A three-dimensional ISAR imaging method based on multi-observation tensor sparse representation

Abstract

The application discloses a three-dimensional ISAR imaging method based on multi-observation tensor sparse representation, and belongs to the field of inverse synthetic aperture radar imaging. In view of the fact that the existing ISAR imaging technology has low imaging resolution when data is insufficient and low imaging quality when noise is large, the application adopts a multi-observation method, utilizes the correlation between signals of multiple channels, and improves the inclusiveness of data. Compared with a traditional algorithm, the reconstruction effect is better under a small signal-to-noise ratio, the resolution of ISAR imaging is improved, a tensorization method is adopted to directly process three-dimensional data, an inverse matrix of an unfolded large matrix is not needed, the efficiency of the algorithm is improved, the three-dimensional structure information of the reconstructed signal is considered, the imaging accuracy is further improved, and the precision and quality of three-dimensional ISAR imaging are improved. The application realizes three-dimensional ISAR imaging based on multi-observation tensor sparse representation, is suitable for the field of inverse synthetic aperture radar imaging, and improves the imaging precision and imaging quality under a low signal-to-noise ratio.

Description

TECHNICAL FIELD

[0001] The present application relates to a three-dimensional ISAR imaging method based on multi-observation tensor sparse representation, and belongs to the field of inverse synthetic aperture radar imaging. BACKGROUND

[0002] Inverse synthetic aperture radar (ISAR) imaging has been widely used in civil and military applications, and is a technique for obtaining two-dimensional radar images of observed targets. However, two-dimensional (2D) ISAR imaging images cannot provide the relative height information of each scattering center on the target. In contrast, three-dimensional (3D) ISAR images have the advantage of giving the accurate position of each scattering center on the target in a higher dimension. From the imaging principle, two-dimensional ISAR images can be understood as the projection of the target in the range-Doppler imaging plane. Unlike two-dimensional ISAR imaging, three-dimensional spatial target imaging adds information of the target perpendicular to the imaging plane to obtain its more realistic structural features, which is beneficial to the identification of the target, is an effective means of spatial target identification, and has a wide application prospect.

[0003] Common 3D-ISAR imaging is a direct extension of the 2D-ISAR concept. This method achieves three-dimensional ISAR imaging of moving targets by illuminating the target in the azimuth and elevation directions while transmitting a wideband waveform (such as a stepped frequency waveform and a linear frequency modulation waveform), and then applying a three-dimensional Fourier transform to obtain the three-dimensional reflectivity of the target.

[0004] The conventional three-dimensional imaging method commonly used at present is based on three-dimensional Fourier transform (3D-FT) to invert the three-dimensional reflectivity of the target. However, due to the limitation of the Shannon-Nyquist sampling law, this Fourier transform (FT) based method requires three-dimensional measurement of radar data, and if the sampling rate is insufficient, it may lead to reduced imaging resolution and imaging accuracy, or even failure to image. In addition, if there is noise in the input signal, it will also seriously affect the imaging quality.

[0005] In the high frequency region, due to the high frequency of the radar transmitting signal, the wavelength of the incident wave is small. Under the observation condition in the high frequency region, the projection size of the radar detected target on the wave front is much larger than the wavelength of the incident wave, and the electromagnetic scattering echo signal of the target can be formed by the electromagnetic scattering superposition of the scattering centers at different positions, so the radar echo signal naturally has the signal sparsity property. The principle of compressive sensing points out that as long as the signal is sparse (only a limited number of non-zero value elements) or can be sparsely represented in a certain transform domain, the signal can be reconstructed with high precision by solving an optimization problem, without the global sample information of the signal, and high resolution radar image can be realized by using limited data. In addition, compressive sensing uses the structural information of sparsity as a statistical prior, which can bring further advantages in signal reconstruction, such as noise removal and sidelobe suppression. At present, the basic sparse signal reconstruction algorithms mainly include orthogonal matching pursuit (Orthogonal Matching Pursuit, OMP) algorithm, smoothed L0 norm reconstruction (Smoothed L0 norm, SL0) algorithm and sparse Bayesian learning (Sparse Bayesian Learning, SBL) algorithm. The radar imaging method using sparse reconstruction at present is usually based on the single measurement vector (Single Measurement Vector, SMV) model, which has certain advantages compared with the traditional three-dimensional Fourier transform imaging method, but the single observation vector model ignores the structural characteristics of the part of the reconstructed signal with the same support set, and the imaging quality will still be greatly reduced in the case of large noise. SUMMARY

