Noise robust micro-motion echo separation method and device based on multi-domain joint constraint

Abstract

The invention discloses a noise robust micro-motion echo separation method and device based on multi-domain joint constraint, and the method comprises the steps: constructing a multi-domain joint constraint micro-motion signal separation iterative algorithm, and constraint terms comprise the sparsity constraint of a main body ISAR image and a micro-motion part echo, the low-rank constraint of the main body echo, the noise constraint and the error constraint; expanding an iterative algorithm into a deep network to obtain a backbone network; constructing a parameter extraction super network, wherein the parameter extraction super network comprises multiple layers of second sub-networks; each layer of second sub-network is used for extracting learnable parameters of the corresponding first sub-network from a main body ISAR image output by the upper layer of first sub-network of the corresponding first sub-network; and according to the backbone network and the super network, constructing and training a multi-domain joint constrained noise robust micro-motion signal separation network, and carrying out micro-motion echo separation by using the trained separation network, thereby improving the main body ISAR image reconstruction precision and the micro-motion echo separation quality.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of radars, and particularly relates to a noise-robust micro-motion echo separation method and device based on multi-domain joint constraints. BACKGROUND

[0002] Inverse synthetic aperture radar (ISAR) is widely used in space target monitoring and radar target recognition. Traditional ISAR imaging methods treat targets as rigid bodies and use range-doppler (RD) methods to achieve focused imaging. However, for targets with micro-motion components, such as propeller aircraft, satellites with rotating antennas, etc., the moving components will produce sidebands around the main Doppler spectrum corresponding to rigid body motion, i.e., the micro-Doppler (m-D) effect, which causes the rigid body ISAR image to be out of focus.

[0003] Existing methods mainly separate micro-motion echoes and main body echoes in the transform domain to remove the m-D effect, but have problems of low computational efficiency and poor algorithm stability. Among them, the micro-motion echo separation method based on sparse signal reconstruction and iterative optimization has high computational complexity, poor noise robustness, and needs fine manual parameter tuning; the model-driven deep network micro-motion echo separation method has limited network capacity and needs to be trained according to different signal-to-noise ratio echoes, and lacks noise robustness; the data-driven deep network micro-motion echo separation method needs a large number of training samples and lacks interpretability.

[0004] For example, in the related art, a patent application with publication number CN114740447A and the invention name of "Micro-motion signal separation method and device based on instance segmentation and computer equipment" discloses a micro-motion signal separation method based on instance segmentation. The method first obtains the echo time-frequency image of the micro-motion target signal according to the micro-motion target signal model, and then labels the time-frequency curves of the micro-motion and rigid body two types of scattering points, and then constructs a micro-motion component separation model containing a multi-scale feature extraction network and an instance segmentation network and trains it. In the test stage, the time-frequency image to be separated is input into the trained model to obtain the micro-motion echo separation result, but this method has high complexity and difficulty in label annotation. In addition, a patent application with publication number CN118915065A and the invention name of "Rotor target ISAR imaging method based on FGSR low-rank representation" discloses an ISAR imaging method for rotor targets based on FGSR low-rank representation. The method designs a micro-motion echo separation optimization objective function by constructing an imaging model, performing low-rank representation, and introducing a relaxation rank function, and then solves the echo separation by numerical iteration. However, this method is only suitable for a specific model, has weak generalization ability, has large numerical iteration calculation amount, is complex in manual parameter tuning, and lacks noise robustness.

[0005] It can be seen that the existing micro-motion echo separation method based on iterative optimization has high computational complexity, poor noise robustness, needs fine manual parameter tuning, and has large micro-motion echo separation error. The micro-motion echo separation method based on model-driven deep network has limited network capacity, needs to be trained according to echoes with different signal-to-noise ratios, and does not have noise robustness. The micro-motion echo separation method based on data-driven deep network needs a large number of training samples, and the function definition of the network structure lacks interpretability. SUMMARY

[0006] In order to solve the above problems existing in the prior art, the present application provides a noise-robust micro-motion echo separation method and device based on multi-domain joint constraint.

[0007] The technical problem to be solved by the present application is solved by the following technical scheme: A noise-robust micro-motion echo separation method based on multi-domain joint constraint comprises: According to the ISAR sparse observation model of the micro-motion target in the range-slow time domain, a multi-domain joint constraint micro-motion signal separation iterative algorithm is constructed, wherein the constraint terms include: sparsity constraints of the main ISAR image and the micro-motion component echo, low-rank constraints of the main echo, noise constraints and error constraints; The iterative algorithm is expanded into a deep network to obtain a backbone network; the backbone network comprises a plurality of cascaded first sub-networks, each first sub-network corresponds to one iteration of the iterative algorithm, and each first sub-network comprises five modules of a micro-motion component reconstruction layer, a main component auxiliary layer, a main ISAR image reconstruction layer, a noise component estimation layer and a Lagrange multiplier updating layer; A parameter extraction super network is constructed; the parameter extraction super network comprises a plurality of second sub-networks; the plurality of second sub-networks correspond to the plurality of first sub-networks one by one; each second sub-network is used to extract learnable parameters of a corresponding first sub-network from a main ISAR image output by a previous first sub-network of the corresponding first sub-network; A multi-domain joint constraint noise-robust micro-motion signal separation network is constructed and trained according to the backbone network and the super network to obtain a trained multi-domain joint constraint noise-robust micro-motion signal separation network; The trained multi-domain joint constraint noise-robust micro-motion signal separation network is used for micro-motion echo separation.

[0008] Optionally, the multi-domain joint constraint micro-motion signal separation iterative algorithm is constructed according to the ISAR sparse observation model of the micro-motion target in the range-slow time domain, comprising: A1, according to the ISAR sparse observation model of the micro-motion target in the range-slow time domain, an optimization problem in the scene of the multi-domain joint constraint micro-motion signal separation is constructed: ; in, Represents a high-resolution range image of the overall target. It is a partial Fourier matrix. Represents the main ISAR image, This is a high-resolution range image of the main target area. Represents a high-resolution range image of the slightly moving portion of the target. This represents Gaussian white noise. Indicates the number of pulses. Indicates the number of Doppler units. Indicates the number of distance units. Weights corresponding to different constraint terms; This indicates that we are looking for the 1-norm. This indicates that we are looking for the F-norm. Represents the nuclear norm; A2. The optimization problem is decomposed into multiple sub-problems using the ADMM algorithm; A3. Define the algorithm iteration process and the iteration termination condition to obtain the multi-domain joint constraint micro-motion signal separation iterative algorithm; wherein, in each iteration, the algorithm is updated step by step by solving the multiple sub-problems one by one. ; For the defined auxiliary variables, Let be the Lagrange multiplier matrix of the augmented Lagrange function of the optimization problem.

