CN114966687A - Sparse ISAR imaging method and system based on low rank and non-local self-similarity - Google Patents

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

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CN114966687A
CN114966687A CN202210584667.5A CN202210584667A CN114966687A CN 114966687 A CN114966687 A CN 114966687A CN 202210584667 A CN202210584667 A CN 202210584667A CN 114966687 A CN114966687 A CN 114966687A
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任笑真
白艳雯
崔静
樊慧玲
张自豪
吕宗旺
孙福艳
王贺鹏
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Henan University of Technology
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    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
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    • G01S13/90—Radar or analogous systems specially adapted for specific applications for mapping or imaging using synthetic aperture techniques, e.g. synthetic aperture radar [SAR] techniques
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    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
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    • G01S13/88—Radar or analogous systems specially adapted for specific applications
    • G01S13/89—Radar or analogous systems specially adapted for specific applications for mapping or imaging
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Abstract

The invention 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, wherein the low rank of an echo signal reconstruction image received by an ISAR system is used as prior information of the reconstruction image, and a sparse imaging model is constructed by utilizing the prior information and image non-local self-similarity constraint; introducing a Lagrange multiplier to perform equivalent transformation on the sparse imaging model, and decomposing the sparse imaging problem into a plurality of subproblems to perform iterative solution; and obtaining the final sparse ISAR imaging according to the iterative solution result. According to the sparse ISAR imaging model, the structural correlation of the ISAR target is mined, and the low-rank prior and the non-local self-similarity of the ISAR target are combined to construct the sparse ISAR imaging model, so that the sparse ISAR imaging quality and the imaging effect are improved.

Description

Sparse ISAR imaging method and system based on low rank and non-local self-similarity
Technical Field
The invention 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
Inverse Synthetic Aperture Radar (ISAR) is capable of synthesizing a larger aperture in the azimuth direction using relative motion between the object and the radar, and therefore it can improve resolution beyond the diffraction limit of the true aperture, and has wide application prospects in many military and civilian fields. In the traditional ISAR imaging method based on Fourier transform, the observation interval must be long enough to obtain high azimuth resolution. However, in practical ISAR applications, the imaging target is always uncooperative or mobile, continuous measurements may not be possible in long coherent processing intervals or the data acquired for some period is invalid, so it is often difficult to obtain well focused ISAR images. In addition, the target motion compensation is much more complex in long coherent processing, so that the research on the sparse aperture ISAR imaging strategy is of great significance.
In order to overcome the defocusing problem of ISAR imaging during sparse aperture, a spatial spectrum estimation method is introduced into ISAR imaging in some researches. Compared with an imaging method based on Fourier transform, the spatial spectrum estimation method can obtain lower side lobes and higher resolution, but is sensitive to noise and modeling errors. Compressed Sensing (CS) is a model-based framework for data acquisition and signal recovery, and if the target to be recovered satisfies sparsity or compressibility, CS can recover the original signal from limited sampling with high probability, and has significant advantages in sparse signal reconstruction. Since ISAR targets are typically composed of a limited number of strong scattering centers, strong spatial sparsity is exhibited. There is therefore increasing research to combine sparse ISAR imaging with CS to improve imaging performance. However, the CS method is susceptible to noise and the imaging quality is not high at low signal-to-noise ratios. In order to improve the imaging quality of the CS algorithm, various sparse prior information is introduced into a sparse ISAR imaging model to improve the imaging quality. The Bayesian compressive sensing method assumes that the ISAR target meets certain prior distribution in the imaging process, and obtains the ISAR target imaging result by using Bayesian estimation, but the calculation burden is heavy, and the imaging quality is not high under the condition of low signal-to-noise ratio. In the sparse ISAR imaging method based on total variation, the smoothness of an ISAR target is constrained in an imaging model to improve the imaging quality, but the imaging result is easy to cause over-smoothness. The low-rank matrix recovery is another signal processing path, and the low-rank matrix recovery seeks global lowest-rank representation of a data matrix and is widely applied to the fields of image processing, synthetic aperture radar imaging, ISAR image denoising and the like. Low rank matrix recovery recovers undersampled data based on the assumption that the matrix is low rank in nature. At present, the sparsity of ISAR target images is mostly simply utilized, the inherent structural correlation of the images is not mined, and the imaging quality needs to be improved.