[0006] In view of the problems of the existing ISAR imaging technology that the imaging resolution is reduced when the data is insufficient and the imaging quality is reduced when the noise is large, the main purpose of the present application is to provide a three-dimensional ISAR imaging method based on multiple observation (Multiple Measurement Vector, MMV) tensor sparse representation, which can effectively realize high-resolution imaging of three-dimensional ISAR, optimize the comprehensive performance of reconstructed three-dimensional ISAR imaging, and improve the imaging accuracy and imaging quality under low signal-to-noise ratio.

[0007] The purpose of the present application is realized by the following technical solutions:

[0008] The three-dimensional ISAR imaging method based on multiple observation tensor sparse representation disclosed by the present application specifically comprises the following steps:

[0009] S1: receiving the effective echo signal and expressing it in the form of a tensor;

[0010] The received echo signal has a dimension of NXMxL, which represents that the target echo record of the observation area is recorded in samples of N different frequencies, M different rotation angles and L different elevation angles.

[0011] S2: the received echo tensor is extracted in the elevation angle direction using a first random unit matrix to realize down-sampling, and an echo tensor down-sampled in the elevation angle direction is obtained; the echo tensor down-sampled in the elevation angle direction is extracted in the distance direction using a second random unit matrix to realize down-sampling, and an echo tensor down-sampled in the distance direction is obtained; the echo tensor down-sampled in the distance direction is extracted in the azimuth direction using a third random unit matrix to realize down-sampling, and an echo tensor down-sampled in the azimuth direction is obtained;

[0012] The dimension of the first random unit matrix is LsubxL, and Lsub is less than L; the echo data down-sampled in the elevation angle direction has a dimension of NXMxLsub; the dimension of the second random unit matrix is NsubxN, and Nsub is less than N; the echo data down-sampled in the distance direction has a dimension of NsubxMxLsub; the dimension of the third random unit matrix is MsubxM, and Msub is less than M; the echo data down-sampled in the azimuth direction has a dimension of NsubxMsubxLsub; the down-sampled echo data is denoted as Ssub, and has a dimension of NsubxMsubxLsub.

[0013] S3: dictionaries of appropriate sizes are constructed in each direction in the dimension of the received signal;

[0014] The dictionaries in each direction are specifically denoted as:

[0015] Θ1=[a1 a2…a p …a P ]

[0016] Θ2=[c1 c2…c k …c K ]

[0017] Θ3=[b1 b2…b q …b Q ]

[0018] Wherein, j represents an imaginary unit, π represents a circular constant, c represents the speed of light, f represents frequency, φ represents the elevation angle, θ represents the azimuth angle, and λ c represents the wavelength corresponding to the center frequency; P, Q and K are the number of grids; p, q and k represent the column serial number of the dictionary;

[0019] S4: based on the constructed dictionaries in the distance direction and the elevation angle direction, a multi-observation algorithm, i.e., the MMV-2DSL0 algorithm, is used to sparsely reconstruct the distance direction and the elevation angle direction;

[0020] S41: initialize the tensor by least square method

[0021]

[0022] wherein is the received down-sampled valid echo signal, Θ1 and Θ2 are the down-sampled dictionaries in range and elevation direction respectively; x d represents the matrix multiplication operation after the tensor is projected to d dimension; represents the pseudo-inverse of the matrix;

[0023] S42: initialize the shape parameter

[0024] wherein i = 1, 2, 3, …, N sub ; j = 1, 2, 3, …, M sub ; k = 1, 2, 3, …, L sub ; represents the absolute value of the data in the i-th row, j-th column and k-th page of the tensor ;

[0025] S43: calculate the maximum value of the unconstrained optimization of the approximation function by formula (2) denoted as and project it to the feasible set again;

[0026]

[0027] wherein exp() represents the exponential operation with the natural constant as the base; μ is the step constant value of gradient descent;