[0009] Optionally, the iterative algorithm is expanded into a deep network to obtain a backbone network, including: The first iteration algorithm The iteration is defined as the first iteration of the backbone network. The backbone network is formed by cascading each first subnetwork; among them... The network depth is preset; in each first sub-network, the micro-motion component reconstruction layer is used to solve and update. The main component auxiliary layer is used to solve and update. The main ISAR image reconstruction layer is used to solve and update The noise component estimation layer is used to solve and update The Lagrange multiplier update layer is used to solve and update .

[0010] Optionally, in each iteration, the updates are performed by solving the multiple subproblems one by one. ,include: ; in, The augmented Lagrangian function represents the optimization problem. is a penalty coefficient, the superscript represents the number of iterations, is a penalty coefficient is a rise factor.

[0011] Optionally, in training the multi-domain joint constraint noise-robust micro-motion signal separation network, a preset error-structure hybrid loss function is used to evaluate the training loss; the error-structure hybrid loss function is: , , , ; wherein, represents an error-structure hybrid loss, represents a main ISAR image output by the multi-domain joint constraint noise-robust micro-motion signal separation network, is a main label ISAR image contained in a training sample, and the subscript of and represents a pixel in the corresponding th Doppler unit and th range unit in the image; represents a high-resolution range image of a target micro-motion part output by the multi-domain joint constraint noise-robust micro-motion signal separation network, is a high-resolution range image label of the target micro-motion part contained in the training sample, represents a mean value of objects in the parentheses, represents a variance of objects in the parentheses, and are preset constants, and are preset weighting coefficients.

[0012] The application further provides a multi-domain joint constraint noise-robust micro-motion echo separation device, comprising: an acquisition module configured to acquire a noisy echo image; a separation module configured to perform micro-motion echo separation on the noisy echo image by using a multi-domain joint constraint noise-robust micro-motion signal separation network that has been pre-trained; wherein the multi-domain joint constraint noise-robust micro-motion signal separation network is obtained by the following way: A. According to the ISAR sparse observation model of the micro-motion target in the range-slow time domain, a multi-domain joint constraint micro-motion signal separation iterative algorithm is constructed, wherein the constraint terms include: the sparsity constraint of the main body ISAR image and the micro-motion component echo, the low-rank constraint of the main body echo, the noise constraint and the error constraint; B. The iterative algorithm is unfolded into a deep network to obtain a backbone network; the backbone network includes a plurality of cascaded first sub-networks, each first sub-network corresponds to an iteration in the iterative algorithm, and each first sub-network includes five modules: a micro-motion component reconstruction layer, a main component auxiliary layer, a main body ISAR image reconstruction layer, a noise component estimation layer and a Lagrange multiplier updating layer; C. A parameter extraction super network is constructed; the parameter extraction super network includes a plurality of second sub-networks; the plurality of second sub-networks correspond to the plurality of first sub-networks one by one; each second sub-network is used to extract the learnable parameters of the corresponding first sub-network from the main body ISAR image output by the last first sub-network of the corresponding first sub-network; D. According to the backbone network and the super network, a multi-domain joint constraint noise-robust micro-motion signal separation network is constructed and trained to obtain a trained multi-domain joint constraint noise-robust micro-motion signal separation network.

[0013] Optionally, the multi-domain joint constraint micro-motion signal separation iterative algorithm is constructed according to the ISAR sparse observation model of the micro-motion target in the range-slow time domain, comprising: A1. According to the ISAR sparse observation model of the micro-motion target in the range-slow time domain, an optimization problem in the multi-domain joint constraint micro-motion signal separation scene is constructed: ; Wherein, represents the high-resolution range image of the whole target, is a partial Fourier matrix, represents the main body ISAR image, is the high-resolution range image of the main body part of the target, represents the high-resolution range image of the micro-motion part of the target, represents Gaussian white noise, represents the number of pulses, represents the number of Doppler units, represents the number of range units, is the weight corresponding to different constraint terms; represents the 1-norm, represents the F-norm, represents the kernel norm; A2. The ADMM algorithm is used to decompose the optimization problem into a plurality of sub-problems; A3, define an algorithm iteration process and define an iteration termination condition, to obtain a multi-domain joint constraint micro-motion signal separation iteration algorithm; wherein in each iteration, the plurality of sub-problems are solved one by one to gradually update ; is a defined auxiliary variable, is a Lagrange multiplier matrix of an augmented Lagrangian function of the optimization problem.

[0014] Optionally, the iteration algorithm is unfolded into a deep network to obtain a backbone network, comprising: the first iteration of the iteration algorithm is defined as the first first sub-network of the backbone network, and each first sub-network is cascaded to obtain the backbone network; wherein, is a preset network depth; in each first sub-network, a micro-motion component reconstruction layer is used to solve and update , a main component auxiliary layer is used to solve and update , a main ISAR image reconstruction layer is used to solve and update , a noise component estimation layer is used to solve and update , and a Lagrange multiplier update layer is used to solve and update .

[0015] Optionally, in each iteration, the plurality of sub-problems are solved one by one to gradually update , comprising: ; wherein, denotes an augmented Lagrangian function of the optimization problem, is a penalty coefficient, the superscript of indicates the number of iterations, is a penalty coefficient .

[0016] Optionally, when training the multi-domain joint constraint noise-robust micro-motion signal separation network, a preset error-structure hybrid loss function is used to evaluate the training loss; the error-structure hybrid loss function is: , , , ; wherein, denotes an error-structure hybrid loss, denotes a main ISAR image output by the multi-domain joint constraint noise-robust micro-motion signal separation network, ​​denote the target micro-motion part of the high-resolution range profile label contained in the training sample, and denote the pixel in the image corresponding to the th Doppler unit and the th range unit; denote the target main body part of the high-resolution range image output by the noise-robust micro-motion signal separation network subject to multi-domain joint constraints, denote the high-resolution range profile label of the target micro-motion part contained in the training sample, denote the mean of the objects in the parentheses, denote the variance of the objects in the parentheses, and are preset constants, and are preset weighting coefficients.

