Sparse ISAR imaging method and system based on low rank and non-local self-similarity

Abstract

The present application belongs to the technical field of radar imaging, and particularly relates to a sparse ISAR imaging method and system based on low rank and non-local self-similarity. The low rank of echo signals received by an inverse synthetic aperture radar (ISAR) system is used to reconstruct an image, and the low rank is used as prior information of the reconstructed image. A sparse imaging model is constructed by using the prior information and a non-local self-similarity constraint of the image. A Lagrange multiplier is introduced to equivalently transform the sparse imaging model, and the sparse imaging problem is decomposed into several sub-problems for iterative solving. The final sparse ISAR imaging is obtained according to the iterative solving result. The present application improves the sparse ISAR imaging quality and imaging effect by mining the structural correlation of an ISAR target, combining the low rank prior of the ISAR target with the non-local self-similarity to construct a sparse ISAR imaging model.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of radar imaging, and particularly relates to a sparse ISAR imaging method and system based on low rank and non-local self-similarity. BACKGROUND

[0002] Inverse synthetic aperture radar (ISAR) can synthesize a larger aperture in the azimuth direction by using the relative motion between the object and the radar, so it can improve the resolution to exceed the diffraction limit of the real aperture, and has a wide application prospect in many military and civilian fields. The traditional ISAR imaging method based on Fourier transform must have a long observation interval to obtain high azimuth resolution. However, in actual ISAR applications, the imaging target is always uncooperative or moving, and continuous measurement may not be possible in a long coherent processing interval or the data collected in some time periods is invalid, so it is often difficult to obtain a well-focused ISAR image. In addition, the target motion compensation in a long coherent processing time is much more complex, so it is of great significance to study the sparse aperture ISAR imaging strategy.

[0003] In order to overcome the defocusing problem of ISAR imaging in sparse aperture, some studies have introduced the spatial spectrum estimation method into ISAR imaging. Compared with the imaging method based on Fourier transform, the spatial spectrum estimation method can obtain lower sidelobes and higher resolution, but it is very sensitive to noise and modeling errors. Compressive sensing (CS) is a model-based data acquisition and signal recovery framework, which can recover the original signal from limited sampling with a high probability if the target to be recovered satisfies the sparsity or compressibility, and has a significant advantage in sparse signal reconstruction. Since the ISAR target is usually composed of a limited number of strong scattering centers, it exhibits strong spatial sparsity. Therefore, more and more studies combine sparse ISAR imaging with CS to improve the imaging performance. However, the CS method is easily affected by noise, and the imaging quality is not high at low signal-to-noise ratio. In order to improve the imaging quality of the CS algorithm, various sparse prior information is introduced into the sparse ISAR imaging model to improve the imaging quality. The Bayesian compressive sensing method assumes that the ISAR target satisfies a certain prior distribution in the imaging process, and uses Bayesian estimation to obtain the ISAR target imaging result, but it has a heavy computational burden and the imaging quality is not high at low signal-to-noise ratio. The sparse ISAR imaging method based on total variation constrains the smoothness of the ISAR target in the imaging model to improve the imaging quality, but the imaging result is prone to over-smoothing. Low-rank matrix recovery is another signal processing path, which seeks the global lowest rank representation of the data matrix, and has been widely used in image processing, synthetic aperture radar imaging and ISAR image denoising. Low-rank matrix recovery restores the under-sampled data based on the assumption that the matrix is essentially low-rank. At present, only the sparsity of the ISAR target image is simply used, and the inherent structural correlation of the image is not exploited, so the imaging quality needs to be improved. SUMMARY

[0004] To this end, the present application provides a sparse ISAR imaging method and system based on low rank and non-local self-similarity, which improves the quality and effect of sparse ISAR imaging by exploiting the structural correlation of ISAR targets, combining the low rank prior of ISAR targets and non-local self-similarity to construct a sparse ISAR imaging model.