[0028] the feasible set is denoted as to ensure that the solution obtained by iteration is in the feasible set, project it to the feasible set; calculate it by ;

[0029] S44: repeat S43 to obtain the local optimal solution under the σ;

[0030] S45: update σ so that σ starts to decay;

[0031] S46: repeat S43 to S45 until the value of the shape parameter σ is less than the threshold value σ min , to obtain the most sparse solution of ;

[0032] S5: based on the azimuth direction dictionary, use the tensor SL0 algorithm to perform sparse reconstruction on the azimuth direction;

[0033] ​S51: initialize tensor by least square method

[0034]

[0035] where χ is the recovered signal of S4, Θ is the azimuth down-sampled dictionary;

[0036] S52: initialize shape parameter

[0037] where i = 1, 2, 3, …, P; j = 1, 2, 3, …, M sub k = 1, 2, 3, …, K; represents the absolute value of the data of the i-th row, the j-th column and the k-th page in the tensor

[0038] S53: calculate the maximum value of the un-constrained optimization of the approximation function by formula (4) denoted as where μ is a step constant factor; project it to the feasible set S again;

[0039]

[0040] where the feasible set is denoted as to ensure that the iteration is in the feasible set, project it to the feasible set; calculate it by

[0041] S54: repeat S53 to obtain a local optimal solution under the σ;

[0042] S55: update σ to start decaying

[0043] S56: repeat S53 to S55 until the value of the shape parameter σ is less than the threshold σ min , to obtain the most sparse solution of

[0044] S6: perform threshold processing on the reconstructed tensor of S4 and S5 to obtain a reconstructed three-dimensional image, improving the precision and quality of three-dimensional ISAR imaging.

[0045] When the amplitude is greater than the threshold value Th, the data remains unchanged; when the amplitude is less than the threshold value Th, it is set to zero; then update the data tensor; obtain a reconstructed three-dimensional image, improving the precision and quality of three-dimensional ISAR imaging.

[0046] Beneficial effects:

[0047] ​​​​1. The three-dimensional ISAR imaging method based on multi-observation tensor sparse representation disclosed by the application adopts a multi-observation method, utilizes the correlation between multiple channel signals, improves the inclusiveness of data, and has better reconstruction effect compared with a traditional algorithm in a case of small signal-to-noise ratio, thereby improving the resolution of ISAR imaging.

[0048] 2. The three-dimensional ISAR imaging method based on multi-observation tensor sparse representation disclosed by the application adopts a tensorization method to directly process three-dimensional data, does not need to calculate an inverse matrix of an unfolded large matrix, thereby improving the efficiency of the algorithm, simultaneously considers the three-dimensional structural information of the reconstructed signal, further improves imaging accuracy, and improves the precision and quality of three-dimensional ISAR imaging. BRIEF DESCRIPTION OF DRAWINGS

[0049] Figure 1 is a flowchart of the three-dimensional ISAR imaging method based on multi-observation tensor sparse representation of the application;

[0050] Figure 2 is a three-dimensional tensor and two-dimensional matrix multiplication diagram of the application;

[0051] Figure 3 is an imaging result after three-dimensional Fourier transform of all pulse data of echo data and threshold screening;

[0052] Figure 4 is an imaging result after processing of echo data by the method of the application;

[0053] Figure 5 is an imaging result of different methods under a condition of-10 dB signal-to-noise ratio after 50% downsampling in the embodiment, wherein figure (a) is an imaging result of the method disclosed in the embodiment, figure (b) is an imaging result of a prior art algorithm 1, and figure (c) is an imaging result of a prior art algorithm 2;

[0054] Figure 6 is a reconstruction error scatter diagram of the method disclosed in the embodiment, the prior art algorithm 1 and the prior art algorithm 2 under different signal-to-noise ratios after 50% downsampling,

[0055] wherein figure (a) is a reconstruction error scatter diagram under a condition of 20 dB signal-to-noise ratio, figure (b) is a reconstruction error scatter diagram under a condition of 0 dB signal-to-noise ratio, and figure (c) is a reconstruction error scatter diagram under a condition of-20 dB signal-to-noise ratio;

[0056] Figure 7 is a comparison diagram of a recovery model and an original simulation model in a one-dimensional case under a condition of-20 dB signal-to-noise ratio after 50% downsampling by using the method disclosed in the embodiment, the prior art algorithm 1 and the prior art algorithm 2.