Disclosure of Invention
Therefore, the invention provides a sparse ISAR imaging method and system based on low rank and non-local self-similarity, which are used for constructing a sparse ISAR imaging model by excavating the structural correlation of an ISAR target and combining the low rank prior and the non-local self-similarity of the ISAR target so as to improve the sparse ISAR imaging quality and the imaging effect.
According to the design scheme provided by the invention, a sparse ISAR imaging method based on low rank and non-local self-similarity is provided, which comprises the following contents:
according to the low rank of an echo signal reconstruction image received by an ISAR (inverse synthetic aperture radar) system, the low rank is used as prior information of the reconstruction image, and a sparse imaging model is constructed by utilizing the prior information and image non-local self-similarity constraint;
introducing a Lagrange multiplier to perform equivalent transformation on the sparse imaging model, and decomposing the sparse imaging problem into a plurality of subproblems to perform iterative solution; and obtaining the final sparse ISAR imaging according to the iterative solution result.
As the sparse ISAR imaging method based on low rank and non-local self-similarity of the present invention, further, the low rank property of the reconstructed image is expressed as:
Figure BDA0003665436400000021
wherein, X tableAnd (3) representing a reconstructed image, wherein phi is a dictionary matrix, S is a distance image, and K is the number of scattering points in an imaging scene.
As the sparse ISAR imaging method based on low rank and non-local self-similarity, further, in the non-local self-similarity representation of the image, decomposing the reconstructed image into a plurality of image blocks, searching a candidate image block most similar to the image block in a search window according to a matching strategy, and stacking all the candidate image blocks into a three-dimensional matrix according to the size of the decomposed image block and the number of the candidate image blocks; and performing orthogonal transformation on the three-dimensional matrix to obtain three-dimensional transformation coefficients of all image blocks, and expressing a non-local self-similarity operator of a reconstructed image by using the three-dimensional transformation coefficients.
As the sparse ISAR imaging method based on low rank and non-local self-similarity, the non-local self-similarity operator of the reconstructed image is expressed as follows:
Figure BDA0003665436400000022
therein, Ψ NL X denotes a non-local self-similarity operator, Θ X Represents all three-dimensional transformation coefficients arranged in a matrix form, and Θ X The column vectors are based on a three-dimensional matrix
Figure BDA0003665436400000023
Resulting transform coefficients
Figure BDA0003665436400000024
Rearranging and constructing according to the order of the dictionary, P represents the number of the decomposed image blocks, X represents the reconstructed image, T 3D Representing a three-dimensional orthogonal transformation operator.
As the sparse ISAR imaging method based on low rank and non-local self-similarity, further, the sparse imaging model is expressed as:
Figure BDA0003665436400000025
wherein X represents a reconstructed image, Y represents an echo signal matrix, phi is a dictionary matrix, S is a distance image, and theta X Representing all three-dimensional transform coefficients arranged in a matrix form, R representing a sparse aperture matrix, λ 1 、λ 2 The regularization parameters are represented.
As the sparse ISAR imaging method based on low rank and non-local self-similarity, the equivalent transformation process of the sparse imaging model is further expressed as follows:
Figure BDA0003665436400000031
wherein, V 1 、V 2 And V 3 Respectively representing introduced Lagrange multipliers, mu representing a penalty parameter, phi being a dictionary matrix, Z and W being auxiliary variables introduced by model equivalent transformation, theta W All three-dimensional transform coefficients of the variable W arranged in a matrix form.
As the sparse ISAR imaging method based on low rank and non-local self-similarity of the present invention, 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 respectively solved iteratively, and the final sparse ISAR imaging is obtained according to the set iteration termination threshold.
