Ultra-wideband radar low sidelobe imaging method and device based on low-rank and sparse prior

Abstract

The present invention provides a method and device for ultra-wideband radar low-sidelobe imaging using a combined low-rank and sparse prior. This method belongs to the field of ultra-wideband radar imaging technology and includes: building a combined low-rank and sparse prior imaging model; deriving an iterative solution form for the combined low-rank and sparse prior imaging model; determining a regularization parameter through a nested search; reconstructing the image based on the obtained regularization parameter and iterative solution form, and determining the termination of the iteration. The present invention effectively suppresses azimuth and range sidelobes in radar imaging results, making them applicable to real-world scenarios.

Description

Technical Field

[0001] The present invention belongs to the technical field of ultra-wideband radar imaging, and in particular relates to an ultra-wideband radar low-sidelobe imaging method and device combining low rank and sparse priors. Background Art

[0002] Ultra-wideband radar's range and azimuth resolution are fundamental to radar imaging. With the increasing focus on radar system portability, small, sparse arrays have become the preferred antenna layout. This results in typical high sidelobes in radar images. Considering the impact of noise, achieving high-quality image reconstruction under low signal-to-noise ratio conditions becomes a key challenge in radar imaging. Existing methods for sidelobe suppression include:

[0003] (1) Special array design can suppress side lobes to a certain extent;

[0004] (2) Coherence weighting methods are widely used in low sidelobe imaging. The coherence factor (CF), phase coherence factor (PCF), and sign coherence factor (SCF) can all achieve sidelobe suppression in the azimuth dimension.

[0005] (3) Compressed sensing theory has shown great potential in high-quality radar imaging. It can reconstruct high-dimensional images with high quality using limited observation data.

[0006] However, the above suppression method has the following defects:

[0007] (1) The sidelobe suppression effect produced by a particular array design is limited by a lower bound, which is related to the number of antennas;

[0008] (2) The coherent weighting method can only suppress the sidelobes in the azimuth dimension, but has no effect on the sidelobes in the range dimension;

[0009] (3) Compressed sensing theory involves large-scale matrix operations, which greatly increases the computational complexity. At the same time, it involves the selection of prior parameters, and inappropriate parameters will produce erroneous results. Large-scale matrix operations and prior parameter debugging make compressed sensing theory difficult to apply in practice;

[0010] (4) All three types of technologies do not take the impact of noise into consideration and have poor noise resistance performance.

[0011] Therefore, how to effectively suppress the azimuth and range sidelobes in radar imaging results with a limited number of antennas and make them applicable to actual scenarios is a problem that needs to be solved. Summary of the Invention

[0012] To solve the above technical problems, the present invention provides an ultra-wideband radar low sidelobe imaging method and device combining low rank and sparse priors.

[0013] In order to achieve the above object, the present invention adopts the following technical solutions:

[0014] A low-sidelobe imaging method for ultra-wideband radar combined with low-rank and sparse priors, comprising the following steps:

[0015] Step A: Build a joint low-rank and sparse prior imaging model;

[0016] Step B: Derive the iterative solution form of the joint low-rank and sparse prior imaging model;

[0017] Step C: Perform nested search to determine the regularization parameter;

[0018] Step D: Reconstruct the image based on the regularization parameter obtained in step C and the iterative solution form obtained in step B, and determine the termination of the iteration.

[0019] The present invention also provides an ultra-wideband radar low sidelobe imaging device combining low rank and sparse priors, comprising the following modules:

[0020] Model building module, building a joint low-rank and sparse prior imaging model;

[0021] A derivation module derives the iterative solution form of the joint low-rank and sparse prior imaging model;

[0022] Parameter determination module, which performs nested search to determine the regularization parameters;

[0023] The image reconstruction module reconstructs the image according to the obtained regularization parameters and iterative solution form, and determines the termination of the iteration.

[0024] The present invention also provides an electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, the steps of the above-mentioned ultra-wideband radar low sidelobe imaging method combining low rank and sparse prior are implemented.

[0025] The present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the above-mentioned ultra-wideband radar low sidelobe imaging method combining low rank and sparse priors.