[0017] The noise-robust micro-motion echo separation method based on multi-domain joint constraints provided by the present application proposes an innovative solution based on multi-domain joint constraints for micro-motion target signal separation and imaging problems. Specifically, the present application designs a multi-domain joint constraint micro-motion signal separation iterative algorithm (JCSS, Joint constraint signal separation) by fully utilizing the sparse characteristics of target main body echoes and the low-rank characteristics of micro-motion component echoes. The algorithm realizes complete and clear main body focusing imaging and accurate micro-motion echo separation simultaneously based on the distance-slow time domain observation model. Further, the present application expands the algorithm into a deep network with a limited number of layers, and sets the hyperparameters in the iterative algorithm as learnable parameters. Through end-to-end training, the present application not only avoids the complex and computationally intensive problem of manual parameter tuning in traditional iterative methods, but also improves the separation accuracy and efficiency. In addition, to enhance noise robustness, the present application innovatively combines the expanded network with the hypernetwork, so as to extract features from the main body ISAR image and adaptively generate optimal hyperparameters (learnable parameters) under different signal-to-noise ratios using the hypernetwork. Compared with the prior art, the present application has the following advantages: compared with traditional iterative optimization methods, the present application realizes automatic parameter tuning and more accurate echo separation; compared with existing model-driven deep network methods, the present application has stronger noise adaptability; compared with data-driven deep network methods, the present application significantly reduces the dependence on the amount of training samples while maintaining the explicit interpretability of the model structure, thereby comprehensively improving the main body ISAR image reconstruction accuracy and micro-motion echo separation quality.

[0018] The present application will be further described in detail below with reference to the accompanying drawings and the present application. BRIEF DESCRIPTION OF DRAWINGS

[0019] Figure 1is a flowchart of a multi-domain joint constraint noise-robust micro-motion echo separation method provided by an embodiment of the present application; Figure 2 A structure diagram of the JCSS-Net provided by the present application is shown. Figure 3 An exemplary structure diagram of the hypernetwork in the JCSS-Net is shown. Figure 3 A structure diagram of the hypernetwork in the JCSS-Net is shown. Figure 4 The main imaging contrast results of the JCSS and the JCSS-Net proposed by the present application and several existing methods on the point-simulation airplane data when the signal-to-noise ratio is 0 dB are shown. Figure 5 The micro-motion echo reconstruction results of the JCSS and the JCSS-Net proposed by the present application and several existing methods on the point-simulation airplane data when the signal-to-noise ratio is 0 dB are shown. DETAILED DESCRIPTION

[0020] The present application will be further described in detail below in combination with specific embodiments, but the embodiments of the present application are not limited thereto.

[0021] The present application proposes a noise-robust micro-motion echo separation method based on multi-domain joint constraint in view of the deficiencies of the prior art. First, according to the sparse characteristics of the main echo and the low-rank characteristics of the micro-motion echo, a multi-domain joint constraint micro-motion signal separation iterative algorithm (JCSS) is proposed, so as to simultaneously realize complete and clear main focusing imaging and accurate micro-motion echo separation. Then, the designed iterative algorithm is expanded into a deep network, and the optimal parameters of the algorithm iteration solving variables are adaptively learned end-to-end through the design of the hypernetwork, so as to obtain noise robustness. Finally, an error-structure hybrid loss is designed to guide network training, so as to further improve the reconstruction accuracy of the main ISAR image and the separation quality of the micro-motion echo. The present application can effectively solve the following problems: 1) the existing micro-motion echo separation method based on iterative algorithm has insufficient separation accuracy, complex parameter adjustment and large calculation amount; 2) the existing micro-motion echo separation method based on model-driven deep network needs to be trained separately at different signal-to-noise ratios, and has poor noise robustness; 3) the existing micro-motion echo separation method based on data-driven deep network needs a large number of training samples, and lacks interpretability.

[0022] The multi-domain joint constraint noise-robust micro-motion echo separation method provided by the present application will be described in detail below, as shown in Figure 1 , which comprises: S10, according to the ISAR sparse observation model of the micro-motion target in the range-slow time domain, a multi-domain joint constraint micro-motion signal separation iterative algorithm is constructed, wherein the constraint terms include: the sparse constraint of the main ISAR image and the micro-motion component echo, the low-rank constraint of the main echo, the noise constraint and the error constraint.

[0023] Specifically, the matrix form of the high-resolution range profile (Hrrp) of the micro-motion target can be expressed as: ; wherein, denotes the high-resolution range profile of the whole target, denotes the high-resolution range profile of the main body of the target, denotes the high-resolution range profile of the micro-motion part of the target, denotes Gaussian white noise, denotes the number of pulses, denotes the number of Doppler units, denotes the number of range units.

[0024] For the micro-motion target, the main body ISAR image and the main body Hrrp have the following relationship: ; wherein, denotes the full-size main body ISAR image to be reconstructed, denotes a partial Fourier matrix, the rows of which are extracted from the Fourier matrix of size according to the indexes of the sparse-aperture pulses.

[0025] Therefore, in the range-slow-time domain, the ISAR sparse observation model of the micro-motion target is: .

[0026] According to the ISAR sparse observation model of the micro-motion target in the range-slow-time domain, a multi-domain joint constraint micro-motion signal separation iterative algorithm (JCSS) is constructed, including: A1. According to the ISAR sparse observation model of the micro-motion target in the range-slow-time domain, an optimization problem in the scene of the multi-domain joint constraint micro-motion signal separation is constructed: (a); wherein, denotes the weight corresponding to different constraint terms, which is also a hyperparameter of the JCSS; denotes the 1-norm, denotes the F-norm, denotes the kernel norm.

[0027] In the optimization problem, five joint constraints are used to limit to obtain a unique solution, including sparsity constraints of the body ISAR image and the micro-motion component echo (the 2nd and 3rd terms of formula (a)), a low-rank constraint of the body echo (the 4th term of formula (a)), a noise constraint (the 5th term of formula (a)) and an error constraint (the 1st term of formula (a)). Among them, the body ISAR image has sparsity; the micro-motion component echo has sparsity and the body echo has low rank; the noise is Gaussian white noise with random characteristics added based on the actual situation. The application adopts norm to constrain sparsity, uses the kernel norm to constrain low rank, and uses the norm to constrain Gaussian white noise. Meanwhile, an error constraint is added.

[0028] In formula (a), auxiliary variables are introduced, and the following optimization problem can be obtained: (b); wherein, is a defined auxiliary variable.

[0029] The augmented Lagrangian function of the optimization problem can be written as: (c); wherein, denotes a Lagrange multiplier matrix of the augmented Lagrangian function of the optimization problem, is a penalty coefficient, denotes an inner product between two matrices.

[0030] A2, the ADMM algorithm is used to decompose the optimization problem into multiple sub-problems.

[0031] Specifically, the ADMM algorithm is used to decompose the optimization problem into the following multiple sub-problems which are easier to handle: ; wherein, denotes an augmented Lagrangian function of the optimization problem, is a penalty coefficient, the superscript of denotes the number of iterations.