[0057] Wherein Figure (a) is the contrast chart under the algorithm of the present patent, Figure (b) is the contrast chart under the existing algorithm 1, Figure (c) is the contrast chart under the existing algorithm 2; DETAILED DESCRIPTION

[0058] The present application will be described in detail below with reference to the accompanying drawings and examples. The technical problems solved by the technical solutions of the present application and the beneficial effects are also described. It should be pointed out that the described examples are only intended to facilitate the understanding of the present application and do not limit it in any way.

[0059] The embodiment discloses a specific implementation of a three-dimensional ISAR imaging method based on multi-observation tensor sparse representation, comprising the following steps:

[0060] S1: receiving valid echo signals, expressing the received target valid echo as a tensor form, denoted as tensor The dimension is 100x50x24. 100 is the frequency of the sampling point number, 50 is the azimuth of the sampling point number, and 24 is the pitch of the sampling point number.

[0061] S2: 50% of the data in the pitch angle direction is randomly extracted by using a first random unit matrix on the received echo tensor, 50% down-sampling is realized, and a pitch angle direction down-sampled echo tensor is obtained;

[0062] Wherein, the first random unit matrix is denoted as l, and the dimension is 12x24; the pitch angle direction down-sampled echo data is denoted as The dimension is 100x50x12.

[0063] S3: the pitch angle direction down-sampled echo tensor is extracted in the range direction by using a second random unit matrix, 50% down-sampling is realized, and a range direction down-sampled echo tensor is obtained;

[0064] Wherein, the second random unit matrix is denoted as Φ, and the dimension is 50x100; the range direction down-sampled echo data is denoted as The dimension is 50x50x12.

[0065] S4: the range direction down-sampled echo tensor is extracted in the azimuth direction by using a third random unit matrix, 50% down-sampling is realized, and an azimuth direction down-sampled echo tensor is obtained;

[0066] Wherein, the third random unit matrix is denoted as Φ m , and the dimension is 25x50; the azimuth direction down-sampled echo data is denoted as The dimension is 50x25x12.

[0067] S5: a dictionary matrix with appropriate size is constructed in each direction according to the dimension of the received signal, and the specific construction is as follows:

[0068] Θ1=[a1 a2…a p …a P ]

[0069] Θ2=[c1 c2…c k …c K ]

[0070] Θ3=[b1 b2…b q …b Q ]

[0071] wherein, j represents an imaginary unit, π represents a circular constant, exp() represents an exponential operation with a natural constant as a base; c represents a light speed; f0=10GHz represents an initial frequency, a frequency step size Δf is set to 5MHz; φ0=0° represents an initial pitch angle, a pitch angle interval θ0=0° represents an initial rotation angle, a rotation angle interval Δθ=0.024°; λ c represents a wavelength corresponding to a center frequency; P=100, Q=50, K=24 are grid numbers, that is, dimensions of a reconstructed signal; p, q, k represent column serial numbers of a dictionary;

[0072] S6: based on the constructed down-sampling dictionary in the range direction and the pitch angle direction, a MMV-2DSL0 algorithm is used to perform sparse reconstruction in the range direction and the pitch angle direction;

[0073] S6, specifically:

[0074] S61: a least square method is used to initialize a tensor is calculated through formula (1):

[0075]

[0076] wherein is a received down-sampling effective echo signal, Θ1 and Θ2 are dictionaries in the range direction and the pitch angle direction after down-sampling in S2; × d represents a matrix multiplication operation after a tensor is projected to a d dimension; represents a pseudo-inverse of a matrix;

[0077] S62: shape parameters are initialized

[0078] wherein, i=1, 2, 3,..., 50; j=1, 2, 3,..., 25; k=1, 2, 3,..., 12; represents an absolute value of data of the i-th row, the j-th column and the k-th page in a tensor ; ​

[0079] S63: Set step factor μ = 2;

[0080] S64: Calculate the maximum value of the approximation function without constraint by formula (2) Denoted as Project to the feasible set again;

[0081]

