ISAR imaging method for sparse aperture micro-motion targets based on deep unfolding network

Abstract

The present invention relates to the field of radar imaging, and discloses a sparse aperture micro-motion target ISAR imaging method based on a deep unfolding network. The method comprises the following steps: obtaining radar echo data, performing preprocessing and modeling according to the echo data; establishing a model-driven deep learning imaging algorithm by using a deep unfolding framework; constructing a corresponding loss function of the deep learning imaging algorithm and selecting a training data set; initializing and setting network parameters, and setting a parameter update optimization algorithm and the number of training rounds; updating and adjusting parameters through an optimization algorithm; and saving optimal network parameters to output an optimal algorithm model when the number of training rounds is met, so as to improve the performance of radar in imaging micro-motion targets under sparse aperture conditions.

Description

Technical Field

[0001] The present application relates to the field of radar imaging, and in particular to an ISAR imaging method for sparse aperture micro-motion targets based on a deep unfolding network. Background Art

[0002] Inverse Synthetic Aperture Radar (ISAR) is a special radar that uses the Doppler information generated by the relative motion between the target and the radar to achieve high-resolution electromagnetic scattering images of the target. It is an important technical approach for radar target identification. Compared with optical imaging and other methods, ISAR imaging has the characteristics of all-day and all-weather. It has been widely used in space target monitoring, radar target identification, etc.

[0003] Traditional ISAR imaging considers the target as a rigid body, such as the steady movement of aircraft and ships. However, some complex moving targets may carry micro-moving parts. Micro-motion refers to the small movement of the target other than the center of mass movement, such as the rotation of the aircraft propeller and the rotation of the antenna on the ship. We call these structures that produce micro-motion effects micro-moving parts. Usually, traditional imaging algorithms can achieve good imaging of steady moving targets under full aperture conditions, but due to the presence of micro-moving parts, the target will produce a micro-Doppler effect, affecting the quality of ISAR images. In addition, the radio wave propagation environment, target switching of multi-channel radars, etc. will cause the radar echo to be partially missing, resulting in sparse aperture echoes. Under sparse aperture conditions, the fast Fourier transform is limited, and the sidelobe and grating lobe interference of the resulting image is high, so traditional algorithms cannot image it well. Therefore, how to image targets with micro-moving parts under sparse aperture conditions is a scientific problem that needs to be solved urgently.

[0004] To solve the problem of the influence of component micro-motion on ISAR imaging, the method usually adopted is to separate the micro-motion signal from the main part signal, and then process the main part signal separately to remove the micro-motion effect. Commonly used methods include Hough transform inverse, Radon transform, etc. In recent years, some new methods, such as wavelet decomposition, empirical mode decomposition, and linear frequency modulation wavelet transform (Chirplet), have shown good results in separating micro-motion signals. However, the image resolution obtained by these methods is limited and the algorithm stability is low. To solve the sparse problem caused by the low radar data rate, the method usually adopted is to use the compressed sensing model to realize image restoration in sparse mode. There are three main types of commonly used compressed sensing methods: greedy algorithm, convex optimization method and sparse Bayesian learning. Unfortunately, these methods cannot eliminate micro-motion signals well. Therefore, how to achieve ISAR imaging of micro-motion targets under sparse conditions is a research focus in the current radar imaging field.

[0005] At present, although some scholars have applied the micro-motion signal separation method to the field of ISAR imaging, it is difficult to perform good target imaging in actual environments due to the low anti-interference ability and stability of the algorithm. In addition, some scholars have conducted in-depth research on ISAR imaging under sparse aperture conditions, but they mainly focus on rigid moving targets without micro-motion components. In recent years, some scholars have begun to conduct relevant research on micro-motion signals under sparse conditions. For example, in 2014, Chen Yijun and others from the Air Force Engineering University proposed a new imaging method based on the orthogonal matching pursuit algorithm to achieve ISAR imaging of micro-motion targets under sparse aperture conditions; in 2020, our team proposed an imaging algorithm based on low-rank and sparse joint constraints (Linearized-Alternating Direction Method of Multipliers, L-ADMM), which can quickly and robustly obtain ISAR images of micro-motion targets under sparse aperture conditions. However, these methods require iterative solutions when solving the main part of the image, with relatively low computational efficiency, and require cumbersome manual adjustment of parameters before use, which is less applicable to ISAR imaging in different scenarios. In order to solve the problems of low efficiency and manual parameter adjustment of convex optimization methods, Yang Yan and others from Xi'an Jiaotong University proposed a deep learning method driven by a compressed sensing model in 2020, which can quickly and accurately restore the original image and is widely used in medical imaging. Deep learning is a neural network model that contains multi-layer perceptrons. It approximates complex functional relationships by designing a certain number of network layers. Theoretically, as long as the number of network layers is set enough, deep learning can approximate any function. In recent years, many scholars have used deep unfolding networks to conduct relevant research on image restoration under compressed sensing models and have made good progress. These studies provide a good reference for us to apply deep learning to the field of ISAR imaging.