[0026] Beneficial effects:

[0027] (1) In the imaging model of the present invention, low-rank and sparse constraints are simultaneously applied to the image of the region of interest, so that the final image has both low azimuth and range sidelobe characteristics;

[0028] (2) The noise constraint in the imaging model of the present invention enables the proposed algorithm to exhibit high noise resistance performance;

[0029] (3) The matrix-based iterative solution of the present invention greatly reduces computational complexity and is less time-consuming than the compressed sensing algorithm, making it feasible in practical use. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 Set up the graph for the simulation scenario;

[0031] Figure 2a Obtain target image for backprojection algorithm;

[0032] Figure 2b Acquire target images for coherence weighting algorithm;

[0033] Figure 2c Obtain target images for compressed sensing algorithms;

[0034] Figure 2d Acquire a target image for the algorithm proposed in the present invention;

[0035] Figure 3a is the imaging result obtained by the back-projection algorithm when the signal-to-noise ratio is 0 dB;

[0036] Figure 3b is the imaging result obtained by the coherence weighted algorithm when the signal-to-noise ratio is 0 dB;

[0037] Figure 3c This is the imaging result obtained by the compressed sensing algorithm when the signal-to-noise ratio is 0 dB;

[0038] Figure 3d This is the imaging result obtained by the algorithm proposed in this invention when the signal-to-noise ratio is 0 dB. DETAILED DESCRIPTION

[0039] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only intended to illustrate the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.

[0040] An embodiment of the present invention provides an ultra-wideband radar low sidelobe imaging method combining low rank and sparse priors, comprising the following steps:

[0041] Step A: Build a joint low-rank and sparse prior imaging model;

[0042] Step B: Derive the iterative solution form of the joint low-rank and sparse prior imaging model;

[0043] Step C: Nested search to determine the regularization parameter;

[0044] Step D: Reconstruct the image based on the regularization parameter obtained in step C and the iterative solution form obtained in step B, and determine the termination of the iteration.

[0045] Specifically, the step A includes:

[0046] for transmit antennas and An ultra-wideband radar system consisting of receiving antennas, the system frequency point number is , the received echo matrix is ​​recorded as , its size is , the image of the region of interest can be regarded as a collection of pixels, forming the image matrix of the region of interest In two-dimensional imaging, the image matrix of the region of interest is The size of , The number of pixels representing the orientation, Represents the number of pixels in the range direction. To build the echo matrix Image matrix with region of interest The linear model between them is vectorized.

[0047] (1)

[0048] in, Represents vectorized operations on matrices. is a matrix The vectorized form of is a matrix The vectorized form of .

[0049] echo vector and vector The sizes are and Therefore, the echo vector The acquisition process can be expressed as the following linear form of matrix multiplication:

[0050] (2)

[0051] in, It is a large-scale sensing matrix, and its specific composition is:

[0052] (3)

[0053] Among them, the elements of C , Emitted for radar systems The frequency point Frequency points, Represents the direction , distance to pixels to The transmitting antenna The time delay of each receiving antenna, exp() represents the exponential function, Is an imaginary unit.

[0054] In practice, the radar echo matrix contains not only the target's reflected echo but also noise. Considering the influence of noise, formula (2) can be updated as follows:

[0055] (4)

[0056] in, represents the noise vector.

[0057] The essence of radar imaging is to reconstruct the image of the region of interest using the echo matrix, that is, to restore the vector using formula (4) This is an ill-posed problem with infinite solutions. Considering that the target occupies only a small number of elements in the image of the region of interest, the imaging result has low-rank and sparse prior characteristics. Therefore, the objective function of the imaging model can be expressed as the following triple constraint:

[0058] (5)

[0059] in, , and represent the nuclear norm, Norm and norm. and are regularization parameters, which are used to control the proportion of sparsity and noise constraints respectively. Represents finding the minimum value of a function.

[0060] Formula (5) contains constraints on vectors, which often leads to large-scale computation in subsequent solutions. In order to reduce computational complexity, the objective function is converted into a matrix form:

[0061] (6)

[0062] in, Represents matrix operations on vectors, represents the F norm, Represents vectorized operations on matrices.

[0063] The three constraints of formula (6) are all related to the image matrix of the region of interest This makes the solution difficult. To further simplify, we introduce the auxiliary matrix and the auxiliary matrix , rewrite the objective function as:

[0064] (7)

[0065] Thus, a combined low-rank and sparse prior imaging model was constructed. The first two constraints are applied to the image of the region of interest. This combined low-rank and sparse prior constraint effectively suppresses the azimuth and range sidelobes in the image reconstruction results. The third constraint is applied to noise, which is the basis for the noise resistance of the method.