[0005] According to the design scheme provided by the present application, a sparse ISAR imaging method based on low rank and non-local self-similarity is provided, which includes the following contents:

[0006] The low rank property of the reconstructed image according to the echo signal received by the inverse synthetic aperture radar (ISAR) system is used as the prior information of the reconstructed image, and the sparse imaging model is constructed by using the prior information and the non-local self-similarity constraint of the image.

[0007] The sparse imaging model is equivalently transformed by introducing a Lagrange multiplier, and the sparse imaging problem is decomposed into several sub-problems for iterative solution; and the final sparse ISAR imaging is obtained according to the iterative solution result.

[0008] As the sparse ISAR imaging method based on low rank and non-local self-similarity of the present application, further, the low rank property of the reconstructed image is expressed as: Wherein, X represents the reconstructed image, Φ is a dictionary matrix, S is a range image, and K is the number of scattering points in the imaging scene.

[0009] As the sparse ISAR imaging method based on low rank and non-local self-similarity of the present application, further, in the expression of the non-local self-similarity of the image, the reconstructed image is decomposed into several image blocks, the most similar candidate image blocks to the image blocks are found in the search window according to the matching strategy, and all the candidate image blocks are stacked into a three-dimensional matrix according to the size of the decomposed image blocks and the number of candidate image blocks; the three-dimensional transformation coefficients of all the image blocks are obtained by orthogonal transformation of the three-dimensional matrix, and the non-local self-similarity operator of the reconstructed image is expressed by using the three-dimensional transformation coefficients.

[0010] As the sparse ISAR imaging method based on low rank and non-local self-similarity of the present application, further, the non-local self-similarity operator of the reconstructed image is expressed as: Wherein, Ψ NL X represents the non-local self-similarity operator, Θ X represents all the three-dimensional transformation coefficients arranged in the form of a matrix, and Θ X The column vector is composed of the transformation coefficients obtained according to the three-dimensional matrix The column vector is composed of the transformation coefficients obtained according to the three-dimensional matrix is rearranged in dictionary order, P represents the number of decomposed image blocks, X represents the reconstructed image, and T 3D represents a three-dimensional orthogonal transformation operator.

[0011] As the sparse ISAR imaging method based on low rank and non-local self-similarity of the application, further, the sparse imaging model is represented as: Where X represents the reconstructed image, Y represents the echo signal matrix, Φ is the dictionary matrix, S is the range image, Θ X represents all three-dimensional transform coefficients arranged in matrix form, R represents the sparse aperture matrix, λ1, λ2 represents the regularization parameter.

[0012] As the sparse ISAR imaging method based on low rank and non-local self-similarity of the application, further, the sparse imaging model is represented as:

[0013] Where V1, V2 and V3 represent the introduced Lagrange multiplier respectively, μ represents the penalty parameter, Φ is the dictionary matrix, Z and W are auxiliary variables introduced by model equivalent transformation, Θ W is all three-dimensional transform coefficients of variable W arranged in matrix form.

[0014] As the sparse ISAR imaging method based on low rank and non-local self-similarity of the application, further, the sparse imaging problem is decomposed into four sub-problems about S, Z, W, X according to S, Z, W, X, the four sub-problems are solved iteratively respectively, and the final sparse ISAR imaging is obtained according to the set iteration termination threshold.

[0015] Further, the application also provides a sparse ISAR imaging system based on low rank and non-local self-similarity, comprising: a model construction module and an imaging solving module, wherein,

[0016] The model construction module is used for constructing the sparse imaging model by using the low rank of the reconstructed image of the echo signal received by the inverse synthetic aperture radar (ISAR) system as the prior information of the reconstructed image, and using the prior information and the non-local self-similarity constraint of the image.

[0017] The imaging solving module is used for equivalent transformation of the sparse imaging model by introducing the Lagrange multiplier, and decomposing the sparse imaging problem into several sub-problems for iterative solving; and obtaining the final sparse ISAR imaging according to the iterative solving result.