[0032] A3, the algorithm iteration process is defined and the iteration termination condition is defined, and a micro-motion signal separation iteration algorithm with multiple domain joint constraints is obtained; wherein is updated step by step by solving the multiple sub-problems one by one in each iteration .

[0033] Specifically, under a given set of hyperparameters, the algorithm process is implemented by defining the flow of a single round of algorithm iteration and performing multiple rounds of iteration. In each iteration, is updated step by step by solving the multiple sub-problems one by one , until the iteration termination condition is satisfied, and the final solution is obtained. This process can be expressed as: ; Specifically, in each iteration, the soft threshold operator is first used to solve equation (1) to update : (i); where denotes the soft threshold operator, and the shrinkage threshold is .

[0034] Then, by solving equation (2), the update of is realized: (ii); Here, let be the singular value shrinkage operator of any matrix : ; where is also a soft threshold operator, and the shrinkage threshold is . In the update formula of , the singular value shrinkage operator of the matrix in the square brackets is denoted by , where the shrinkage threshold of the soft threshold operator used is set to , denotes the step size, which is also a hyperparameter of the JCSS algorithm, used to adjust the speed of the algorithm iteration. is the singular value decomposition of , is the diagonal function, is the left singular vector matrix, is the right singular vector matrix, and the upper index H denotes the matrix conjugate transpose, is the singular value vector of .

[0035] Then, the soft threshold operator is used to solve equation (3) to update : (iii); where denotes the soft threshold operator, and the shrinkage threshold is . Next, update the noise : (iv); Finally, update and : (v), (vi); wherein, is a penalty coefficient is an ascending factor of is also a hyper-parameter of JCSS algorithm.

[0036] The above completes one iteration, and then adjusts the hyper-parameter to return to formula (1) for continuous iteration, until the iteration termination condition is reached. The iteration termination condition can be set as: ; wherein, represents the output of the noise-robust micro-motion signal separation network of the multi-domain joint constraint in the i-th iteration , represents the output of the noise-robust micro-motion signal separation network of the multi-domain joint constraint in the i-th iteration , represents the output of the noise-robust micro-motion signal separation network of the multi-domain joint constraint in the i-th iteration , represents a preset precision, is less than .

[0037] In addition, for the parameter initialization in the first iteration, the following can be allowed: , and are simply initialized with zero matrices.

[0038] Exemplarily, the following algorithm 1 shows the pseudo-code implementation of the micro-motion signal separation algorithm (JCSS) based on multi-domain joint constraint:

[0039] S20, the iteration algorithm is unfolded into a deep network to obtain a backbone network; the backbone network includes cascaded multiple layers of first sub-networks, each layer of first sub-networks corresponds to one iteration in the iteration algorithm, and each layer of first sub-networks includes five modules of micro-motion component reconstruction layer, main component auxiliary layer, main ISAR image reconstruction layer, noise component estimation layer and Lagrange multiplier updating layer.

[0040] Specifically, the iteration algorithm (JCSS) is unfolded into a deep network to obtain a backbone network, including: The i-th iteration of the iteration algorithm (JCSS) is defined as the j-th first sub-network of the backbone network, and each first sub-network is cascaded to obtain the backbone network; wherein, is a preset network depth; in each first sub-network, the micro-motion component reconstruction layer is used to solve and update ​​The main component auxiliary layer is used to solve and update. The main ISAR image reconstruction layer is used to solve and update The noise component estimation layer is used to solve and update The Lagrange multiplier update layer is used to solve and update .

[0041] See Figure 2 Let the number of cascaded layers of the first subnetwork include Layer, of which the first The first sub-network of layer 1 corresponds to the first layer of JCSS. In the next iteration, in the first sub-network of this layer, the micro-motion component reconstruction layer... The definition is given in equation (i) above, for the main component auxiliary layer. The definition is given in equation (ii) above, for the main ISAR image reconstruction layer. The definition is given in equation (iii) above, for the noise component estimation layer. See equation (iv) above for the definition of the Lagrange multiplier update layer. The definition is given in equation (v) above. The learnable parameters of the first sub-network in each layer include... Therefore, compared with existing data-driven deep network-based micro-motion echo separation methods, the functional definition of the backbone network in this invention is interpretable.

[0042] It is worth mentioning the number of cascaded layers in the first sub-network. This is not equal to the number of iterations when the JCSS algorithm converges, but can be selected from 3 to 20 layers, for example, preferably 11 layers. This is because, in this invention, a hypernetwork is constructed to extract features from the main ISAR image output by the first subnetwork, thereby outputting appropriate hyperparameters for the first subnetwork. That is, the learnable parameters of the hypernetwork are actually the hyperparameters of the JCSS algorithm. For the specific implementation, please continue to step S30.

[0043] S30. Construct a parameter extraction supernetwork; the parameter extraction supernetwork includes multiple layers of second subnetworks; each layer of second subnetwork corresponds one-to-one with a layer of first subnetwork; each layer of second subnetwork is used to extract the learnable parameters of the corresponding first subnetwork from the main ISAR image output by the first subnetwork above the corresponding first subnetwork.

[0044] In this invention, in order to achieve noise robustness of the network, a hypernetwork is introduced to extract the learnable parameters of the first subnetwork from the main ISAR image output by the first subnetwork of each layer of the backbone network. This allows the hyperparameters of the JCSS algorithm corresponding to the first subnetwork to be adaptively adjusted according to the change of signal-to-noise ratio without retraining the model.

[0045] See Figure 2 The input to the second subnetwork of each layer is the output of the first subnetwork of the previous layer. The output is the first... Learnable parameters of the first subnetwork of the layer .

[0046] Specifically, hypernetworks The definition is as follows: ; in, These are the weights of the hypernetwork. For the ... In a hypernetwork, the input to the layer is the output of the layer above. After internal computation by the hypernetwork, learnable parameters are output. To guide the first Forward propagation of layers.

[0047] Convolutional layers and max-pooling / average-pooling layers are used, combined with the ReLU activation function. Finally, the learnable parameters are output. To guide the first Forward propagation of layers.

[0048] Figure 3 The diagram illustrates the structure of the second sub-network, which is a CNN (Convolutional Neural Network), with the output of the previous layer... After passing through convolutional layers and max-pooling / average-pooling layers in a CNN, and combined with the ReLU activation function, learnable parameters are output. Where Conv.C8_k3_s1_p1 indicates that the number of channels is 8 and the kernel size is [value missing]. A convolutional layer with a stride of 1 and padding of 1, where MaxPool_k4_s4 indicates the kernel size is... A maximum pooling layer with a step size of 4.