[0066] Specifically, the step B includes:

[0067] The objective function in step A is a multivariable optimization problem, and the optimal solution in iterative form can be obtained using the alternating direction multiplier method. According to formula (7), the corresponding augmented Lagrange multiplier function can be obtained :

[0068] (8)

[0069] in, and is the Lagrange multiplier matrix, and is the penalty factor, Represents the matrix inner product.

[0070] Fixing other variables and solving the iterative solution of a single variable in turn is the core of the alternating direction multiplication method. The core steps can be summarized as follows:

[0071] (9)

[0072] in, Iteration index, superscript and Representing the Second and The parameter values ​​obtained after iterations are Is an incremental factor used to control the change of the penalty factor. . Represents finding the optimal The value makes the function value in the brackets minimum, Represents finding the optimal The value makes the function value in the brackets minimum, Represents finding the optimal The value that minimizes the function in parentheses.

[0073] The first three steps in formula (9) are three sub-optimization problems, and the iterative solutions of the three sub-optimization problems are derived in turn. The sub-optimization problem can be further expressed as:

[0074] (10)

[0075] According to the singular value threshold algorithm, The iterative formula can be written as:

[0076] (11)

[0077] Here, the superscript H represents the conjugate transpose operation of the matrix. 、 and for The singular value decomposition results of are the left singular matrix, the right singular matrix and the singular value matrix, and the relationship between them is:

[0078] (12)

[0079] in, is the soft threshold function, indicating The elements relative to The size of the output matrix can be expressed in element form as:

[0080] (13)

[0081] in, Represents the soft threshold function in matrix form No. elements, Indicates taking the maximum value of the two elements in the brackets.

[0082] about The sub-optimization problem can be further expressed as:

[0083] (14)

[0084] Therefore, about The iterative formula can also be expressed using the soft threshold function:

[0085] (15)

[0086] about The sub-optimization problem can be further expressed as:

[0087] (16)

[0088] Calculation formula (16) about The zero point of the first-order derivative can be obtained about The iterative formula is:

[0089] (17)

[0090] Finally, update , , and :

[0091] (18)

[0092] Formula (11), Formula (15), Formula (17) and Formula (18) together form the iterative solution form of the joint low-rank and sparse prior imaging model.

[0093] Specifically, the step C includes:

[0094] After obtaining the iterative solution in step B, the regularization parameter needs to be determined before starting the iteration. 、 , using nesting to quickly determine the appropriate regularization parameter value.

[0095] Assign initial values ​​to the following parameters:

[0096] (19)

[0097] At the same time, set , and The search range is the same, but to make it wide enough, it is set to exponential form: , is a positive integer, here it is set to 9. value, and for each value, Traverse from small to large to form a nested search. Under each value, calculate the first two iterations Image entropy difference :

[0098] (20)

[0099] in, represents the image entropy, For example, the calculation formula of image entropy is:

[0100] (twenty one)

[0101] in, Representative Matrix No. Each element. It is a mathematical expression for calculating image entropy, which has no specific meaning. P and Q are The number of rows and columns, PQ represents the product of P and Q, that is The total number of elements of Representatives The sum of the squares of the moduli of all elements in .

[0102] Select Regularization coefficient corresponding to the maximum value and The value is taken as the final regularization parameter value.

[0103] Specifically, the step D includes:

[0104] After the regularization parameter is determined in step C, it is iterated along the iterative solution obtained in step B according to the initial value of formula (19) to continuously update The process is called image reconstruction. As the iteration proceeds, The change of gradually decreases. To avoid redundancy, the image entropy is used to determine the termination of iteration.

[0105] Setting the iteration threshold , when the image entropy difference between the two image update results is lower than the threshold, the iteration terminates, that is, the condition for the iteration termination is:

[0106] (twenty two)

[0107] in, and Respectively Second and The resulting image of the region of interest is generated after iterations.

[0108] This paper transfers the traditional low-rank constraint on the echo matrix to the region-of-interest image, establishing a novel combined low-rank and sparse prior imaging model. The noise constraint in the imaging model makes the proposed algorithm resistant to noise interference. The matrix-form constraint and the derivation using the alternating direction multiplier method avoid high-dimensional matrix operations and reduce algorithm runtime. The nested search used to determine the regularization parameter adapts to environmental changes and enables efficient iterative convergence. Finally, image entropy is used as the termination criterion to avoid redundant iterations.