[0006] Therefore, how to solve the problem of "difficult to obtain" images of micro-moving targets under sparse aperture conditions and improve the performance of radar in imaging micro-moving targets under sparse aperture conditions has become a technical problem that needs to be solved urgently.

[0007] The above contents are only used to assist in understanding the technical solution of the present invention and do not constitute an admission that the above contents are prior art. Summary of the invention

[0008] The main purpose of the present invention is to provide a sparse aperture micro-moving target ISAR imaging method based on a deep unfolding network, aiming to solve the technical problem of how to improve the performance of radar in imaging micro-moving targets under sparse aperture conditions.

[0009] To achieve the above object, the present invention provides a sparse aperture micro-motion target ISAR imaging method based on a deep unfolding network, the method comprising:

[0010] Acquire radar echo data, and perform preprocessing and modeling according to the echo data;

[0011] Use the deep unfolding framework to build a model-driven deep learning imaging algorithm;

[0012] Constructing a loss function corresponding to the deep learning imaging algorithm and selecting a training data set;

[0013] Initialize the network parameters, set the parameter update optimization algorithm and the number of training rounds;

[0014] Update and adjust parameters through optimization algorithms;

[0015] When the number of training rounds is met, the optimal network parameters are saved to output the optimal algorithm model.

[0016] Optionally, the step of acquiring radar echo data and performing preprocessing and modeling according to the echo data includes:

[0017] Acquire radar echo data, and perform translation compensation on a one-dimensional range image of the radar echo data, wherein the translation compensation includes: envelope alignment and self-focusing;

[0018] The formula of the one-dimensional range image after translation compensation is as follows:

[0019] ;

[0020] in, represents the one-dimensional range image sequence of the target after translation compensation, , Represents fast time and slow time respectively. , Indicates the number of pulses contained in the full-aperture radar echo. , , They represent the center frequency, bandwidth and propagation speed of radar signals respectively. and Respectively represent the target body part The reflection coefficient of a scattering center and the instantaneous rotation distance relative to the radar, and Respectively represent the target micro-motion components The reflection coefficient of a scattering center and the instantaneous rotation distance relative to the radar, , , Indicates that the target body contains Scattering centers, Indicates that the target micro-motion components include scattering centers;

[0021] Modeling is performed according to the one-dimensional range profile formula.

[0022] Optionally, the step of modeling according to the one-dimensional range profile formula includes:

[0023] Under sparse aperture conditions, the one-dimensional range profile formula can be expressed in the following matrix form:

[0024]

[0025] in , and Represent the one-dimensional range image sequence of the target, the main part of the target and the micro-moving parts of the target respectively, express The complex matrix of and They represent the number of pulses and the number of range units in the sparse aperture one-dimensional range image sequence respectively; for sparse aperture data, the number of pulses is less than the number of pulses contained in the full aperture radar echo, that is, , and the pulse number set is a subset of the full-aperture pulse number, that is, ,in represents a set of sparse aperture pulse numbers;

[0026] For the target with micro-moving parts, the ISAR image of the main part of the target and the one-dimensional range image sequence of the main part of the target They are Fourier transform pairs, namely:

[0027]

[0028] in ISAR image showing the main part of the target, represents the partial Fourier matrix, assuming that the complete Fourier matrix is ,but By extracting The sequence number set of the extracted row vectors is the sparse aperture pulse sequence number set. ;

[0029] Add constraints: 1. One-dimensional range image sequence of the main part of the target The column correlation is strong and has low rank characteristics; 2. One-dimensional range image sequence of the target micro-movement part The energy of the target is scattered in different distance units, which has a sparse characteristic. Third, the ISAR image of the target body is generally composed of a few scattering centers, which has a strong sparse characteristic. It can be modeled as:

[0030]

[0031] in and They represent the nuclear norm and Norm, used to characterize the rank and sparsity of the matrix respectively; , represents the regularization parameter, which is used to adjust the weights of matrix decomposition and ISAR imaging. ;

[0032] The triple-constrained underdetermined problem is modeled, and the following model is finally obtained:

[0033] ;

[0034] Using the linear alternating direction multiplier method algorithm, we can get the following solution:

[0035] ;

[0036] in represents the inner product of two matrices, , represents the Lagrange multiplier matrix, , represents the punishment factor, represents the F norm of the matrix; Indicates The variables obtained by iteration are Indicates the rising factor, used to control the punishment factor , The upward trend ,in, Represents a partial Fourier matrix The conjugate transpose of ; represents the singular value shrinkage factor. Specifically, for any matrix With any scalar ,have:

[0037] ;

[0038] in express ; singular value decomposition, , is a unitary matrix, express The singular value vector of represents a diagonal matrix consisting of vectors; represents a soft threshold operator, for any scalar , ,have ,in represents the sign operator; for any vector ,have ,in Representation vector No. elements.