[0049] Of course, the structure of the second sub-network includes, but is not limited to, CNNs, and there are other alternatives, such as ResNets.

[0050] S40. Construct and train a noise-robust micro-motion signal separation network with multi-domain joint constraints based on the backbone network and supernetwork, and obtain the trained noise-robust micro-motion signal separation network with multi-domain joint constraints.

[0051] Specifically, the main network and the super network are combined to obtain the final multi-domain jointly constrained noise-robust micro-motion signal separation network (JCSS-Net), such as... Figure 2The main network layer input contains the previous layer network output of the micro-motion component reconstruction matrix, the main component auxiliary matrix, the main ISAR image reconstruction matrix, the noise component estimation matrix, the Lagrange multiplier update matrix and the super network generated super parameter; the super network input is the full size ISAR image output by the previous layer.

[0052] Regarding the training of JCSS-Net, the inventors independently generated a simulation data set for network training. The simulation data set contains 1100 samples, of which 1000 are used for training and 100 are used for testing. According to the actual situation, each sample target is composed of 300 scattering points, of which the main part image is composed of 280 isolated scattering points randomly generated according to a uniform distribution, and the scattering point amplitude is subject to a Gaussian distribution, as the main label ISAR image. The echo image of the micro-motion component is simulated by setting the radar parameters and the micro-motion component scattering point position. The radar carrier frequency is set to 10 GHz, the bandwidth is 0.5 GHz, and the pulse repetition frequency is 100 Hz. From the 280 scattering points of the main part, 2 scattering points are randomly selected as the rotation center, and 10 scattering points are randomly generated around each rotation center to rotate around the center as the scattering points on the micro-motion component. According to the actual situation, the rotation frequency of each sample is randomly generated between 20 Hz and 30 Hz, and the resulting echo is used as the micro-motion label image, i.e. the high-resolution range image label of the target micro-motion part. The main part echo and the micro-motion part echo are superimposed to obtain the overall echo of the sample, with a size of Noise is added to the original sample echo, and the noise is subject to a standard Gaussian distribution with a signal-to-noise ratio ranging from 0 to 20 dB.

[0053] Then, the above training data is used to generate a missing noisy echo image, which is input into the multi-domain joint constraint noise robust micro-motion signal separation network in the training, and the network weight is updated through the loss function back propagation and gradient descent algorithm, and the training is completed.

[0054] Wherein, in the training of the multi-domain joint constraint noise robust micro-motion signal separation network, a preset error-structure hybrid loss function is used to evaluate the training loss; the error-structure hybrid loss function is: , , , ; Wherein, represents the error-structure hybrid loss, represents the main ISAR image output by the multi-domain joint constraint noise robust micro-motion signal separation network, is the main label ISAR image contained in the training sample, and The subscript indicates that the corresponding index in the image is taken. The first Doppler unit, the first Pixels per distance unit; This represents the high-resolution range profile of the target's micro-motion component output by a noise-robust micro-motion signal separation network with multi-domain joint constraints. This refers to high-resolution range image labels for the target micro-motion parts contained in the training samples. This indicates calculating the mean of the objects within the parentheses. This indicates calculating the variance of the object within the parentheses. and As a preset constant, , It is a constant. Represents the dynamic range of pixel values, typically , , and These are the preset weighting coefficients.

[0055] This invention proposes an error-structure hybrid loss, which consists of two parts: the root mean square error (MSE) of the reconstructed subject image and the subject label image. And the structural similarity between the output micro-motion echo and the echo tag of the micro-motion component, that is... This method aims to guide the accurate reconstruction of focused ISAR imaging of the target subject and the echoes of micro-moving components. The closer the SSIM value is to 1, the higher the similarity between the two variables; therefore, the difference from 1 is used as the loss. Furthermore, the loss component in the error-structure hybrid loss function includes, but is not limited to, the mean square error between the output image and the label image. Other alternative methods exist, such as the F-norm and root mean square error.

[0056] After training the noise-robust micro-motion signal separation network with multi-domain joint constraints, the network is tested using samples from a test set. This test set consists of the aforementioned 100 simulation data points and point-simulated aircraft data, but is not limited to these. Once the test is passed, the trained noise-robust micro-motion signal separation network with multi-domain joint constraints is obtained.

[0057] It is worth mentioning that the present invention trains the network on a dataset composed of random signal-to-noise ratio and defect rate echoes, and only one training is required to achieve subject focusing imaging and micro-motion echo separation under different signal-to-noise ratio conditions.

[0058] Exemplarily, in one specific example, all the training and testing of the present application are run on a NVIDIA GeForce RTX 4090 GPU with PyTorch implementation. The network training adopts an Adam optimizer to update the learning of network parameters, a total of 300 epochs are trained, the learning rate is set to , the exponential decay rate is 0.99; the batch size is set to 25.

[0059] S50, using the trained multi-domain joint constraint noise robust micro-motion signal separation network to separate the micro-motion echo.

[0060] Specifically, the noisy echo image received by the radar receiver is input into the trained multi-domain joint constraint noise robust micro-motion signal separation network (JCSS-Net), so as to output the main body ISAR image and the micro-motion component echo, thereby obtaining the focused imaging result and the separated micro-motion signal image.

[0061] Here, unlike other methods which only focus on the reconstruction of the main body image, the JCSS-Net can simultaneously separate the main body ISAR image and the micro-motion echo with higher quality. In addition, under different signal-to-noise ratio conditions, the JCSS-Net can obtain better separation precision than the pure expansion network without retraining, and only one training can adapt to different noise intensities. The following takes a low signal-to-noise ratio environment as an example.

[0062] Table 1 shows the comparison of the main body indicators of the JCSS and JCSS-Net proposed in the present application with several existing methods under the condition of a signal-to-noise ratio of 0 dB, specifically, the normalized mean square error (NMSE) and the structural similarity (SSIM) of the main body imaging result under the corresponding conditions. Table 2 shows the comparison of the micro-motion echo indicators of the JCSS and JCSS-Net proposed in the present application with several existing methods under the condition of a signal-to-noise ratio of 0 dB, specifically, the normalized mean square error (NMSE) and the structural similarity (SSIM) of the main body imaging result under the corresponding conditions. Table 3 shows the comparison of the comprehensive indicators of the JCSS and JCSS-Net proposed in the present application with several existing methods under the condition of a signal-to-noise ratio of 0 dB. Table 4 shows the comparison of the average running time of the JCSS and JCSS-Net proposed in the present application with several existing methods under the condition of a signal-to-noise ratio of 0 dB.

