Super-network based sparse ISAR translation compensation and imaging integration method

Abstract

The application discloses a kind of sparse ISAR translation compensation and imaging integration method based on super network, mainly solve the precision of prior art under low signal-to-noise ratio condition translation compensation and the quality of ISAR imaging is poor, echo signal-to-noise ratio is not robust, spatial complexity is high and the problem of low efficiency.Its implementation scheme includes: the establishment of sparse observation model under echo defect condition;According to sparse observation model, construct target function based on L1 norm optimization;Iterative solution target function, construct translation compensation and ISAR imaging integration network based on super network;Scattering point is used to generate training set and train integration network;Real-time data is input into trained integration network, and the final ISAR image is obtained by network forward propagation.The application significantly improves the precision of translation compensation and the quality of ISAR imaging and the robustness of network to echo signal-to-noise ratio, reduces time and spatial complexity, and can be used for ship-borne, airborne ISAR system to extract target important information.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of radar remote sensing, and further provides an ISAR translation compensation and imaging integrated method, which can be used for ship-borne and airborne ISAR systems to extract important information of target shape, structure and attitude. BACKGROUND

[0002] Inverse synthetic aperture radar (ISAR) can obtain high-resolution two-dimensional images of non-cooperative targets at all times and in all weather, and thus plays an important role in space and air target monitoring. However, radar cannot continuously observe targets due to its working mode, resulting in missing of azimuth echoes. Meanwhile, the electromagnetic environment is becoming increasingly complex, and the signal-to-noise ratio of target echoes is very low. Since existing methods solve the translation compensation and imaging problems step by step, the translation compensation performance sharply decreases under the above-mentioned low signal-to-noise ratio and echo missing conditions, resulting in defocusing of the image or even failure to image. At the same time, the initialization parameters of the existing translation compensation and imaging method are sensitive to the signal-to-noise ratio of echoes, and usually need to be manually optimized for multiple times, thereby greatly limiting its practicability. Therefore, it is urgent to study an ISAR motion compensation and imaging integrated processing method under complex observation conditions such as low signal-to-noise ratio and echo missing.

[0003] The patent document with the application number CN202110263357.9 discloses a "range alignment method and system for inverse synthetic aperture radar imaging". The technology is completed in four parts. Firstly, the ISAR original data after pulse compression is saved, and the frequency domain data of each pulse is obtained by performing Fourier transform on each pulse echo pulse compression. Then, the recursive parameters are obtained by recursive algorithm for each pulse frequency domain data, and the information outside the radar transmitting signal bandwidth is recursively obtained. Then, the pulse frequency domain data after recursion is imaged by inverse Fourier transform to obtain a super-resolution image. Finally, the super-resolution image is processed by a global minimum entropy algorithm to obtain the range alignment error of each pulse compression image. This method takes the minimum average range image Shannon entropy as the target, estimates the offset of the range image envelope, and the algorithm iteration times are more, resulting in longer algorithm operation time.

[0004] The patent document with the application number CN2020975711.6 discloses a "SR-ISAR imaging and self-focusing method based on CV-ADMMN", which firstly models the sparse aperture ISAR echo signal, then constructs a CV-ADMMN forward propagation model including a reconstruction layer, a noise reduction layer and a multiplier update layer, and embeds a self-focusing module into the forward propagation model, and finally uses CV-ADMMN to solve the L1 norm optimization problem to obtain the final imaging result. However, this method regards different echo signal-to-noise ratio scenes as different tasks, and needs to train different imaging networks according to different signal-to-noise ratios during training, so it lacks echo signal-to-noise ratio robustness, greatly increasing the time and space complexity. SUMMARY

[0005] The present application aims to overcome the shortcomings of the prior art and provides a sparse ISAR translation compensation and imaging integrated method based on a hypernetwork, which improves the accuracy of translation compensation and the quality of ISAR imaging under low signal-to-noise ratio conditions, improves the robustness of the network to echo signal-to-noise ratio, and reduces the time and space complexity.

[0006] The technical solution of the present application is to expand the iterative method of integrating translation compensation and ISAR imaging into a deep network with a limited number of layers, and introduce a hypernetwork that can extract echo noise features to generate deep network parameters for different signal-to-noise ratio echoes. The implementation steps include the following:

[0007] (1) According to the translation matrix F(θ) and the sparse observation matrix Φ a that generates translation errors for echoes, and by performing distance Fourier transform D r and azimuth Fourier transform D a on the ISAR image, a sparse observation model S under echo loss is established:

[0008] S=F(θ)☉(D r XD a Φ a )+Z

[0009] Where θ represents the translation parameter, X represents the ISAR image to be solved, Z represents the noise, and ⊙ represents Hadamard product.