[0039] Until the relative error of the ISAR images of the target main part obtained in two adjacent iterations ( ) is less than the set threshold, the ISAR image of the main part of the target with micro-moving components under sparse aperture conditions can be obtained. .

[0040] Optionally, the step of establishing a model-driven deep learning imaging algorithm using a deep unfolding framework comprises:

[0041] The L-ADMM algorithm, a solution algorithm for ISAR images of micro-moving targets under sparse aperture conditions, is expanded into a cascade network.

[0042] Assume the number of iterations of the L-ADMM algorithm is n, and the number of layers of the cascade network is also set to n;

[0043] Each layer of the network contains 4 unknown parameters, namely , , , , the L-ADMM algorithm sets the unknown parameters when used;

[0044] The parameter initialization settings of each layer of the network are consistent with the initial values ​​of the L-ADMM algorithm so that during the training phase, L-ADMM-net continuously updates the parameters of each layer according to the loss function. During the testing phase, the network parameters are directly imaged.

[0045] Optionally, the step of constructing a loss function corresponding to the deep learning imaging algorithm and selecting a training data set includes:

[0046] Constructing a loss function corresponding to the deep learning imaging algorithm;

[0047] The one-dimensional range image H of the micro-moving target under sparse aperture conditions is set as the input of the training set data, the output is the ISAR image X of the main part under sparse aperture conditions, and the label data is the ISAR image X of the main part under full aperture echo.

[0048] Optionally, the step of constructing a loss function corresponding to the deep learning imaging algorithm includes:

[0049] Construct the following loss function:

[0050] ;

[0051] Where N represents the total number of training data sets. represents the F-norm of the matrix, It represents the ISAR image of the main part of the target obtained by calculating the one-dimensional range image H of the target under sparse aperture conditions through a neural network. It represents the main part of the ISAR image under the full aperture echo. represents the regularization parameter, represents the one-norm of a vector, It means stretching the matrix into a one-dimensional vector in column order.

[0052] Optionally, after the step of setting the one-dimensional range image H of the micro-moving target under the sparse aperture condition as the input end of the training set data, the output end is the ISAR image X of the main part under the sparse aperture condition, and the label data is the ISAR image X of the main part under the full aperture echo, the method further includes:

[0053] A preset number of network layers are set, and the parameters are automatically adjusted through learning and training to obtain a mapping model between the one-dimensional range image H of the target under sparse aperture and the ISAR image X of the main part.

[0054] Optionally, the step of initializing the network parameters and setting the parameter update optimization algorithm and the number of training rounds includes:

[0055] The Adam algorithm is used to update and optimize the parameters. The principle of the Adam algorithm is as follows:

[0056] ;

[0057] ;

[0058] in is the first-order estimate of the gradient, is a hyperparameter, is the second-order estimate of the gradient, is a hyperparameter, is the loss function, is the desired parameter;

[0059] After bias correction, we get:

[0060] ;

[0061] ;

[0062] in, , are the first-order and second-order estimates of the corrected gradient;

[0063] In addition, the specific update formula of the neural network parameters is as follows:

[0064] ;

[0065] Where t is the number of iterations, is the parameter value at time t+1, is the parameter value at time t, is the learning rate of the neural network model, is the error constant.

[0066] The present invention obtains radar echo data, performs preprocessing and modeling according to the echo data; establishes a model-driven deep learning imaging algorithm using a deep unfolding framework; constructs a corresponding loss function of the deep learning imaging algorithm and selects a training data set; initializes network parameters, sets a parameter update optimization algorithm and the number of training rounds; adjusts parameter updates through the optimization algorithm; and when the number of training rounds is met, saves the optimal network parameters to output the optimal algorithm model, thereby improving the performance of radar in imaging micro-motion targets under sparse aperture conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Figure 1 It is a flow chart of a first embodiment of a sparse aperture micro-motion target ISAR imaging method based on a deep unfolding network according to the present invention;

[0068] Figure 2 It is a network expansion diagram of the L-ADMM-net algorithm of the first embodiment of the sparse aperture micro-motion target ISAR imaging method based on the deep expansion network of the present invention;

[0069] Figure 3 In the first embodiment of the sparse aperture micro-motion target ISAR imaging method based on the deep unfolding network of the present invention, (a) is the aircraft used for the test - Cessna aircraft, and (b) is the result of imaging the target using the RD algorithm under full aperture conditions;