[0018] The application has the following beneficial effects:

[0019] The present application deeply mines the structure correlation of the ISAR target, combines the low-rank prior and the non-local self-similarity of the ISAR target, considers the influence of noise in the model, constructs a sparse ISAR imaging model, can effectively improve the sparse ISAR imaging quality, and still can obtain better imaging results under the influence of limited pulses and noise; and in the solving process, the constructed sparse ISAR imaging model is decomposed into four sub-optimization problems for iterative solving, can improve the sparse ISAR imaging quality and the imaging efficiency, and has a good application prospect. BRIEF DESCRIPTION OF DRAWINGS

[0020] Figure 1 It is sparse ISAR imaging method flowchart in the embodiment;

[0021] Figure 2 It is sparse ISAR imaging algorithm principle schematic diagram in the embodiment;

[0022] Figure 3 It is full-aperture ISAR imaging result schematic diagram obtained by the traditional RD algorithm in the embodiment;

[0023] Figure 4 It is sparse ISAR imaging result schematic diagram obtained by the CS algorithm and the algorithm of the application using 50% pulse number when the signal-to-noise ratio is 10dB in the embodiment, (a) CS algorithm imaging result, (b) the imaging result of the algorithm of the application;

[0024] Figure 5 It is sparse ISAR imaging result schematic diagram obtained by the CS algorithm and the algorithm of the application using 25% pulse number when the signal-to-noise ratio is 10dB in the embodiment, (a) CS algorithm imaging result, (b) the imaging result of the algorithm of the application;

[0025] Figure 6 It is sparse ISAR imaging result schematic diagram obtained by the CS algorithm and the algorithm of the application using 50% pulse number when the signal-to-noise ratio is 0dB in the embodiment, (a) CS algorithm imaging result, (b) the imaging result of the algorithm of the application;

[0026] Figure 7 It is sparse ISAR imaging result schematic diagram obtained by the CS algorithm and the algorithm of the application using 25% pulse number when the signal-to-noise ratio is 0dB in the embodiment, (a) CS algorithm imaging result, (b) the imaging result of the algorithm of the application. DETAILED DESCRIPTION

[0027] In order to make the purpose, technical scheme and advantages of the present application more clear, specific and apparent, the present application will be further described in detail below with reference to the drawings and technical scheme.

[0028] In the embodiment of the present application, referring to Figure 1 As shown in the figure, a sparse ISAR imaging method based on low-rank and non-local self-similarity is provided, which comprises the following contents:

[0029] S101, according to the low rank of the echo signal received by the inverse synthetic aperture radar (ISAR) system to reconstruct the image, taking the low rank as the prior information of the reconstructed image, and using the prior information and the non-local self-similarity constraint of the image to construct a sparse imaging model;

[0030] S102, introducing a Lagrange multiplier to equivalently transform the sparse imaging model, and decomposing the sparse imaging problem into several sub-problems for iterative solving; and obtaining the final sparse ISAR imaging according to the iterative solving result.

[0031] In the embodiments of the present case, by deeply mining the structural correlation of the ISAR target, combining the low rank prior of the ISAR target and the non-local self-similarity, and considering the influence of noise in the model, a sparse ISAR imaging model is constructed, which can effectively improve the sparse ISAR imaging quality and still obtain good imaging results under the influence of limited pulses and noise.

[0032] The echo signal received by the ISAR system is pulse compressed in the range direction, and then the signal after the range migration correction is discretely sampled, so that a distance unit corresponds to a range compressed signal s=Φδ, wherein s=[s(Δτ), s(2Δτ), …, s(L·Δτ)] T represents a full-aperture range compressed signal corresponding to a distance unit, δ=[δ1, δ2, …, δ M ] T represents a complex-valued scattering coefficient, and its non-zero elements correspond to the amplitudes of the K strongest scattering points. The dictionary matrix Φ is composed of [φ1, φ2, …, φ m ,…,φ M ], wherein φ m =exp[-j2πf a (m)τ] T .