[0082] Wherein

[0083] The feasible set is denoted as To ensure that the iteration obtained in the feasible set, project to the feasible set; by Calculate to obtain;

[0084] S65: Repeat S64 for 3 times;

[0085] S66: Set the attenuation factor d = 0.7, and calculate σ = σd;

[0086] S67: Set the shape parameter threshold σ min = 0.001, if the value of the shape parameter σ is greater than the threshold σ min , repeat S64 to S66 until the value of the shape parameter σ is not greater than the threshold σ min ;

[0087] So far, from S61 to S67, the MMV-2DSL0 algorithm is completed;

[0088] S7: Based on the orientation dictionary, use the tensor SL0 algorithm to sparsely reconstruct the orientation; the specific steps are as follows:

[0089] S71: Use the least square method to initialize the tensor Calculate by formula (3):

[0090]

[0091] Wherein is the signal recovered by S6, and Θ is the dictionary after down-sampling the orientation in S2;

[0092] S72: Initialize the shape parameter

[0093] Wherein, i = 1, 2, 3,..., 100; j = 1, 2, 3,..., 25; k = 1, 2, 3,..., 24; represents the absolute value of the data of the i-th row, the j-th column and the k-th page in the tensor ;

[0094] ​S73: Set the step factor μ = 2;

[0095] S74: Calculate the maximum value of the approximation function unconstrained optimization corresponding to denoted as Project to the feasible set S again;

[0096]

[0097] where the feasible set is denoted as To ensure that the iteration obtained in the feasible set, project to the feasible set; by Calculate

[0098] S75: Repeat S74 three times;

[0099] S76: Set the decay factor d = 0.7, and calculate σ = σd;

[0100] S77: Set the shape parameter threshold σ min = 0.001, if the value of the shape parameter σ is greater than the threshold σ min , repeat S74 to S76 until the value of the shape parameter σ is not greater than the threshold σ min ;

[0101] So far, from S71 to S77, the tensor type SL0 algorithm is completed.

[0102] S8: Threshold processing is performed on the reconstructed tensor to obtain a reconstructed three-dimensional image; specifically:

[0103] S81: Set the residual threshold Th = 0.2;

[0104] S82: Compare the amplitude of the recovered data with the threshold value Th; when the amplitude is greater than the threshold value Th, the data remains unchanged; when the amplitude is less than the threshold value Th, it is set to zero;

[0105] S83: Update the data tensor;

[0106] So far, the threshold screening step is completed, and a reconstructed three-dimensional ISAR image is obtained.

[0107] The beneficial effects of the method described in the application are further illustrated by the following simulation:

[0108] The simulation experiment of the application is compiled on Matlab R2019b.

[0109] 1. Simulation content.

[0110] Simulation Experiment 1: Perform three-dimensional Fourier transform on all pulse data of echo data, and the imaging result is as shown in Figure 3 .

[0111] Simulation experiment 2: after full sampling of echo data, the imaging result after reconstruction by the algorithm proposed in the patent is as follows Figure 4 .

[0112] Simulation experiment 3: after 1 / 2 down-sampling of echo data, the simulation reconstruction is performed by using the existing two methods and the method proposed in the patent, and the one-dimensional data form is stretched, and the reconstruction performance of each method is compared under different signal-to-noise ratios. The comparison results are shown in Figure 5 , Figure 6 and Figure 7 .

[0113] Simulation experiment 4: comparison of reconstruction error of the method disclosed in the embodiment and the existing method under different signal-to-noise ratios is shown in Table 1.

[0114] Table 1 reconstruction error energy table of different methods under different signal-to-noise ratios

[0115]

[0116]

[0117] Simulation experiment 5: comparison of reconstruction error of the method disclosed in the embodiment and the existing method under different sampling rates at a signal-to-noise ratio of 10 dB is shown in Table 2.

[0118] Table 2 reconstruction error energy table of different methods under different sampling rates

[0119] Sampling rate 100％ 80％ 60％ 40％ 20％ The method of the present embodiment 0.0503 0.0483 0.31 4.65 20.30 Existing algorithm 1 0.0503 0.0482 1.60 6.07 53.45 Existing algorithm 2 0.0503 0.0481 1.68 19.20 62.62

[0120] Analysis of Table 1 results, as the signal-to-noise ratio gradually decreases, the reconstruction error of each method increases significantly; under each signal-to-noise ratio, the reconstruction error of the method disclosed in the embodiment is smaller than that of the existing algorithm, which reflects good noise resistance. The method disclosed in the embodiment uses a multi-observation algorithm, which can reduce the reconstruction error in the presence of noise and significantly improve the reconstruction performance.