[0070] Figure 4 The target ISAR images obtained by different algorithms under the random sparse condition with a sparsity of 50% in the first embodiment of the sparse aperture micro-motion target ISAR imaging method based on the deep unfolding network of the present invention, wherein (a) RD; (b) Chirplet; (c) L-ADMM; (d) L-ADMM-net;

[0071] Figure 5 The first embodiment of the sparse aperture micro-motion target ISAR imaging method based on the deep unfolding network of the present invention is a target ISAR image obtained by different algorithms under the condition of 25% random sparseness, wherein (a) RD; (b) Chirplet; (c) L-ADMM; (d) L-ADMM-net;

[0072] Figure 6 This is the first embodiment of the sparse aperture micro-motion target ISAR imaging method based on the deep unfolding network of the present invention. The sparsity is 12.5% ​​and the target ISAR images are obtained by different algorithms under random sparse conditions, where (a) RD; (b) Chirplet; (c) L-ADMM; (d) L-ADMM-net. DETAILED DESCRIPTION

[0073] It should be understood that the specific embodiments described herein are only used to explain the present invention, and are not used to limit the present invention.

[0074] The embodiment of the present invention provides a sparse aperture micro-motion target ISAR imaging method based on a deep unfolding network, referring to Figure 1 , Figure 1 It is a flow chart of the first embodiment of the sparse aperture micro-motion target ISAR imaging method based on the deep unfolding network of the present invention.

[0075] Step S10: Acquire radar echo data, and perform preprocessing and modeling based on the echo data.

[0076] In the specific implementation, before the Inverse Synthetic Aperture Radar (ISAR) imaging, the one-dimensional range image of the radar echo data needs to be compensated for translation. The translation compensation mainly includes two steps, namely envelope alignment and self-focusing. At present, the translation compensation part of the technology is relatively mature. Therefore, this embodiment has performed translation compensation on the one-dimensional range image before building the model. The one-dimensional range image after translation compensation is as follows:

[0077] ;

[0078] in, represents the one-dimensional range image sequence of the target after translation compensation, , Represents fast time and slow time respectively. , Indicates the number of pulses contained in the full-aperture radar echo. , , They represent the center frequency, bandwidth and propagation speed of radar signals respectively. and Respectively represent the target body part The reflection coefficient of a scattering center and the instantaneous rotation distance relative to the radar, and Respectively represent the target micro-motion components The reflection coefficient of a scattering center and the instantaneous rotation distance relative to the radar, , , Indicates that the target body contains Scattering centers, Indicates that the target micro-motion components include scattering centers; for the main part of the target The instantaneous rotation distance of the scattering center relative to the radar It can be expressed as:

[0079] ;

[0080] in, Indicates the target body part The coordinates of the scattering centers in the target body coordinate system, Indicates the angular velocity of the main part of the target. Since the ISAR imaging accumulation time is short, the target's rotation angle relative to the radar during the imaging accumulation time is smaller, so there are: , ; Assume that the scattering centers of the target micro-movement components revolve around the point Rotate, then for the target micro-motion component The instantaneous rotation distance of the scattering center relative to the radar It can be expressed as:

[0081] ;

[0082] in, Indicates the target micro-motion component The coordinates of the scattering centers in the target body coordinate system, , and Respectively represent the target micro-motion components The micro-motion amplitude, angular velocity and initial phase of each scattering center. The instantaneous rotation distance of a scattering center relative to the radar Contains cosine terms In the ISAR imaging process, this item will produce micro-Doppler (mD) effect interference, affecting the quality of ISAR images.

[0083] Furthermore, the step of obtaining radar echo data and performing preprocessing and modeling according to the echo data includes: obtaining radar echo data, and performing translation compensation on a one-dimensional range image of the radar echo data, wherein the translation compensation includes: envelope alignment and self-focusing; the formula of the one-dimensional range image after translation compensation is as follows:

[0084] ;

[0085] in, represents the one-dimensional range image sequence of the target after translation compensation, , Represents fast time and slow time respectively. , Indicates the number of pulses contained in the full-aperture radar echo. , , They represent the center frequency, bandwidth and propagation speed of radar signals respectively. and Respectively represent the target body part The reflection coefficient of a scattering center and the instantaneous rotation distance relative to the radar, and Respectively represent the target micro-motion components The reflection coefficient of a scattering center and the instantaneous rotation distance relative to the radar, , , Indicates that the target body contains Scattering centers, Indicates that the target micro-motion components include scattering centers; modeling is performed according to the one-dimensional range profile formula.