Further, the present invention also provides a sparse ISAR imaging system based on low rank and non-local self-similarity, comprising: a model building module and an imaging solution module, wherein,
the model construction module is used for constructing a sparse imaging model by using prior information and image non-local self-similarity constraint according to the low rank of an echo signal reconstruction image received by an inverse synthetic aperture radar ISAR system and taking the low rank as the prior information of the reconstruction image;
the imaging solving module is used for carrying out equivalent transformation on the sparse imaging model by introducing a Lagrange multiplier and decomposing the sparse imaging problem into a plurality of subproblems for iterative solution; and obtaining the final sparse ISAR imaging according to the iterative solution result.
The invention has the beneficial effects that:
according to the invention, the structural correlation of the ISAR target is deeply excavated, the low-rank prior and the non-local self-similarity of the ISAR target are combined, and the influence of noise is considered in the model to construct a sparse ISAR imaging model, so that the sparse ISAR imaging quality can be effectively improved, and a better imaging result can still be obtained under the influence of finite pulse and noise; and the constructed sparse ISAR imaging model is decomposed into four sub-optimization problems in the solving process for iterative solution, so that the imaging efficiency of the sparse ISAR imaging model can be improved while the sparse ISAR imaging quality is improved, and the sparse ISAR imaging model has a good application prospect.
Description of the drawings:
FIG. 1 is a flow diagram of a sparse ISAR imaging method in an embodiment;
FIG. 2 is a schematic diagram of a sparse ISAR imaging algorithm in an embodiment;
FIG. 3 is a diagram illustrating the full aperture ISAR imaging results obtained by the conventional RD algorithm in an embodiment;
FIG. 4 is a schematic diagram of a CS algorithm and a sparse ISAR imaging result obtained by the algorithm with a 50% pulse number in an embodiment when the signal-to-noise ratio is 10dB, (a) the CS algorithm imaging result, and (b) the algorithm imaging result;
FIG. 5 is a schematic diagram of a CS algorithm and a sparse ISAR imaging result obtained by the algorithm with a 25% pulse number in case of a signal-to-noise ratio of 10dB in the embodiment, wherein (a) the imaging result of the CS algorithm is shown, and (b) the imaging result of the algorithm is shown;
FIG. 6 is a schematic diagram of a CS algorithm and a sparse ISAR imaging result obtained by the algorithm with a 50% pulse number in an embodiment when the signal-to-noise ratio is 0dB, (a) the CS algorithm imaging result, and (b) the algorithm imaging result;
FIG. 7 shows sparse ISAR imaging results obtained by a CS algorithm and the algorithm using a 25% pulse number in an embodiment when the signal-to-noise ratio is 0dB, (a) CS algorithm imaging results, and (b) the algorithm imaging results.
The specific implementation mode is as follows:
in order to make the objects, technical solutions and advantages of the present invention clearer and more obvious, the present invention is further described in detail below with reference to the accompanying drawings and technical solutions.
An embodiment of the present invention, as shown in fig. 1, provides a sparse ISAR imaging method based on low rank and non-local self-similarity, including the following contents:
s101, according to the low rank of an echo signal reconstruction image received by an ISAR (inverse synthetic aperture radar) system, taking the low rank as prior information of the reconstruction image, and constructing a sparse imaging model by utilizing the prior information and image non-local self-similarity constraint;
s102, introducing a Lagrange multiplier to perform equivalent transformation on the sparse imaging model, and decomposing the sparse imaging problem into a plurality of subproblems to perform iterative solution; and obtaining the final sparse ISAR imaging according to the iterative solution result.
In the embodiment of the scheme, the structural correlation of the ISAR target is deeply excavated, the low-rank prior and the non-local self-similarity of the ISAR target are combined, meanwhile, the influence of noise is considered in the model, and the sparse ISAR imaging model is constructed, so that the sparse ISAR imaging quality can be effectively improved, and a better imaging result can still be obtained under the influence of limited pulse and noise.