[0033] All the range compressed signals corresponding to the distance units are combined together to obtain a range focusing result S L×N =Φ L×M X M×N , wherein S=[s1, s2, …, s N ] and X=[δ1, δ2, …, δ N ].

[0034] Under non-ideal conditions, some measured echo signals are lost or the received signals are invalid in some time periods. In addition, the received echo signals are often affected by noise. Therefore, the observation signal of the ISAR system can be represented as

[0035] Y=RS+N (1)

[0036] where R denotes the sparse aperture matrix, and N is the additive noise matrix. Therefore, the purpose of ISAR imaging is to recover the unknown image X from the noisy signal matrix Y.

[0037] According to the rank of the ISAR system range image S, rank(S)≤K, it is derived that the rank of the ISAR imaging result X satisfies

[0038]

[0039] Therefore, the ISAR image X has a low rank, and the low rank property of the image X can be used to improve the sparse ISAR imaging quality. It is obtained that

[0040]

[0041] Since it is difficult to solve the rank minimization problem, the nuclear norm of the matrix X, ||X||*, is used to replace the rank of the matrix X in solving. *

[0042] Further, in the image non-local self-similarity representation of the embodiments of the present case, the reconstructed image is decomposed into a plurality of image blocks, the most similar candidate image blocks to the image blocks are searched in a search window according to a matching strategy, and all the candidate image blocks are stacked into a three-dimensional matrix according to the size of the decomposed image blocks and the number of candidate image blocks. The three-dimensional transform coefficients of all the image blocks are obtained by performing orthogonal transformation on the three-dimensional matrix, and the non-local self-similarity operator of the reconstructed image is represented by using the three-dimensional transform coefficients.

[0043] The ISAR image X is decomposed into P image blocks X p , each with a size of L×L. In a search window of T×T, c-1 image blocks most similar to X p are searched according to a block matching strategy, and then all the most similar blocks are stacked into a three-dimensional matrix with a size of L×L×c. When the three-dimensional transform coefficients of all the image blocks are obtained, the formula of the non-local self-similarity can be expressed as

[0044]

[0045] where Ψ NL X represents the non-local self-similarity operator. Θ X represents all the three-dimensional transform coefficients arranged in the form of a matrix, and the column vector of Θ X is constructed by rearranging in dictionary order.

[0046] ​​​​The proposed sparse ISAR imaging model can be expressed as:

[0047]

[0048] where λ1 and λ2 are regularization parameters.

[0049] The proposed sparse ISAR imaging model is converted into the following equivalent form by introducing Lagrange multipliers V1, V2 and V3:

[0050]

[0051] where μ is a penalty parameter, and <,·> is the inner product of two matrices.

[0052] Further, in the embodiments of the present case, the sparse imaging problem is decomposed into four sub-problems about S, Z, W and X according to S, Z, W and X, the four sub-problems are iteratively solved respectively, and the final sparse ISAR imaging is obtained according to the set iteration termination threshold.

[0053] In order to effectively obtain the sparse ISAR imaging result, the optimization problem (6) is decomposed into four sub-optimization problems for iterative solution. The specific imaging steps can be described as follows:

[0054] 4a) The sub-problem S is given by the following formula:

[0055]

[0056] The derivative of the above formula is taken and is equal to 0 to obtain the solution of the sub-problem S as:

[0057]

[0058] 4b) The sub-problem Z is given by the following formula:

[0059]

[0060] The solution of the sub-problem Z is obtained by the singular value threshold method as

[0061]

[0062] where D τ (·) represents the singular value threshold operator, which is defined as

[0063]

[0064] where M = UΣ r V H is the singular value decomposition of the matrix M with rank r.