[0086] Furthermore, the step of modeling according to the one-dimensional range image formula includes: under the sparse aperture condition, the one-dimensional range image formula can be expressed in the following matrix form:

[0087]

[0088] in , and Represent the one-dimensional range image sequence of the target, the main part of the target and the micro-moving parts of the target respectively, express The complex matrix of and They represent the number of pulses and the number of range units in the sparse aperture one-dimensional range image sequence respectively; for sparse aperture data, the number of pulses is less than the number of pulses contained in the full aperture radar echo, that is, , and the pulse number set is a subset of the full-aperture pulse number, that is, ,in represents the set of sparse aperture pulse numbers; for the target with micro-moving parts, the ISAR image of the main part of the target and the one-dimensional range image sequence of the main part of the target They are Fourier transform pairs, namely:

[0089]

[0090] in ISAR image showing the main part of the target, represents the partial Fourier matrix, assuming that the complete Fourier matrix is ,but By extracting The sequence number set of the extracted row vectors is the sparse aperture pulse sequence number set. ;

[0091] Add constraints: 1. One-dimensional range image sequence of the main part of the target The column correlation is strong and has low rank characteristics; 2. One-dimensional range image sequence of the target micro-movement part The energy of the target is scattered in different distance units, which has a sparse characteristic. Third, the ISAR image of the target body is generally composed of a few scattering centers, which has a strong sparse characteristic. It can be modeled as:

[0092] ;

[0093] in and They represent the nuclear norm and Norm, used to characterize the rank and sparsity of the matrix respectively; , represents the regularization parameter, which is used to adjust the weights of matrix decomposition and ISAR imaging. ;

[0094] The triple-constrained underdetermined problem is modeled, and the following model is finally obtained:

[0095] ;

[0096] Using the linear alternating direction multiplier method algorithm, we can get the following solution:

[0097] ;

[0098] in represents the inner product of two matrices, , represents the Lagrange multiplier matrix, , represents the punishment factor, represents the F norm of the matrix; Indicates The variables obtained by iteration are Indicates the rising factor, used to control the punishment factor , The upward trend ,in, Represents a partial Fourier matrix The conjugate transpose of ; represents the singular value shrinkage factor. Specifically, for any matrix With any scalar ,have:

[0099] ;

[0100] in express ; singular value decomposition, , is a unitary matrix, express The singular value vector of represents a diagonal matrix consisting of vectors; represents a soft threshold operator, for any scalar , ,have ,in represents the sign operator; for any vector ,have ,in Representation vector No. elements.

[0101] Until the relative error of the ISAR images of the target main part obtained in two adjacent iterations ( ) is less than the set threshold, the ISAR image of the main part of the target with micro-moving components under sparse aperture conditions can be obtained. .

[0102] Step S20: Establish a model-driven deep learning imaging algorithm using the deep unfolding framework.

[0103] It should be noted that deep learning is a new emerging direction in machine learning. Since deep learning was proposed, it has set off a revolutionary craze in the field of artificial intelligence and is currently widely used in image recognition, natural language processing, and multimedia vision. The essence of deep learning is an extension of the structure of artificial neural networks. Usually, a perceptron containing multiple hidden layers can be regarded as a framework for deep learning. Deep learning combines a certain number of hidden layer network structures to form a deep network that can map more complex and abstract structural features, so that it can process some more complex information and features. However, deep learning has also encountered some "difficulties" while being applied. For example, deep learning can often only judge the effectiveness of the model from the output results, and its specific internal principles cannot be known; therefore, some scholars call them "black boxes". In recent years, some scholars have combined some scientific problem-solving models with deep learning to construct interpretable model-driven deep neural networks, realizing the transformation of "black boxes" into mathematical models with practical significance. Based on the idea of ​​deep network expansion, this paper aims at the problem of ISAR imaging of micro-moving targets under sparse aperture conditions. The solution algorithm for ISAR images of micro-moving targets under sparse aperture conditions, the L-ADMM algorithm, is expanded into a cascade network, and a new interpretable deep learning network, the L-ADMM-net, is constructed. This improves the imaging accuracy, computational efficiency and stability, and provides a new solution for ISAR imaging of micro-moving targets under sparse aperture conditions in the future.

[0104] Furthermore, the step of establishing a model-driven deep learning imaging algorithm using a deep unfolding framework includes: unfolding the L-ADMM algorithm, a solution algorithm for ISAR images of micro-motion targets under sparse aperture conditions, into a cascade network; setting the number of iterations of the L-ADMM algorithm to n, and the number of layers of the cascade network to n; each layer of the network contains 4 unknown parameters, which are , , , , the L-ADMM algorithm sets the unknown parameters when in use; the parameter initialization setting of each layer of the network is consistent with the initial value of the L-ADMM algorithm so that during the training phase, L-ADMM-net continuously updates the parameters of each layer according to the loss function, and during the testing phase, the network parameters are directly imaged.