[0121] Analysis of Table 2 results, when the data volume is relatively large, the reconstruction error energy of the method disclosed in the embodiment and the existing two algorithms is relatively small and the difference between the algorithms is not large; but when the sampling rate decreases, it can be found that the reconstruction error energy of the method disclosed in the embodiment is smaller than that of the existing two methods. The method disclosed in the embodiment combines a multi-observation algorithm, which can reduce the reconstruction error in the case of small sampling rate and significantly improve the reconstruction performance.

[0122] Figure 3 is the imaging result of three-dimensional Fourier transform of all pulse data of echo data after threshold screening, Figure 4is the imaging result of echo data processed by the method of the application after threshold screening. Overall, the image after threshold processing is not much different, and both existing methods can well restore the original scattering point model under full sampling conditions.

[0123] Figure 5 (a), Figure 5 (b), Figure 5 (c) is the imaging result of the proposed method and the two existing methods respectively after downsampling under the condition of-10dB signal-to-noise ratio. It can be seen that after threshold processing, the existing methods still have false point targets, resulting in contour fragmentation. While Figure 5 (a) The proposed method has a certain tolerance for data, and no false point targets are found after threshold processing, and Figure 5 Compared with the existing three-dimensional ISAR imaging method in the prior art, the three-dimensional ISAR imaging effect of the proposed method is better.

[0124] Figure 6 (a), Figure 6 (b), Figure 6 (c) is the reconstruction error energy scatter plot of the proposed method and the two existing methods respectively under the condition of 50% downsampling, 20dB signal-to-noise ratio, 0dB signal-to-noise ratio and-20dB signal-to-noise ratio. It can be found that the reconstruction error energy of the proposed method is basically below Figure 6 the existing three-dimensional ISAR imaging method in the prior art, indicating the superiority of the reconstruction effect of the proposed method.

[0125] Figure 7 (a), Figure 7 (b), Figure 7 (c) is the comparison diagram of the recovered model and the original simulation model in one-dimensional case under the condition of-20dB signal-to-noise ratio after 50% downsampling of the proposed method and the two existing methods. It can be found that compared with the two existing algorithms, the data recovered by the proposed method is closer to the simulation standard model, indicating that the proposed method has certain advantages compared with the two existing algorithms in the case of small data volume and large noise.

[0126] The above specific description further details the purpose, technical solution and beneficial effects of the application. It should be understood that the above description is only a specific embodiment of the application and is not used to limit the protection scope of the application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principles of the application shall be included in the protection scope of the application.

Claims

1. A three-dimensional ISAR imaging method based on multi-observation tensor sparse representation, characterized in that: It comprises the following steps, S1: receiving valid echo signals and expressing them in tensor form; S2: using a first random unit matrix to extract the pitch angle direction of the received echo tensor, realizing down-sampling, obtaining the pitch angle direction down-sampled echo tensor; using a second random unit matrix to extract the distance direction of the pitch angle direction down-sampled echo tensor, realizing down-sampling, obtaining the distance direction down-sampled echo tensor; using a third random unit matrix to extract the azimuth direction of the distance direction down-sampled echo tensor, realizing down-sampling, obtaining the azimuth direction down-sampled echo tensor; S3: constructing a dictionary of appropriate size in each direction in the dimension of the received signal; S4: based on the constructed distance direction and pitch angle direction dictionaries, using a multi-observation algorithm, i.e., the MMV-2DSL0 algorithm, to sparsely reconstruct the distance direction and pitch angle direction; S5: based on the azimuth direction dictionary, using a tensor-type SL0 algorithm to sparsely reconstruct the azimuth direction; S6: threshold processing the tensors reconstructed in S4 and S5 to obtain a reconstructed three-dimensional image, improving the precision and quality of three-dimensional ISAR imaging. 2.The 3-D ISAR imaging method based on multi-observation tensor sparse representation according to claim 1, wherein: The implementation method of S1 is, The dimension of the received echo signal is N×M×L, indicating that the target echo record of the observation area is recorded in N different frequencies, M different rotation angles, and L different pitch angles. 3.The 3-D ISAR imaging method based on multi-observation tensor sparse representation according to claim 2, wherein: The implementation method of S2 is, The dimension of the first random unit matrix is Lsub×L, and Lsub is less than L; the pitch angle direction down-sampled echo data has a dimension of N×M×Lsub; The dimension of the second random unit matrix is Nsub×N, and Nsub is less than N; the distance direction down-sampled echo data has a dimension of Nsub×M×Lsub; The dimension of the third random unit matrix is Msub×M, and Msub is less than M; the azimuth direction down-sampled echo data has a dimension of Nsub×Msub×Lsub; the down-sampled echo data is denoted as Ssub, and has a dimension of Nsub×Msub×Lsub.