[0109] Example:

[0110] By setting up multi-objective distribution situations, the feasibility of the present invention is simulated and analyzed.

[0111] The distribution positions of antennas and targets in the simulation are as follows: Figure 1 As shown, the array consists of 2 transmitting antennas and 5 receiving antennas, and the target distribution range is relatively wide.

[0112] The relevant parameter settings are shown in Table 1:

[0113] Table 1 Simulation parameter settings

[0114]

[0115] Under this setting, the target echo signal is simulated and the target image is obtained using the back projection algorithm, coherence weighted algorithm, compressed sensing algorithm and the algorithm proposed in this invention. Their results correspond to Figure 2a , Figure 2b , Figure 2c , Figure 2d In the imaging results of the back-projection algorithm, there are both azimuth and range sidelobes, which seriously interfere with target recognition. In the imaging results of the coherent weighting algorithm, the azimuth sidelobes are suppressed, but the range sidelobes are not improved. In the imaging results of the compressed sensing algorithm, the sidelobes in both dimensions are suppressed, but some still remain. In the imaging results of the algorithm proposed in the present invention, the sidelobes in both dimensions are well suppressed.

[0116] In order to further verify the anti-noise performance of the proposed algorithm, noise is added to the simulated echo signal. When the signal-to-noise ratio is 0 dB, the imaging results obtained by the back projection algorithm, coherence weighted algorithm, compressed sensing algorithm and the algorithm proposed in this invention are shown in Figure 2. Figure 3a , Figure 3b , Figure 3c , Figure 3d The first three algorithms cannot achieve good noise interference suppression, and the algorithm proposed in this invention has the best anti-noise performance.

[0117] To verify the feasibility of the present invention in terms of processing time, the processing times of the four algorithms described above were recorded, as shown in Table 2. The compressed sensing algorithm took the longest time and is not practically usable. The backprojection algorithm took the shortest time. The coherent weighting algorithm and the algorithm proposed in this invention both took slightly longer times, but not significantly more than an order of magnitude. Therefore, the present invention is feasible in terms of processing time.

[0118] Table 2 Algorithm processing time

[0119]

[0120] Taking into account the sidelobe suppression effect and processing time, the algorithm proposed in the present invention effectively suppresses the sidelobes in two dimensions without significantly increasing the processing time, thereby greatly improving the image reconstruction effect.

[0121] The present invention is not limited by radar system and array form, and is applicable to various situations such as pulse system and continuous wave system, and is not limited to various forms such as linear array, uniform array, and planar array. It is applicable to both two-dimensional plane image reconstruction and three-dimensional space image reconstruction.

[0122] The present invention also provides an ultra-wideband radar low sidelobe imaging device combining low rank and sparse priors, comprising the following modules:

[0123] Model building module, building a joint low-rank and sparse prior imaging model;

[0124] A derivation module derives the iterative solution form of the joint low-rank and sparse prior imaging model;

[0125] Parameter determination module, nested search to determine the regularization parameters;

[0126] The image reconstruction module reconstructs the image according to the obtained regularization parameters and iterative solution form, and determines the termination of the iteration.

[0127] The present invention also provides an electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, the steps of the above-mentioned ultra-wideband radar low sidelobe imaging method combining low rank and sparse prior are implemented.

[0128] The present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the above-mentioned ultra-wideband radar low sidelobe imaging method combining low rank and sparse priors.

[0129] Those skilled in the art will appreciate that embodiments of the present invention may be provided as methods, systems, or computer program products. Thus, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk drives, CD-ROMs, optical storage devices, etc.) containing computer-usable program code. The solutions in the embodiments of the present invention may be implemented using various computer languages, such as the object-oriented programming language Java and the interpreted scripting language JavaScript.

[0130] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowcharts and / or block diagrams, as well as combinations of processes and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowcharts and / or block diagrams. Figure 1 a process or multiple processes and / or boxes Figure 1A device that provides the functions specified in a block or multiple blocks.

[0131] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0132] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0133] Although the preferred embodiments of the present invention have been described, those skilled in the art may make additional changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present invention.

[0134] Obviously, those skilled in the art may make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if such changes and modifications fall within the scope of the claims and their equivalents, the present invention is intended to include such changes and modifications.