[0063] Table 1 Comparison of main body indicators of airplane point simulation data under the condition of a signal-to-noise ratio of 0 dB

[0064] Table 2 Comparison of micro-motion echo indicators of airplane point simulation data under the condition of a signal-to-noise ratio of 0 dB

[0065] Table 3 Comparison of comprehensive indexes of aircraft point simulation data under the condition of signal-to-noise ratio of 0dB

[0066] Table 4 Average running time of different methods

[0067] wherein, RPCA (Robust Principal Component Analysis) refers to an existing robust principal component analysis method, L-ADMM (Linearized Alternating Direction Method of Multipliers) refers to an existing linearized alternating direction multiplier method, NL-ADMM (NonLinear Alternating Direction Method of Multipliers) refers to an existing nonlinear alternating direction multiplier method, and L-ADMM-Net (Linearized ADMM-based Neural Network) refers to an existing neural network based on linearized ADMM.

[0068] The evaluation indexes in Table 1 and Table 2 show that the JCSS and JCSS-Net methods proposed in the application obtain lower NMSE and higher SSIM, and the JCSS-Net is improved compared with the JCSS, verifying the excellent performance of the separation network. In addition, Table 4 also shows that compared with other traditional methods, the JCSS-Net proposed in the application has shorter time consumption and greatly improved computing efficiency.

[0069] Figure 4 Figures 1 and 2 show the main imaging comparison results of the JCSS and JCSS-Net proposed in the application and several existing methods on the point simulation aircraft data when the signal-to-noise ratio is 0dB, Figure 5 Figures 3 and 4 show the micro-motion echo reconstruction results of the JCSS and JCSS-Net proposed in the application and several existing methods on the point simulation aircraft data when the signal-to-noise ratio is 0dB. Wherein, (a) is RPCA, (b) is L-ADMM, (c) is NL-ADMM, (d) is L-ADMM-Net, (e) is the JCSS proposed in the application, and (f) is the JCSS-Net proposed in the application. From the figures, it can be seen that the JCSS and JCSS-Net proposed in the application have better reconstruction results than the existing methods. Figure 4 and Figure 5As can be seen, the existing method RPCA cannot eliminate noise under low signal-to-noise ratio conditions, resulting in serious noise points in the main body image and micro-motion echo; and the existing methods L-ADMM, NL-ADMM and NL-ADMM can obtain focused main body ISAR images, but it is difficult to effectively suppress the noise of the micro-motion echo. In contrast, the JCSS and JCSS-Net proposed in the present application can simultaneously obtain a main body ISAR image with good focusing, clean background and complete structure, and accurately separated micro-motion echo under low signal-to-noise ratio conditions.

[0070] In summary, the noise-robust micro-motion echo separation method based on multi-domain joint constraint provided by the present application proposes an innovative solution based on multi-domain joint constraint for the problem of micro-motion target signal separation and imaging. Specifically, the present application fully utilizes the sparse characteristics of the target main body echo and the low-rank characteristics of the micro-motion component echo, and designs a multi-domain joint constraint micro-motion signal separation iterative algorithm (JCSS). The algorithm realizes complete and clear main body focusing imaging and accurate micro-motion echo separation simultaneously based on the distance-slow time domain observation model. Further, the present application expands the algorithm into a deep network with a limited number of layers, and sets the hyperparameters in the iterative algorithm as learnable parameters. Through end-to-end training, the present application not only avoids the complex and computationally intensive problem of manual parameter tuning in traditional iterative methods, but also improves the separation accuracy and efficiency. In addition, to enhance noise robustness, the present application innovatively combines the expanded network with the hypernetwork, so as to extract features from the main body ISAR image using the hypernetwork and adaptively generate optimal hyperparameters (learnable parameters) under different signal-to-noise ratios. Compared with the prior art, the present application has the following advantages: compared with traditional iterative optimization methods, the present application realizes automatic parameter tuning and more accurate echo separation; compared with existing model-driven deep network methods, the present application has stronger noise adaptability; compared with data-driven deep network methods, the present application significantly reduces the dependence on the amount of training samples while maintaining the explicit interpretability of the model structure, thereby comprehensively improving the main body ISAR image reconstruction accuracy and micro-motion echo separation quality.

[0071] The present application can be applied to China's ground-based broadband radar to realize high-resolution focused imaging of micro-motion aerospace targets in a complex noise environment, thereby improving the ability to acquire important information such as target shape, structure and motion. At the same time, the present application can also be applied to ship-borne and airborne ISAR systems, thereby significantly improving the monitoring and feature extraction capabilities of micro-motion targets.

[0072] Based on the same inventive concept, the embodiments of the present application also provide a noise-robust micro-motion echo separation device based on multi-domain joint constraint, which is a computer program product, comprising: an acquisition module and a separation module.

[0073] The acquisition module is configured to acquire a noisy echo image. Specifically, in practice, the radar receiver receives a return, and according to the return, a noisy echo image can be formed and input to the acquisition module.

[0074] The separation module is configured to separate the noisy echo image by using a multi-domain joint constraint noise-robust micro-motion signal separation network trained in advance. The multi-domain joint constraint noise-robust micro-motion signal separation network is obtained by the following method: A. According to the ISAR sparse observation model of the micro-motion target in the range-slow time domain, a multi-domain joint constraint micro-motion signal separation iterative algorithm is constructed, wherein the constraint terms include: the sparsity constraint of the main body ISAR image and the micro-motion component echo, the low-rank constraint of the main body echo, the noise constraint and the error constraint. B. The iterative algorithm is unfolded into a deep network to obtain a backbone network; the backbone network includes a plurality of cascaded first sub-networks, each first sub-network corresponds to one iteration of the iterative algorithm, and each first sub-network includes five modules: a micro-motion component reconstruction layer, a main component auxiliary layer, a main body ISAR image reconstruction layer, a noise component estimation layer and a Lagrange multiplier update layer. C. A parameter extraction super network is constructed; the parameter extraction super network includes a plurality of second sub-networks; the plurality of second sub-networks correspond one-to-one to the plurality of first sub-networks; each second sub-network is used to extract the learnable parameters of the corresponding first sub-network from the main body ISAR image output by the previous layer of the corresponding first sub-network. D. According to the backbone network and the super network, a multi-domain joint constraint noise-robust micro-motion signal separation network is constructed and trained to obtain a trained multi-domain joint constraint noise-robust micro-motion signal separation network.