4. The method of claim 3, wherein the method is based on multi-observation tensor sparse representation. The implementation method of S3 is, The dictionary in each direction is specifically represented as: Θ1 = [a1 a2 … a p … a P ] Θ2 = [c1 c2 … c k … c K ] Θ3 = [b1 b2 … b q … b Q ] wherein j represents the imaginary unit, π represents the circular constant; c represents the speed of light; f represents the frequency, φ represents the pitch angle, θ represents the azimuth angle, λ c represents the wavelength corresponding to the center frequency; P, Q, K are the grid numbers; p, q, k represent the column serial number of the dictionary.

5. The method of claim 4, wherein the method is based on multi-observation tensor sparse representation. The implementation method of S4 is, S41: initialize the tensor using least square method wherein Θ1 and Θ2 are the dictionaries after range and elevation angle direction downsampling, respectively, for the received downsampled valid echo signal; d denotes the matrix multiplication operation after the tensor is projected to d dimensions; denotes the pseudo-inverse of a matrix; S42: initialize shape parameters where i = 1, 2, 3,..., N sub ; j = 1, 2, 3,..., M sub ; k = 1, 2, 3,..., L sub ; represents the absolute value of the data in the i-th row, j-th column, and k-th page of the tensor X . S43: Calculate the maximum value of the unconstrained optimization of the approximation function by formula (2) corresponding to denoted as Projecting again to the feasible set; wherein exp() denotes the exponential operation with the natural constant as base; σ is a step constant value for gradient descent; The feasible set is denoted as To ensure that the solution obtained by iteration is in the feasible set, the projection of the feasible set is calculated by The projection of the feasible set is calculated. S44: repeatedly performing S43 so that a local optimal solution is obtained under the σ; S45: updating σ so that σ starts to decay; S46: repeat S43 to S45 until the value of the shape parameter σ is less than a threshold value σ min , resulting in the sparsest solution of 6. The method of claim 5, wherein the method is based on multi-observation tensor sparse representation. The implementation method of S5 is, S51: initialize the tensor with least square method wherein is the recovered signal for S4, and Θ is the azimuth downsampled dictionary; S52: initialize shape parameters where i = 1, 2, 3,..., P; j = 1, 2, 3,..., M sub ; k = 1, 2, 3,..., K represents the absolute value of the data in the i-th row, j-th column, and k-th page of the tensor X ​ S53: Calculate the maximum of the unconstrained optimization of the approximation function by formula (4) corresponding to denoted as where μ is a step constant factor; project again to the feasible set S; Where the feasible set is denoted by To ensure that the iteration is in the feasible set, the projection onto the feasible set is calculated by The projection is calculated by S54: repeatedly performing S53 so that a local optimal solution is obtained under the σ; S55: updating σ so that it starts to decay; S56: repeat S53 to S55 until the value of the shape parameter σ is less than a threshold value σ min , resulting in the sparsest solution.

7. The method of claim 6, wherein the method is based on multi-observation tensor sparse representation. The implementation method of S6 is, When the amplitude is greater than the threshold value Th, the data remains unchanged; when the amplitude is less than the threshold value Th, it is set to zero; then the data tensor is updated to obtain a reconstructed three-dimensional image, improving the precision and quality of three-dimensional ISAR imaging.

Images