Performing pulse compression on an echo signal received by an ISAR system in a range direction, and then performing discrete sampling on the signal subjected to range migration correction to obtain a range compression signal s ═ phi delta corresponding to a range cell, wherein s ═ phi (delta tau), s (2 delta tau), …, s (L delta tau)] T Representing a full aperture distance compressed signal corresponding to a distance cell, δ ═ δ 1 ,δ 2 ,…,δ M ] T Representing the complex scattering coefficient whose non-zero elements correspond to the amplitudes of the K strongest scattering points. Dictionary matrix phi is composed of 1 ,φ 2 ,…,φ m ,…,φ M ]Is formed of phi m ＝exp[-j2πf a (m)τ] T 。
Combining the distance compressed signals corresponding to all the distance units together to obtain a distance focusing result S L×N ＝Φ L×M X M×N Wherein S ═ S 1 ,s 2 ,…,s N ]And X ═ δ 1 ,δ 2 ,…,δ N ]。
Under non-ideal conditions, some measurement echo signals are lost or the received signal is invalid for some period of time. Furthermore, the received echo signals are often affected by noise. Thus, the observed signal of an ISAR system may be represented as
Y＝RS+N (1)
Where R represents the sparse aperture matrix and N is the additive noise matrix. The purpose of ISAR imaging is therefore to recover the unknown image result X from the noise contaminated signal matrix Y.
According to the fact that the rank of the ISAR system range image S meets rank (S) is less than or equal to K, the rank of the ISAR imaging result X obtained through derivation meets the requirement
Figure BDA0003665436400000051
Therefore, the ISAR image X has low rank property, and the low rank property of the image X can be used to improve the sparse ISAR imaging quality. To obtain
Figure BDA0003665436400000052
Because solving the rank minimization problem is troublesome, the kernel norm | X | survival of the matrix X is used in solving * Instead of the rank of matrix X.
Further, in the image non-local self-similar representation of the embodiment of the present disclosure, the reconstructed image is decomposed into a plurality of image blocks, a candidate image block most similar to the image block is 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 block and the number of the candidate image blocks; and performing orthogonal transformation on the three-dimensional matrix to obtain three-dimensional transformation coefficients of all image blocks, and expressing a non-local self-similarity operator of a reconstructed image by using the three-dimensional transformation coefficients.
Decomposing ISAR image X into P image blocks X of size L × L p Finding X in a T × T search window according to a block matching strategy p C-1 most similar image blocks, and then all the most similar blocks are stacked into a three-dimensional matrix of size L × L × c
Figure BDA0003665436400000053
To pair
Figure BDA0003665436400000054
Performing three-dimensional orthogonal transformation to obtain transformation coefficients of
Figure BDA0003665436400000055
When the three-dimensional transformation coefficients of all image blocks are obtained, the formula of non-local self-similarity can be expressed as
Figure BDA0003665436400000056
Therein Ψ NL X denotes a non-local self-similarity operator. Theta X Representing all three-dimensional transformation coefficients, Θ, arranged in matrix form X Is composed of
Figure BDA0003665436400000057
And rearranging the constructed object according to the dictionary order.
By combining the low-rank prior and the non-local self-similarity constraint of the ISAR image and considering the influence of noise, the proposed sparse ISAR imaging model can be expressed as:
Figure BDA0003665436400000058
wherein λ 1 And λ 2 Is a regularization parameter.
Introducing lagrange multiplier V 1 、V 2 And V 3 The proposed sparse ISAR imaging model is converted into the following equivalent form:
Figure BDA0003665436400000059
where μ is the penalty parameter, <, > is the inner product of the two matrices.
Further, in the embodiment of the present disclosure, the sparse imaging problem is decomposed into four sub-problems related to S, Z, W, X according to S, Z, W, X, the four sub-problems are respectively solved iteratively, and a final sparse ISAR imaging is obtained according to a set iteration termination threshold.
In order to effectively obtain a sparse ISAR imaging result, aiming at the optimization problem (6), the optimization problem is decomposed into four sub-optimization problems to be subjected to iterative solution. Specific imaging procedures can be described as follows:
4a) the sub-problem S is given by:
Figure BDA0003665436400000061
the derivation of the above equation and making it equal to 0 yields the solution of the sub-problem S:
Figure BDA0003665436400000062
4b) the subproblem Z is given by:
Figure BDA0003665436400000063
solution of the sub-problem Z obtained by singular value thresholding
Figure BDA0003665436400000064
Wherein D τ (. represents a singular value threshold operator, defined as
Figure BDA0003665436400000065
Wherein M ═ U ∑ r V H Is the singular value decomposition of the matrix M of rank r.