[0075] Optionally, the multi-domain joint constraint micro-motion signal separation iterative algorithm is constructed according to the ISAR sparse observation model of the micro-motion target in the range-slow time domain, including: A1. According to the ISAR sparse observation model of the micro-motion target in the range-slow time domain, an optimization problem in the multi-domain joint constraint micro-motion signal separation scenario is constructed: ; Wherein, denotes the high-resolution range image of the whole target, is a partial Fourier matrix, denotes the main body ISAR image, is the high-resolution range image of the target main body part, denotes the high-resolution range image of the target micro-motion part, denotes Gaussian white noise, denotes the number of pulses, Indicates the number of Doppler units. Indicates the number of distance units. Weights corresponding to different constraint terms; This indicates that we are looking for the 1-norm. This indicates that we are looking for the F-norm. Represents the nuclear norm.

[0076] A2. The optimization problem is decomposed into multiple sub-problems using the ADMM algorithm; A3. Define the algorithm iteration process and the iteration termination condition to obtain the micro-motion signal separation iterative algorithm with multi-domain joint constraints; wherein, in each iteration, the algorithm is updated step by step by solving the multiple sub-problems one by one. ; For the defined auxiliary variables, Let be the Lagrange multiplier matrix of the augmented Lagrange function of the optimization problem.

[0077] Optionally, the iterative algorithm is expanded into a deep network to obtain a backbone network, including: The first iteration algorithm The iteration is defined as the first iteration of the backbone network. The backbone network is formed by cascading each first subnetwork; among them... The network depth is preset; in each first sub-network, the micro-motion component reconstruction layer is used to solve and update. The main component auxiliary layer is used to solve and update. The main ISAR image reconstruction layer is used to solve and update The noise component estimation layer is used to solve and update The Lagrange multiplier update layer is used to solve and update .

[0078] Optionally, in each iteration, the updates are performed by solving the multiple subproblems one by one. ,include: ; in, The augmented Lagrangian function represents the optimization problem. It is the penalty coefficient. The superscript indicates the iteration number. Penalty coefficient The increasing factor.

[0079] Optionally, when training the noise-robust micro-motion signal separation network with multi-domain joint constraints, a preset error-structure hybrid loss function is used to evaluate the training loss; the error-structure hybrid loss function is: , , , ; wherein, denotes the error-structure hybrid loss, denotes the subject ISAR image output by the multi-domain joint constraint noise-robust micro-motion signal separation network, is the subject label ISAR image contained in the training sample, and the subscript of denotes the pixel in the corresponding th Doppler unit and th range unit in the image; denotes the high-resolution range image of the target micro-motion part output by the multi-domain joint constraint noise-robust micro-motion signal separation network, is the high-resolution range image label of the target micro-motion part contained in the training sample, denotes the mean of the objects in the parentheses, denotes the variance of the objects in the parentheses, and are preset constants, and are preset weighting coefficients.

[0080] It should be noted that, for the device embodiment, since it is basically similar to the method embodiment, the description is relatively simple, and the related parts can be referred to the part of the method embodiment, and the device embodiment can obtain the same beneficial effects as the method embodiment.

[0081] It should be noted that the terms "first", "second", and the like are used to distinguish similar objects, and do not necessarily have to be used to describe a particular order or sequence. It should be understood that the data used in this way can be interchanged under appropriate circumstances, so that the embodiments of the application described herein can be implemented in an order other than those illustrated or described herein. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the present application. Rather, they are merely examples of devices and methods consistent with some aspects of the present application.

[0082] In the description of the specification, the description of the terms "one embodiment", "some embodiments", "an example", "a specific example", or "some examples" etc. means that the specific features or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present application. In the specification, the illustrative description of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features or characteristics described can be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art can combine and combine different embodiments or examples described in the specification.

[0083] Although the present application is described herein in conjunction with various embodiments, those skilled in the art, with the benefit of the description and drawings presented herein, can understand and appreciate other variations and modifications in the disclosed embodiments. In the description of the present application, the word "comprising" does not exclude other components or steps, "a" or "one" does not exclude a plurality, and "a plurality" means two or more, unless otherwise expressly specified. In addition, some measures are described in different embodiments, but this does not mean that these measures cannot be combined to produce good results.

[0084] The above is a further detailed description of the present application in conjunction with specific preferred embodiments, and cannot be considered as limiting the specific implementation of the present application to these descriptions. For those skilled in the art, without departing from the concept of the present application, a number of simple deductions or substitutions can be made, which should be considered as falling within the scope of protection of the present application.

Claims

1. A noise-robust micro-motion echo separation method based on multi-domain joint constraints, characterized in that, The method comprises the steps of: According to the ISAR sparse observation model of the micro-motion target in the range-slow time domain, a multi-domain joint constraint micro-motion signal separation iterative algorithm is constructed, wherein the constraint terms include: the sparsity constraint of the main body ISAR image and the micro-motion component echo, the low rank constraint of the main body echo, the noise constraint and the error constraint; The iterative algorithm is unfolded into a deep network to obtain a backbone network; the backbone network comprises a plurality of cascaded first sub-networks, each first sub-network corresponds to one iteration of the iterative algorithm, and each first sub-network comprises five modules: a micro-motion component reconstruction layer, a main component auxiliary layer, a main body ISAR image reconstruction layer, a noise component estimation layer and a Lagrange multiplier updating layer; A parameter extraction super network is constructed; the parameter extraction super network comprises a plurality of second sub-networks; the plurality of second sub-networks correspond to the plurality of first sub-networks one by one; each second sub-network is used to extract the learnable parameters of the corresponding first sub-network from the main body ISAR image output by the last first sub-network of the corresponding first sub-network; According to the backbone network and the super network, a multi-domain joint constraint noise-robust micro-motion signal separation network is constructed and trained to obtain a trained multi-domain joint constraint noise-robust micro-motion signal separation network; The trained multi-domain joint constraint noise-robust micro-motion signal separation network is used for micro-motion echo separation.

2. The method of claim 1, wherein, The method comprises the steps of: A1, according to the ISAR sparse observation model of the micro-motion target in the range-slow time domain, an optimization problem in the scene of the multi-domain joint constraint micro-motion signal separation is constructed: ； wherein, denotes the high resolution range profile of the whole target, is a partial Fourier matrix, denotes the main body ISAR image, denotes the high resolution range profile of the target main body part, denotes the high resolution range profile of the target micro-motion part, denotes the Gaussian white noise, denotes the number of pulses, denotes the number of Doppler units, denotes the number of range units, is the weight corresponding to different constraint terms; denotes the 1-norm, denotes the F-norm, denotes the kernel norm; A2, the ADMM algorithm is used to decompose the optimization problem into a plurality of sub-problems; A3, define an algorithm iteration process and define an iteration termination condition, to obtain a multi-domain joint constraint micro-motion signal separation iteration algorithm; wherein in each iteration, the plurality of sub-problems are solved one by one to gradually update ; is a defined auxiliary variable, is a Lagrange multiplier matrix of an augmented Lagrange function of the optimization problem.

