number spectrum correction problem is converted into a constrained multi-objective problem, and the expression is as follows: wherein r1(w), r2(w) represent the projection bandwidth after the wave number spectrum correction, η(w) represents the data amount after the wave number spectrum correction, S mWS (w) represents the area of the corrected wave number spectrum and the area of the window, ψ represents the search space of w, k W (w) represents the area of the corrected wave number spectrum and the area of the window, ψ represents the search space of w, k xc ,k x1 ,k x2 ∈[k xmin ,k xmax ],k yc ,k y1 ,k y2 ∈[k ymin ,k ymax ],k xmin ,k xmax ,k ymin ,k ymax represents the range boundary of the wave number domain in the k x ,k y direction. Step 4, solving the constrained multi-objective problem and high-quality imaging; A multi-objective particle swarm optimization algorithm (MOPSO) is used to solve the constrained multi-objective problem obtained in step 3; First, the wave number spectrum correction problem is initialized, including: radar system parameters, platform initial position and velocity, vector w; and the particle swarm in MOPSO is initialized, including particle number M, maximum iteration number I max , inertia weight w; The radar system parameters include signal carrier frequency, signal bandwidth, synthetic aperture time, pulse repetition time and pulse repetition frequency; Then the objective function (6) of the particle is calculated and a pareto solution set is formed, before the iteration is terminated, the position and velocity of the particle are updated, the fitness of the particle is calculated, and the pareto optimal solution set is updated; Finally, the optimized correction result is selected from the optimal solution set; by reasonably correcting the wave-number spectrum, the data loss is reduced while maintaining high resolution, and the imaging performance is improved; based on the corrected wave-number spectrum, a polar coordinate multi-baseline SAR imaging algorithm is used to obtain the high-quality imaging result after optimized correction.

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