4c) The subproblem W is given by:
Figure BDA0003665436400000066
wherein
Figure BDA0003665436400000067
Since theta W For non-local self-similar transform coefficients, Θ W Is different from the matrix W. Thus the invention makes use of
Figure BDA0003665436400000068
Establishing, transforming the sub-optimization problem (12) into
Figure BDA0003665436400000069
Wherein N is W Is the number of elements in W,
Figure BDA00036654364000000610
is theta W The number of elements in (1).
Obtaining theta based on a soft threshold method W Closed form solution of
Figure BDA00036654364000000611
Wherein soft (x, λ) ═ sgn (x) · max (x- λ, 0). To obtain
Figure BDA0003665436400000071
Then, the solution of the W sub-problem (12) can be given according to the inverse of the non-local self-similarity
Figure BDA0003665436400000072
Wherein omega NL Is the inverse process of non-local self-similarity.
4d) The subproblem X is given by:
Figure BDA0003665436400000073
taking the derivative of the above equation and making it equal to 0 yields the solution of the sub-problem X:
Figure BDA0003665436400000074
4e) lagrange multiplier V 1 、V 2 And V 3 Update of
Figure BDA0003665436400000075
4f) And repeating the steps 4a) to 4e) until a preset iteration termination threshold is met, and obtaining a final sparse ISAR imaging result X.
Further, based on the foregoing method, an embodiment of the present invention further provides a sparse ISAR imaging system based on low rank and non-local self-similarity, including: a model building module and an imaging solution module, wherein,
the model construction module is used for constructing a sparse imaging model by using prior information and image non-local self-similarity constraint according to the low rank of an echo signal reconstruction image received by an inverse synthetic aperture radar ISAR system and taking the low rank as the prior information of the reconstruction image;
the imaging solving module is used for carrying out equivalent transformation on the sparse imaging model by introducing a Lagrange multiplier and decomposing the sparse imaging problem into a plurality of subproblems for iterative solution; and obtaining the final sparse ISAR imaging according to the iterative solution result.
To verify the validity of the scheme, the following algorithm and experimental data are further explained with reference to fig. 2:
data used for the experiment: the proposed sparse ISAR imaging method is validated using measured echo data of the Yak-42 aircraft. The main radar parameters are as follows: the carrier frequency was 5.6GHz, the bandwidth was 400MHz, the pulse repetition frequency was 800Hz, the number of azimuth pulses was 256, and the number of range cells was 256.
Inputting: the measured echo data matrix of the Yak-42 airplane, the Fourier transform matrix phi, the number of available pulses and the value of the signal-to-noise ratio
Firstly, the echo signal of the actual measurement Yak-42 aircraft is subjected to pulse compression in the range direction, and then range migration correction is carried out to obtain a range focusing result S. And determining a sparse sampling matrix R according to the preset available pulse number, and determining a noise matrix N according to the set signal-to-noise ratio value. And obtaining an observation signal Y of the sparse ISAR system from Y-RS + N.
And then performing iterative solution. The detailed process can be designed as follows:
1) obtaining an initial solution X of the ISAR image by using partial Fourier transform on the observation signal Y 0 Here, the number of azimuth sampling points of the image X is 256. Setting initial values of Lagrange multipliers
Figure BDA0003665436400000081
The iteration number i is 0;
2) at the ith iteration, the solution of the sub-problem S is used
Figure BDA0003665436400000082
Updating S i+1 The value of (c).
3) To pair
Figure BDA0003665436400000083
Performing singular value decomposition to obtain
Figure BDA0003665436400000084
And then using the solution of the sub-problem Z
Figure BDA0003665436400000085
Updating Z i+1 The value of (c).