[0105] In the specific implementation, Figure 2 As shown, Figure 2 Each layer of the cascaded network shown in corresponds to an iterative step in the L-ADMM algorithm, and the variables in each layer of the network are based on the following formula:

[0106] ;

[0107] The loop is passed to the next layer of the network and finally to the output layer. Assume that the number of iterations of the L-ADMM algorithm is n. To facilitate the comparison of the algorithm results, the number of layers in the cascade network should also be set to n. Each layer of the network contains 4 unknown parameters, which are , , , . The L-ADMM algorithm needs to set these unknown parameters before use. Similar to the L-ADMM algorithm, the network also needs to initialize these parameters before use. To facilitate the comparison of algorithm results, the parameter initialization settings of each layer of the network are consistent with the initial values ​​of the L-ADMM algorithm. During the training phase, L-ADMM-net can continuously update the parameters of each layer according to the loss function; during the testing phase, the network parameters do not need to be manually adjusted and imaging can be performed directly. Compared with the L-ADMM algorithm, L-ADMM-net does not require manual parameter adjustment every time it is used, and is more adaptable and stable to ISAR imaging in different scenarios.

[0108] Step S30: construct a loss function corresponding to the deep learning imaging algorithm and select a training data set.

[0109] Furthermore, the step of constructing a loss function corresponding to the deep learning imaging algorithm and selecting a training data set includes: constructing a loss function corresponding to the deep learning imaging algorithm; setting a one-dimensional range image H of the micro-motion target under sparse aperture conditions as the input end of the training set data, and the output end is the ISAR image X of the main part under sparse aperture conditions, and the label data is the ISAR image X of the main part under full aperture echo.

[0110] Furthermore, the step of constructing a loss function corresponding to the deep learning imaging algorithm includes: constructing the following loss function:

[0111] ;

[0112] Where N represents the total number of training data sets. represents the F-norm of the matrix, It represents the ISAR image of the main part of the target obtained by calculating the one-dimensional range image H of the target under sparse aperture conditions through a neural network. It represents the main part of the ISAR image under the full aperture echo. represents the regularization parameter, represents the one-norm of a vector, It means stretching the matrix into a one-dimensional vector in column order.

[0113] Furthermore, after the step of setting the one-dimensional range image H of the micro-motion target under sparse aperture conditions as the input end of the training set data, the output end as the ISAR image X of the main part under sparse aperture conditions, and the label data as the ISAR image X of the main part under full aperture echo, it also includes: setting a preset number of network layers, and automatically adjusting parameters through learning and training to obtain a mapping model between the one-dimensional range image H of the target under sparse aperture and the ISAR image X of the main part.

[0114] Step S40: Initialize the network parameters, set the parameter update optimization algorithm and the number of training rounds.

[0115] Furthermore, the steps of initializing the network parameters, setting the parameter update optimization algorithm and the number of training rounds include: using the Adam algorithm to update and optimize the parameters, and the principle of the Adam algorithm is as follows:

[0116] ;

[0117] ;

[0118] in is the first-order estimate of the gradient, is a hyperparameter, is the second-order estimate of the gradient, is a hyperparameter, is the loss function, is the desired parameter; after deviation correction, we can get:

[0119] ;

[0120] ;

[0121] in, , are the modified first-order and second-order estimates of the gradient; in addition, the specific update formula of the neural network parameters is as follows:

[0122] ;

[0123] Where t is the number of iterations, is the parameter value at time t+1, is the parameter value at time t, is the learning rate of the neural network model, is the error constant.

[0124] Step S50: updating and adjusting the parameters through an optimization algorithm.

[0125] Step S60: When the number of training rounds is met, the optimal network parameters are saved to output the optimal algorithm model.

[0126] In the specific implementation, Figure 3 As shown, the Cessna aircraft contains a propeller micro-motion component in its nose part, which will produce an mD effect and affect the quality of the ISAR image. Due to the existence of this propeller, the image has obvious sidelobe interference in its nose part and there is a lot of noise.

[0127] In the specific implementation, Figure 4 As shown in the figure, the RD algorithm has the worst imaging effect under the condition of 50% random sparse mode because the echo pulse coherence is destroyed; the Chirplet algorithm can remove part of the micro-motion effect compared with the RD algorithm, but the background noise caused by the sparse aperture is still very significant; L-ADMM can better remove most of the background noise caused by the sparse aperture and micro-motion effect, and the imaging result is greatly improved compared with the RD algorithm and the Chirplet algorithm, but there is still some strong interference noise that cannot be removed; and the result of L-ADMM-net is better than the denoising effect of the L-ADMM algorithm, and can remove the micro-motion interference noise that L-ADMM cannot eliminate.