3. The method of claim 2, wherein, The iterative algorithm is unfolded into a deep network to obtain a backbone network, comprising: The first iteration algorithm The iteration is defined as the first iteration of the backbone network. The backbone network is formed by cascading each first subnetwork; among them... The network depth is preset; in each first sub-network, the micro-motion component reconstruction layer is used to solve and update. The main component auxiliary layer is used to solve and update. The main ISAR image reconstruction layer is used to solve and update The noise component estimation layer is used to solve and update The Lagrange multiplier update layer is used to solve and update .

4. The method of claim 2, wherein, In each iteration, the plurality of sub-problems are solved one by one to update the solution step by step comprising: ； wherein denotes an augmented Lagrangian function of the optimization problem, is a penalty coefficient, the superscript of denotes the iteration number, is a penalty coefficient is a step-up factor.

5. The method of claim 2, wherein, When training the multi-domain joint constraint noise-robust micro-motion signal separation network, a preset error-structure hybrid loss function is used to evaluate the training loss; the error-structure hybrid loss function is: ， ， ， ； in, This represents the error-structure hybrid loss. The main ISAR image is represented by the output of a noise-robust micro-motion signal separation network with multi-domain joint constraints. These are the ISAR images with subject labels contained in the training samples. and The subscript indicates that the corresponding index in the image is taken. The first Doppler unit, the first Pixels per distance unit; This represents the high-resolution range profile of the target's micro-motion component output by a noise-robust micro-motion signal separation network with multi-domain joint constraints. This refers to high-resolution range image labels for the target micro-motion parts contained in the training samples. This indicates calculating the mean of the objects within the parentheses. This indicates calculating the variance of the object within the parentheses. and As a preset constant, and These are the preset weighting coefficients.

6. A noise-robust micro-motion echo separation device based on multi-domain joint constraints, characterized in that, The method comprises the steps of: An acquisition module is configured to acquire a noisy echo image; A separation module is configured to use a pre-trained multi-domain joint constraint noise-robust micro-motion signal separation network to separate the micro-motion echo of the noisy echo image; The multi-domain joint constraint noise-robust micro-motion signal separation network is obtained by the following methods: A, according to the ISAR sparse observation model of the micro-motion target in the range-slow time domain, a multi-domain joint constraint micro-motion signal separation iterative algorithm is constructed, wherein the constraint terms include: the sparsity constraint of the main body ISAR image and the micro-motion component echo, the low rank constraint of the main body echo, the noise constraint and the error constraint; B, the iterative algorithm is unfolded into a deep network to obtain a backbone network; the backbone network comprises a plurality of cascaded first sub-networks, each first sub-network corresponds to one iteration of the iterative algorithm, and each first sub-network comprises five modules: a micro-motion component reconstruction layer, a main component auxiliary layer, a main body ISAR image reconstruction layer, a noise component estimation layer and a Lagrange multiplier updating layer; C. a parameter extraction hypernetwork; the parameter extraction hypernetwork comprises a plurality of second subnetworks; the plurality of second subnetworks correspond to the plurality of first subnetworks one by one; each second subnetwork is configured to extract learnable parameters of a corresponding first subnetwork from a subject ISAR image output by a previous layer of the corresponding first subnetwork; D. constructing and training the multi-domain joint constraint noise-robust micro-motion signal separation network according to the backbone network and the hypernetwork to obtain a trained multi-domain joint constraint noise-robust micro-motion signal separation network.

7. The multi-domain joint constraint based noise-robust micro-motion echo separation device according to claim 6, characterized in that, The multi-domain joint constraint micro-motion signal separation iterative algorithm is constructed according to the ISAR sparse observation model of a micro-motion target in a range-slow time domain, and comprises: A1. constructing an optimization problem in a multi-domain joint constraint micro-motion signal separation scenario according to the ISAR sparse observation model of a micro-motion target in a range-slow time domain: ； wherein, represents a high resolution range profile of the whole target, is a partial Fourier matrix, represents a main body ISAR image, is a high resolution range profile of the target main body part, represents a high resolution range profile of the target micro-motion part, represents a Gaussian white noise, represents a number of pulses, represents a number of Doppler units, represents a number of range units, is a weight corresponding to different constraint terms; represents a 1-norm, represents an F-norm, represents a kernel norm; A2. decomposing the optimization problem into a plurality of sub-problems by using an ADMM algorithm; A3, define an algorithm iteration process and define an iteration termination condition, to obtain a multi-domain joint constraint micro-motion signal separation iteration algorithm; wherein in each iteration, the plurality of sub-problems are solved one by one to gradually update ; is a defined auxiliary variable, is a Lagrange multiplier matrix of an augmented Lagrange function of the optimization problem.

8. The multi-domain joint constraint based noise-robust micro-motion echo separation device according to claim 7, characterized in that, The iterative algorithm is unfolded into a deep network to obtain a backbone network, comprising: The first iteration algorithm The iteration is defined as the first iteration of the backbone network. The backbone network is formed by cascading each first subnetwork; among them... The network depth is preset; in each first sub-network, the micro-motion component reconstruction layer is used to solve and update. The main component auxiliary layer is used to solve and update. The main ISAR image reconstruction layer is used to solve and update The noise component estimation layer is used to solve and update The Lagrange multiplier update layer is used to solve and update .

9. The multi-domain joint constraint based noise-robust micro-motion echo separation device according to claim 7, wherein, In each iteration, the plurality of sub-problems are solved one by one to update the solution step by step comprising: ； wherein denotes an augmented Lagrangian function of the optimization problem, is a penalty coefficient, the superscript of denotes the iteration number, is a penalty coefficient is a step-up factor.

10. The multi-domain joint constraint based noise-robust micro-motion echo separation device according to claim 7, characterized in that, When training the multi-domain joint constraint noise-robust micro-motion signal separation network, a preset error-structure hybrid loss function is used to evaluate training loss; the error-structure hybrid loss function is: ， ， ， ； in, This represents the error-structure hybrid loss. The main ISAR image is represented by the output of a noise-robust micro-motion signal separation network with multi-domain joint constraints. These are the ISAR images with subject labels contained in the training samples. and The subscript indicates that the corresponding index in the image is taken. The first Doppler unit, the first Pixels per distance unit; This represents the high-resolution range image of the target body output by a noise-robust micro-motion signal separation network with multi-domain joint constraints. This refers to high-resolution range image labels for the target micro-motion parts contained in the training samples. This indicates calculating the mean of the objects within the parentheses. This indicates calculating the variance of the object within the parentheses. and As a preset constant, and These are the preset weighting coefficients.

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