4) Computing matrices
Figure BDA0003665436400000086
Will matrix H i Decomposed into matrix blocks H of size 4 x 4 p Overlapping 2 elements between adjacent matrix blocks, finding H in a 20 × 20 search window according to a block matching strategy p 7 most similar matrix blocks, after which all most similar blocks are stacked into a three-dimensional matrix of size 4 x 8
Figure BDA0003665436400000087
For is to
Figure BDA0003665436400000088
Performing three-dimensional orthogonal transformation to obtain transformation coefficients of
Figure BDA0003665436400000089
After the three-dimensional transformation coefficients of all matrix blocks are obtained, constructing the transformation coefficients arranged in the form of matrix
Figure BDA00036654364000000810
Herein, the
Figure BDA00036654364000000811
Is constructed by transforming each three-dimensional transformation matrix
Figure BDA00036654364000000812
Arranged into a column vector according to the dictionary sequence and then used as a matrix
Figure BDA00036654364000000813
A column vector of (2). To obtain
Figure BDA00036654364000000814
After-utilization of
Figure BDA00036654364000000815
Can obtain the product
Figure BDA00036654364000000816
After which the solution of the subproblem W is utilized
Figure BDA00036654364000000817
Updating W i+1 The value of (c).
5) By updated S i+1 ，Z i+1 And W i+1 Using the solution of the subproblem X
Figure BDA00036654364000000818
Updating X i+1 The value of (c).
6) Updating lagrange multipliers
Figure BDA00036654364000000819
And
Figure BDA00036654364000000820
the value of (c).
7) Judge | | | X i+1 -X i+1 || 2 And if the value is larger than the preset iteration termination threshold delta, making i equal to i +1, and returning to the step 2). Otherwise, iteration is terminated, and the final estimation result X is output i+1 。
Fig. 3 is an ISAR imaging result obtained by using a conventional RD algorithm at full aperture, fig. 4 is a sparse ISAR imaging result obtained by using a 50% pulse number for a CS algorithm and a proposed method at a signal-to-noise ratio of 10dB, fig. 5 is a sparse ISAR imaging result obtained by using a 25% pulse number for a CS algorithm and a proposed method at a signal-to-noise ratio of 10dB, fig. 6 is a sparse ISAR imaging result obtained by using a 50% pulse number for a CS algorithm and a proposed method at a signal-to-noise ratio of 0dB, and fig. 7 is a sparse ISAR imaging result obtained by using a 25% pulse number for a CS algorithm and a proposed method at a signal-to-noise ratio of 0 dB. As can be seen from fig. 3 to fig. 7, when the signal-to-noise ratio is 0dB, the algorithm can still obtain a better imaging result by using a 25% pulse number, further proving the effectiveness of the scheme.
Unless specifically stated otherwise, the relative steps, numerical expressions, and values of the components and steps set forth in these embodiments do not limit the scope of the present invention.
Based on the foregoing method and/or system, an embodiment of the present invention further provides a server, including: one or more processors; a storage device for storing one or more programs which, when executed by the one or more processors, cause the one or more processors to implement the method described above.
Based on the method and/or system, the embodiment of the invention further provides a computer readable medium, on which a computer program is stored, wherein the program, when executed by a processor, implements the method.
In all examples shown and described herein, any particular value should be construed as merely exemplary, and not as a limitation, and thus other examples of example embodiments may have different values.
It should be noted that: like reference numbers and letters refer to like items in the following figures, and thus, once an item is defined in one figure, it need not be further defined and explained in subsequent figures.
Finally, it should be noted that: although the present invention has been described in detail with reference to the foregoing embodiments, it should be understood by those skilled in the art that the following descriptions are only illustrative and not restrictive, and that the scope of the present invention is not limited to the above embodiments: any person skilled in the art can modify or easily conceive the technical solutions described in the foregoing embodiments or equivalent substitutes for some technical features within the technical scope of the present disclosure; such modifications, changes or substitutions do not depart from the spirit and scope of the embodiments of the present invention, and they should be construed as being included therein. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (10)

1. A sparse ISAR imaging method based on low rank and non-local self-similarity is characterized by comprising the following contents:
according to the low rank of an echo signal reconstruction image received by an ISAR (inverse synthetic aperture radar) system, the low rank is used as prior information of the reconstruction image, and a sparse imaging model is constructed by utilizing the prior information and image non-local self-similarity constraint;
introducing a Lagrange multiplier to perform equivalent transformation on the sparse imaging model, and decomposing the sparse imaging problem into a plurality of subproblems to perform iterative solution; and obtaining the final sparse ISAR imaging according to the iterative solution result.