Claims

1. A low-sidelobe imaging method for ultra-wideband radar using a low-rank and sparse prior, characterized in that: The steps include: Step A: Build a joint low-rank and sparse prior imaging model: （7） in, and are the image matrix of the echo matrix and the image matrix of the region of interest, and is the auxiliary matrix, is a large-scale sensing matrix, , and represent the nuclear norm, Norm and F-norm, Represents vectorized operations on matrices, Represents matrix operations on vectors; and are regularization parameters, which are used to control the proportion of sparsity and noise constraints respectively. Represents finding the minimum value of a function; Step B: Derive the iterative solution form of the joint low-rank and sparse prior imaging model; Step C: Perform a nested search to determine the regularization parameters, including: Set the index search range: , is a positive integer, and the regularization parameter is searched within the index range and regularization parameter Perform nested search and select image entropy difference The regularization parameter corresponding to the maximum value of and regularization parameter The value is taken as the final regularization parameter value; （20） in, represents the image entropy, and The image matrices representing the regions of interest for the two iterations respectively; Step D: Reconstruct the image based on the regularization parameter determined in step C and the iterative solution derived in step B, and determine when to terminate the iteration.

2. The method for ultra-wideband radar low sidelobe imaging using a combined low-rank and sparse prior according to claim 1, wherein: In step B, the auxiliary matrix Iterate and get: （11） in, 、 and for The singular value decomposition results are the left singular matrix, the right singular matrix and the singular value matrix respectively. The superscript k is the iteration index, which is used to indicate the kth iteration of each parameter. is the Lagrange multiplier matrix, is the penalty factor, is the soft threshold function, representing the singular value matrix The elements in The superscript H represents the conjugate transpose operation of the matrix.

3. The method for ultra-wideband radar low sidelobe imaging using a combined low-rank and sparse prior according to claim 2, wherein: In step B, the relationship between the left singular matrix, the right singular matrix and the singular value matrix is: （12） in, is a soft threshold function, and its output matrix is ​​expressed in element form as: （13） in, Represents the soft threshold function in matrix form No. elements, Indicates taking the maximum value of the two elements in the brackets.

4. The method for ultra-wideband radar low sidelobe imaging using a combined low-rank and sparse prior according to claim 3, wherein: In step B, the auxiliary matrix The iterative formula is expressed using the soft threshold function: （15） Image matrix of the region of interest The iterative formula is: （17） , , and The iterative formula is: （18） Among them, k represents the iteration index, and is the Lagrange multiplier matrix, and is the penalty factor, and is the regularization parameter, is the increment factor.

5. The method for ultra-wideband radar low sidelobe imaging using a combined low-rank and sparse prior according to claim 4, wherein: The step D comprises: Setting the iteration threshold , when the difference in image entropy between two image update results is lower than the iteration threshold When , the iteration terminates, that is, the condition for the iteration termination is: （22） in, and Respectively Second and The resulting image of the region of interest is generated after iterations.

6. A low-sidelobe imaging device for ultra-wideband radar using a low-rank and sparse prior, characterized in that: Includes the following modules: Model building module, building a joint low-rank and sparse prior imaging model is: （7） in, and are the image matrix of the echo matrix and the image matrix of the region of interest, and is the auxiliary matrix, is a large-scale sensing matrix, , and represent the nuclear norm, Norm and F-norm, Represents vectorized operations on matrices, Represents matrix operations on vectors; and are regularization parameters, which are used to control the proportion of sparsity and noise constraints respectively. Represents finding the minimum value of a function; A derivation module derives the iterative solution form of the joint low-rank and sparse prior imaging model; The parameter determination module performs nested search to determine the regularization parameters, including: Set the index search range: , is a positive integer, and the regularization parameter is searched within the index range and regularization parameter Perform nested search and select image entropy difference The regularization parameter corresponding to the maximum value of and regularization parameter The value is taken as the final regularization parameter value; （20） in, represents the image entropy, and The image matrices representing the regions of interest for the two iterations respectively; The image reconstruction module reconstructs the image according to the obtained regularization parameters and iterative solution form, and determines the termination of the iteration.

7. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the steps of the ultra-wideband radar low sidelobe imaging method with combined low rank and sparse prior are implemented as described in any one of claims 1 to 5.

8. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the ultra-wideband radar low sidelobe imaging method with combined low rank and sparse prior are implemented as described in any one of claims 1 to 5.

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