[0065] 4c) The sub-problem W is given by:

[0066]

[0067] where Since Θ W is a non-local self-similar transform coefficient, Θ W has a different dimension from matrix W. Therefore, the present application utilizes to transform the sub-optimization problem (12) into

[0068]

[0069] where N W is the number of elements in W, is the number of elements in Θ W .

[0070] Based on the soft-thresholding method, the closed-form solution of Θ W is

[0071]

[0072] where soft(x, λ) = sgn(x) max(x - λ, 0). After obtaining , the solution of the W sub-problem (12) can be given according to the inverse process of the non-local self-similarity as

[0073]

[0074] where Ω NL is the inverse process of the non-local self-similarity.

[0075] 4d) The sub-problem X is given by:

[0076]

[0077] Taking the derivative of the above equation and setting it equal to 0, the solution of the sub-problem X is:

[0078]

[0079] 4e) Update of the Lagrange multipliers V1, V2 and V3

[0080]

[0081] 4f) Repeat 4a) to 4e) in the above steps until a pre-set iteration termination threshold is met, and obtain the final sparse ISAR imaging result X.

[0082] Further, based on the above method, the embodiment of the present application further provides a sparse ISAR imaging system based on low rank and non-local self-similarity, comprising a model construction module and an imaging solving module, wherein,

[0083] The model construction module is used for reconstructing the low rank of the echo signal received by the inverse synthetic aperture radar (ISAR) system, taking the low rank as the prior information of the reconstructed image, and constructing a sparse imaging model by using the prior information and the non-local self-similarity constraint of the image.

[0084] The imaging solving module is used for equivalently converting the sparse imaging model by introducing a Lagrange multiplier, decomposing the sparse imaging problem into a plurality of sub-problems for iterative solving, and obtaining the final sparse ISAR imaging according to the iterative solving result.

[0085] To verify the effectiveness of the scheme, the following further explains and describes the algorithm and test data in Figure 2 .

[0086] The data used in the experiment: the measured echo data of Yak-42 aircraft is used to verify the proposed sparse ISAR imaging method. The main radar parameters are as follows: the carrier frequency is 5.6 GHz, the bandwidth is 400 MHz, the pulse repetition frequency is 800 Hz, the number of pulses in the azimuth direction is 256, and the number of distance units is 256.

[0087] Input: the measured echo data matrix of Yak-42 aircraft, the Fourier transform matrix Φ, the number of available pulses, and the value of signal-to-noise ratio

[0088] First, the measured echo signal of Yak-42 aircraft is pulse compressed in the range direction, and then the range migration correction is performed to obtain the range focusing result S. The sparse sampling matrix R is determined according to the pre-set number of available pulses, and the noise matrix N is determined according to the set value of signal-to-noise ratio. The observation signal Y of the sparse ISAR system is obtained by Y = RS + N.

[0089] Then, the iterative solving is performed. The detailed process can be designed as follows:

[0090] 1) The initial solution X of the ISAR image is obtained by using the partial Fourier transform on the observation signal Y 0 , wherein the number of azimuth sampling points of the image X is 256. The initial value of the Lagrange multiplier is set as The iteration number i = 0.

[0091] 2) In the i-th iteration, the solution S of the sub-problem is used to update the value of S i+1 .

[0092] 3) The singular value decomposition is performed on S to obtain . Then use the solution to subproblem Z Update Z i+1 The value of .

[0093] 4) Calculate the matrix matrix H i Decomposed into a 4×4 matrix block H p Adjacent matrix blocks overlap by two elements. Within a 20×20 search window, a block matching strategy is used to find elements matching H. p The 7 most similar matrix blocks are then stacked into a 4×4×8 three-dimensional matrix. right The transformation coefficients are obtained by performing a three-dimensional orthogonal transformation. After obtaining the three-dimensional transformation coefficients of all matrix blocks, construct the transformation coefficients arranged in matrix form. Here The construction process involves converting each three-dimensional transformation matrix into a single matrix. Arrange them lexicographically into a column vector, and then use them as a matrix. A column vector. (The result is...) Post-use achievable The update, followed by the solution to subproblem W. Update W i+1 The value of .