2. Low rank and non-local self-similarity based sparse ISAR according to claim 1Imaging method characterized in that the low rank property of the reconstructed image is expressed as:
Figure FDA0003665436390000011
wherein X represents a reconstructed image, phi is a dictionary matrix, S is a distance image, and K is the number of scattering points in an imaging scene.
3. The sparse ISAR imaging method based on low rank and non-local self-similarity as claimed in claim 1, wherein in the image non-local self-similarity representation, the reconstructed image is decomposed into a plurality of image blocks, a candidate image block most similar to the image block is found 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 block and the number of the candidate image blocks; and performing orthogonal transformation on the three-dimensional matrix to obtain three-dimensional transformation coefficients of all image blocks, and expressing a non-local self-similarity operator of a reconstructed image by using the three-dimensional transformation coefficients.
4. The sparse ISAR imaging method based on low rank and non-local self-similarity according to claim 3, wherein the non-local self-similarity operator of the reconstructed image is expressed as:
Figure FDA0003665436390000012
therein, Ψ NL X denotes a non-local self-similarity operator, Θ X Represents all three-dimensional transformation coefficients arranged in a matrix form, and Θ X The column vectors are based on a three-dimensional matrix
Figure FDA0003665436390000014
Resulting transform coefficients
Figure FDA0003665436390000015
Rearranging and constructing according to the order of the dictionary, P represents the number of the decomposed image blocks, X represents the reconstructed image, T 3D Representing a three-dimensional orthogonal transformation operator.
5. The low rank and non-local self-similarity based sparse ISAR imaging method according to claim 1, wherein the sparse imaging model is represented as:
Figure FDA0003665436390000013
wherein X represents a reconstructed image, Y represents an echo signal matrix, phi is a dictionary matrix, S is a distance image, and theta X Representing all three-dimensional transform coefficients arranged in a matrix form, R representing a sparse aperture matrix, λ 1 、λ 2 The regularization parameters are represented.
6. The sparse ISAR imaging method based on low rank and non-local self-similarity according to claim 5, wherein the equivalent transformation process performed on the sparse imaging model is represented as:
Figure FDA0003665436390000021
wherein, V 1 、V 2 And V 3 Respectively representing introduced Lagrange multipliers, mu representing a penalty parameter, phi being a dictionary matrix, Z and W being auxiliary variables introduced by model equivalent transformation, theta W All three-dimensional transform coefficients of the variable W arranged in a matrix form.
7. The sparse ISAR imaging method based on low rank and non-local self-similarity according to claim 6, wherein the sparse imaging problem is decomposed into four sub-problems related to S, Z, W, X according to S, Z, W, X, the four sub-problems are solved iteratively, and the final sparse ISAR imaging is obtained according to the set iteration termination threshold.
8. A sparse ISAR imaging system based on low rank and non-local self-similarity, comprising: a model building module and an imaging solution module, wherein,
the model construction module is used for constructing a sparse imaging model by using prior information and image non-local self-similarity constraint according to the low rank of an echo signal reconstruction image received by an inverse synthetic aperture radar ISAR system and taking the low rank as the prior information of the reconstruction image;
the imaging solving module is used for carrying out equivalent transformation on the sparse imaging model by introducing a Lagrange multiplier and decomposing the sparse imaging problem into a plurality of subproblems for iterative solution; and obtaining the final sparse ISAR imaging according to the iterative solution result.
9. A computer readable storage medium having stored thereon computer program instructions which, when executed by a processor, implement the steps of the low rank and non-local self-similarity based sparse ISAR imaging method of any of claims 1 to 7.
10. A terminal device, comprising: one or more processors; storage means for storing one or more programs which, when executed by the one or more processors, cause the one or more processors to carry out the steps of the low rank and non-local self-similarity based sparse ISAR imaging method of any one of claims 1 to 7.
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CN115508835A (en) * 2022-10-28 2022-12-23 广东工业大学 Tomography SAR three-dimensional imaging method based on blind compressed sensing
CN115508835B (en) * 2022-10-28 2024-03-15 广东工业大学 Chromatographic SAR three-dimensional imaging method based on blind compressed sensing

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