[0128] In the specific implementation, Figure 5 As shown in the figure, under 25% sparse conditions, the defocusing degree of RD, Chirplet algorithm, and L-ADMM algorithm increases, while the L-ADMM-net method can still obtain high-resolution images, further indicating that L-ADMM-net can achieve better imaging of micro-moving targets under sparse conditions.

[0129] In the specific implementation, Figure 6 As shown in the figure, under the 12.5% ​​sparse condition, the defocusing degree of RD, Chirplet algorithm, and L-ADMM algorithm is seriously aggravated, while L-ADMM-net can still obtain a high-resolution image of the target, which further verifies the effectiveness of the algorithm of the present invention.

[0130] This embodiment obtains radar echo data, performs preprocessing and modeling based on the echo data; uses a deep unfolding framework to establish a model-driven deep learning imaging algorithm; constructs a corresponding loss function for the deep learning imaging algorithm and selects a training data set; initializes network parameters, sets a parameter update optimization algorithm and the number of training rounds; adjusts parameter updates through the optimization algorithm; and when the number of training rounds is met, saves the optimal network parameters to output the optimal algorithm model, thereby improving the performance of radar imaging of micro-motion targets under sparse aperture conditions.

[0131] It should be noted that, in this article, the terms "include", "comprises" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, article or system including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or system. In the absence of further restrictions, an element defined by the sentence "comprises a ..." does not exclude the existence of other identical elements in the process, method, article or system including the element.

[0132] The serial numbers of the above embodiments of the present invention are only for description and do not represent the advantages or disadvantages of the embodiments.

[0133] Through the description of the above implementation methods, those skilled in the art can clearly understand that the above-mentioned embodiment methods can be implemented by means of software plus a necessary general hardware platform, and of course by hardware, but in many cases the former is a better implementation method. Based on such an understanding, the technical solution of the present invention, or the part that contributes to the prior art, can be embodied in the form of a software product, which is stored in a storage medium (such as a read-only memory / random access memory, a magnetic disk, or an optical disk), and includes a number of instructions for enabling a terminal device (which can be a mobile phone, a computer, a server, an air conditioner, or a network device, etc.) to execute the methods described in each embodiment of the present invention.

[0134] The above are only preferred embodiments of the present invention, and are not intended to limit the patent scope of the present invention. Any equivalent structure or equivalent process transformation made using the contents of the present invention specification and drawings, or directly or indirectly applied in other related technical fields, are also included in the patent protection scope of the present invention.

Claims

1. A sparse aperture micro-motion target ISAR imaging method based on deep unfolding network, characterized in that: The method comprises: Acquire radar echo data, and perform preprocessing and modeling according to the echo data; Use the deep unfolding framework to build a model-driven deep learning imaging algorithm; Constructing a loss function corresponding to the deep learning imaging algorithm and selecting a training data set; Initialize the network parameters, set the parameter update optimization algorithm and the number of training rounds; Update and adjust parameters through optimization algorithms; When the number of training rounds is met, the optimal network parameters are saved to output the optimal algorithm model; The step of establishing a model-driven deep learning imaging algorithm using a deep unfolding framework includes: The L-ADMM algorithm, a solution algorithm for ISAR images of micro-moving targets under sparse aperture conditions, is expanded into a cascade network. Assume the number of iterations of the L-ADMM algorithm is n, and the number of layers of the cascade network is also set to n; Each layer of the network contains 4 unknown parameters, namely , , , , the L-ADMM algorithm sets the unknown parameters when used; The parameter initialization settings of each layer of the network are consistent with the initial values ​​of the L-ADMM algorithm so that during the training phase, L-ADMM-net continuously updates the parameters of each layer according to the loss function. During the testing phase, the network parameters are directly imaged; The step of constructing a loss function corresponding to the deep learning imaging algorithm and selecting a training data set includes: Constructing a loss function corresponding to the deep learning imaging algorithm; The one-dimensional range image H of the micro-moving target under sparse aperture conditions is set as the input of the training set data, the output is the ISAR image X of the main part under sparse aperture conditions, and the label data is the ISAR image X of the main part under full aperture echo; The step of constructing a loss function corresponding to the deep learning imaging algorithm comprises: Construct the following loss function: ； Where N represents the total number of training data sets. represents the F-norm of the matrix, It represents the ISAR image of the main part of the target obtained by calculating the one-dimensional range image H of the target under sparse aperture conditions through a neural network. It represents the main part of the ISAR image under the full aperture echo. represents the regularization parameter, represents the one-norm of a vector, It means stretching the matrix into a one-dimensional vector in column order.