[0094] 5) By the updated S i+1 Z i+1 and W i+1 The value of is obtained by using the solution to subproblem X. Update X i+1 The value of .

[0095] 6) Update the Lagrange multipliers and The value of .

[0096] 7) Determine ||X i+1 -X i+1 If ||2 is less than the pre-set iteration termination threshold δ, and it is greater, then let i = i + 1 and return to step 2). Otherwise, the iteration terminates, and the final estimated result X is output. i+1 .

[0097] Figure 3 This refers to ISAR imaging results obtained using the traditional RD algorithm at full aperture. Figure 4 The results of sparse ISAR imaging obtained by the CS algorithm and the proposed method using 50% of the pulse number at a signal-to-noise ratio of 10dB are presented. Figure 5 The results show sparse ISAR imaging obtained by the CS algorithm and the proposed method using 25% pulse number at a signal-to-noise ratio of 10dB.Figure 6 Sparse ISAR imaging results obtained by the proposed method using 50% pulses when the SNR is 0dB, Figure 7 Sparse ISAR imaging results obtained by the proposed method using 25% pulses when the SNR is 0dB. From Figures 3 to 7 It can be seen that the algorithm in the case can still obtain good imaging results using 25% pulses when the SNR is 0dB, further proving the effectiveness of the scheme in the case.

[0098] Unless specifically stated otherwise, the relative arrangement of components and steps, numerical expressions, and numerical values set forth in the examples herein are not limitations of the scope of the application.

[0099] Based on the above method and / or system, the embodiment of the application further provides a server, comprising: one or more processors; a storage device for storing one or more programs, when the one or more programs are executed by the one or more processors, so that the one or more processors implement the above method.

[0100] Based on the above method and / or system, the embodiment of the application further provides a computer readable medium having a computer program stored thereon, wherein the program is executed by a processor to implement the above method.

[0101] In all examples shown and described herein, any specific values should be interpreted as merely exemplary and not limiting, and thus other examples of the example embodiments can have different values.

[0102] It should be noted that: similar labels and letters represent similar items in the following drawings, therefore, once an item is defined in one drawing, it does not need to be further defined and explained in subsequent drawings.

[0103] Finally, it should be noted that: the above described embodiments are only specific embodiments of the application, for explaining the technical solutions of the application, but not limiting it, the protection scope of the application is not limited to this, although the application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand: any person skilled in the art within the technical range disclosed by the application, still can modify or easily think of changes to the technical solutions recorded in the foregoing embodiments, or make equivalent replacement to part of the technical features; and these modifications, changes or replacements do not make the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the application, all should be covered in the protection scope of the application. Therefore, the protection scope of the application should be limited to the protection scope of the claims.