2. The method according to claim 1, characterized in that The step of obtaining radar echo data and performing preprocessing and modeling according to the echo data includes: Acquire radar echo data, and perform translation compensation on a one-dimensional range image of the radar echo data, wherein the translation compensation includes: envelope alignment and self-focusing; The formula of the one-dimensional range image after translation compensation is as follows: ； in, represents the one-dimensional range image sequence of the target after translation compensation, , Represent fast time and slow time respectively. , Indicates the number of pulses contained in the full-aperture radar echo. , , They represent the center frequency, bandwidth and propagation speed of radar signals respectively. and Respectively represent the target body part The reflection coefficient of a scattering center and the instantaneous rotation distance relative to the radar, and Respectively represent the target micro-motion components The reflection coefficient of a scattering center and the instantaneous rotation distance relative to the radar, , , Indicates that the target body contains Scattering centers, Indicates that the target micro-motion components include scattering centers; Modeling is performed according to the one-dimensional range profile formula.

3. The method according to claim 2, characterized in that The step of modeling according to the one-dimensional range profile formula includes: Under sparse aperture conditions, the one-dimensional range profile formula can be expressed in the following matrix form: in , and Represent the one-dimensional range image sequence of the target, the main part of the target and the micro-moving parts of the target respectively, express The complex matrix of and They represent the number of pulses and the number of range units in the sparse aperture one-dimensional range image sequence respectively; for sparse aperture data, the number of pulses is less than the number of pulses contained in the full aperture radar echo, that is, , and the pulse number set is a subset of the full-aperture pulse number, that is, ,in represents a set of sparse aperture pulse numbers; For the target with micro-moving parts, the ISAR image of the main part of the target and the one-dimensional range image sequence of the main part of the target They are Fourier transform pairs, namely: in ISAR image showing the main part of the target, represents the partial Fourier matrix, assuming that the complete Fourier matrix is ,but By extracting The sequence number set of the extracted row vectors is the sparse aperture pulse sequence number set. ; Add constraints:

1. One-dimensional range image sequence of the main part of the target The column correlation is strong and has low rank characteristics; 2. One-dimensional range image sequence of the target micro-movement part The energy of the target is scattered in different distance units, which has a sparse characteristic. Third, the ISAR image of the target body is generally composed of a few scattering centers, which has a strong sparse characteristic. It can be modeled as: ； in and They represent the nuclear norm and Norm, used to characterize the rank and sparsity of the matrix respectively; , represents the regularization parameter, which is used to adjust the weights of matrix decomposition and ISAR imaging. ; The triple-constrained underdetermined problem is modeled, and the following model is finally obtained: ； Using the linear alternating direction multiplier method algorithm, we can get the following solution: ； in represents the inner product of two matrices, , represents the Lagrange multiplier matrix, , represents the punishment factor, represents the F norm of the matrix; Indicates The variables obtained by iteration are Indicates the rising factor, used to control the punishment factor , The upward trend ,in, Represents a partial Fourier matrix The conjugate transpose of ; represents the singular value shrinkage factor. Specifically, for any matrix With any scalar ,have: ； in express ; singular value decomposition, , is a unitary matrix, express The singular value vector of represents a diagonal matrix consisting of vectors; represents a soft threshold operator, for any scalar , ,have ,in represents the sign operator; for any vector ,have ,in Representation vector No. elements, Until the relative error of the ISAR images of the target main part obtained in two adjacent iterations ( ) is less than the set threshold, the ISAR image of the main part of the target with micro-moving components under sparse aperture conditions can be obtained. .

4. The method according to claim 1, characterized in that After the step of setting the one-dimensional range image H of the micro-moving target under the sparse aperture condition as the input end of the training set data, the output end is the ISAR image X of the main part under the sparse aperture condition, and the label data is the ISAR image X of the main part under the full aperture echo, the method further includes: A preset number of network layers are set, and the parameters are automatically adjusted through learning and training to obtain a mapping model between the one-dimensional range image H of the target under sparse aperture and the ISAR image X of the main part.

5. The method according to claim 1, characterized in that The steps of initializing the network parameters and setting the parameter update optimization algorithm and the number of training rounds include: The Adam algorithm is used to update and optimize the parameters. The principle of the Adam algorithm is as follows: ; ; in is the first-order estimate of the gradient, is a hyperparameter, is the second-order estimate of the gradient, is a hyperparameter, is the loss function, is the desired parameter; After bias correction, we get: ; ; in, , are the first-order and second-order estimates of the corrected gradient; In addition, the specific update formula of the neural network parameters is as follows: ; Where t is the number of iterations, is the parameter value at time t+1, is the parameter value at time t, is the learning rate of the neural network model, is the error constant.

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