Claims

1. A sparse ISAR imaging method based on low rank and non-local self-similarity, characterized in that, The sparse imaging model is equivalently transformed by introducing a Lagrange multiplier, and the sparse imaging problem is decomposed into several sub-problems for iterative solving; and the final sparse ISAR imaging is obtained according to the iterative solving result. According to low rank of echo signal received by inverse synthetic aperture radar (ISAR) system to reconstruct image, the low rank is used as prior information of the reconstructed image, and a sparse imaging model is constructed by using the prior information and non-local self-similarity constraint of the image; wherein the sparse imaging model is expressed as: wherein, represents the reconstructed image, represents an echo signal matrix, is a dictionary matrix, S is a range image, X represents all three-dimensional transform coefficients arranged in a matrix form, and R represents a sparse aperture matrix, represents a regularization parameter; The equivalent transformation process of the sparse imaging model is represented as: The sparse imaging problem is decomposed into four sub-problems about S, Z, W and X according to S, Z, W and X, the four sub-problems are respectively solved iteratively, and the final sparse ISAR imaging is obtained according to the set iteration termination threshold; wherein, wherein, respectively denote introduced Lagrange multipliers, denotes a penalty parameter, is a dictionary matrix, is an auxiliary variable introduced for model equivalence transformation, is a matrix of all three-dimensional transformation coefficients of the variable W; The sub-problem S is: The sub-problem Z is: ； The sub-problem W is: ； The sub-problem X is: wherein ; In the image non-local self-similarity representation, the reconstructed image is decomposed into a plurality of image blocks, the most similar candidate image blocks to the image blocks are searched in a search window according to a matching strategy, and all the candidate image blocks are stacked into a three-dimensional matrix according to the size of the decomposed image blocks and the number of the candidate image blocks; the three-dimensional transformation coefficients of all the image blocks are obtained by orthogonal transformation of the three-dimensional matrix, and the non-local self-similarity operator of the reconstructed image is represented by the three-dimensional transformation coefficients. 。 2. The sparse ISAR imaging method based on low-rank and nonlocal self-similarity according to claim 1, characterized in that, The low-rank representation of the reconstructed image is given by: where X denotes the reconstructed image, is a dictionary matrix, and S is the distance image, K is the number of scattering points in the imaged scene.

3. The sparse ISAR imaging method based on low rank and nonlocal self-similarity according to claim 1, characterized in that, The model construction module and the imaging solving module are included, wherein, 4. The sparse ISAR imaging method based on low rank and nonlocal self-similarity according to claim 3, characterized in that, The non-local self-similarity operator for reconstructing the image is expressed as: wherein, denotes the non-local self-similarity operator, denotes all three-dimensional transform coefficients arranged in a matrix form, and a column vector is constructed by rearranging in a dictionary order the transform coefficients obtained from a three-dimensional matrix P denotes the number of decomposed image blocks, X denotes the reconstructed image, denotes a three-dimensional orthogonal transform operator.​​ 5. A sparse ISAR imaging system based on low-rank and nonlocal self-similarity, characterized in that, The imaging solving module is configured to equivalently transform the sparse imaging model by introducing a Lagrange multiplier, decompose the sparse imaging problem into several sub-problems for iterative solving, and obtain the final sparse ISAR imaging according to the iterative solving result; wherein, the equivalent transformation process of the sparse imaging model is represented as: The model construction module is used for reconstructing the low rank of an image according to echo signals received by an inverse synthetic aperture radar (ISAR) system, taking the low rank as prior information of the reconstructed image, and constructing a sparse imaging model by using the prior information and a non-local self-similarity constraint of the image; wherein the sparse imaging model is expressed as: wherein, represents the reconstructed image, represents an echo signal matrix, is a dictionary matrix, S is a range image, X represents all three-dimensional transform coefficients arranged in a matrix form, and R represents a sparse aperture matrix, represents a regularization parameter; The sparse imaging problem is decomposed into four sub-problems about S, Z, W and X according to S, Z, W and X, the four sub-problems are respectively solved iteratively, and the final sparse ISAR imaging is obtained according to the set iteration termination threshold; wherein, wherein, respectively denote introduced Lagrange multipliers, denotes a penalty parameter, is a dictionary matrix, is an auxiliary variable introduced for model equivalence transformation, is a matrix of all three-dimensional transformation coefficients of the variable W; The sub-problem S is: The sub-problem Z is: ； The sub-problem W is: ； The sub-problem X is: wherein ; 6. A computer readable storage medium having stored thereon computer program instructions which, when executed by a processor, implement the steps of the sparse ISAR imaging method based on low rank and non-local self-similarity according to any one of claims 1-4. 。 One or more processors; 7. A terminal device comprising: A storage device is configured to store one or more programs, when the one or more programs are executed by the one or more processors, so that the one or more processors implement the steps of the sparse ISAR imaging method based on low rank and non-local self-similarity according to any one of claims 1-4. ​

Images