[0010] (2) According to the sparse observation model S under echo loss, construct a sparse ISAR translation compensation and imaging optimization objective function J1(X, θ) based on L1 norm optimization:

[0011]

[0012] Where E(θ)=(F(θ)) * , (·) * represents the conjugate operation, and ||·||F Let ||·||1 represent the F-norm and 1-norm of the matrix, respectively, and λ be the weight coefficients;

[0013] (3) Solve the optimization objective function J1(X,θ) iteratively according to the TMC-EADMM algorithm to obtain the iterative formula at the current iteration number t, that is, update the ISAR image X. (t) And estimate the translational parameter θ (t) :

[0014]

[0015] Among them, S (t) It means after E(θ) (t) The t-th echo after compensation, S( t) =E(θ) (t) )⊙S (t-1) X (t) Let θ represent the ISAR image reconstructed in the t-th iteration. (t) Let D represent the translational parameter estimated in the t-th iteration. r and D a Φ represents the distance dictionary and the location dictionary, respectively. a Represents a sparse observation matrix;

[0016] (4) According to the iterative formula X (t) and θ (t) Constructing a sparse ISAR translational compensation and imaging integrated network based on a supernetwork:

[0017] 4a) Extract T iterations from the iterative algorithm, and extract the iterative formula X(t-th iteration) from iterative formula X(t-th iteration). t ) and θ( t This corresponds to the image reconstruction module and the translation compensation module;

[0018] 4b) The image reconstruction module and the translation compensation module are connected sequentially to obtain the t-th layer subnetwork. Then, multiple subnetworks are cascaded to obtain a backbone network containing T layers of subnetworks.

[0019] 4c) Design a supernetwork based on residual networks, extract features of ISAR images with different signal-to-noise ratios through the supernetwork, and generate optimal parameters such as regularization coefficient λ, penalty factor ρ and relaxation factor γ for each layer of the backbone network based on these features.

[0020] 4d) Combine the backbone network and the corresponding supernetworks of each layer to form an integrated translational compensation and ISAR imaging network;

[0021] (5) Randomly generate N b Given a scattering point X whose amplitude follows a normal distribution and whose phase follows a uniform distribution, different ISAR scenes are obtained by setting different signal-to-noise ratios, and then N is generated. bEcho data in different scenarios As a training set

[0022] (6) The training set is input into the translation compensation and ISAR imaging integrated network, and the gradient descent method is used for training, so that the trained translation compensation and ISAR imaging integrated network is obtained;

[0023] (7) The measured Yak-42 data is input into the trained translation compensation and imaging integrated network, and the final ISAR imaging result is obtained through network forward propagation.

[0024] Compared with the prior art, the present application has the following advantages:

[0025] Firstly, the present application constructs a sparse ISAR translation compensation and imaging optimization objective function based on L1 norm optimization, and proposes a sparse ISAR joint translation compensation and imaging method TMC-EADMM, so as to improve the translation compensation precision and ISAR imaging quality, and realize high-quality focused imaging better than the existing algorithm.

[0026] Secondly, the present application constructs a sparse ISAR translation compensation and high-resolution imaging integrated network based on a super network, extracts ISAR image features of different signal-to-noise ratios through the super network, dynamically generates optimal internal parameters of the backbone network, and improves the operation efficiency and robustness to different signal-to-noise ratios.

[0027] Thirdly, the present application designs a sparse ISAR translation compensation and imaging integrated loss function, realizes effective training of the network, and effectively improves the translation compensation precision and imaging quality under low signal-to-noise ratio and echo loss. BRIEF DESCRIPTION OF DRAWINGS

[0028] Figure 1 The flowchart of the present application is shown in the figure;

[0029] Figure 2 The sparse ISAR translation compensation and imaging integrated network structure based on the super network in the present application is shown in the figure;

[0030] Figure 3 The backbone network structure constructed in the present application is shown in the figure;

[0031] Figure 4 The super network structure constructed in the present application is shown in the figure;

[0032] Figure 5 The envelope alignment comparison results obtained by respectively using the present application and the existing minimum entropy envelope alignment and unfolding network self-focusing imaging method under 50% loss conditions, and testing the echo signal-to-noise ratio at 5dB and 10dB are shown in the figure.

[0033] Figure 6 The imaging contrast results obtained by the present application and the existing minimum entropy envelope alignment and unfolding network self-focusing imaging method under 50% missing condition, respectively, are tested under echo signal-to-noise ratio of 5dB and 10dB. DETAILED DESCRIPTION

[0034] The embodiments and effects of the present application will be further described in detail below with reference to the drawings, and the embodiments are only used to illustrate the implementation of the present application and do not constitute any limitation on the present application. Obviously, for those skilled in the art, after understanding the content and principles of the present application, various modifications and changes in form and details can be made without departing from the principles and structures of the present application, and these modifications and changes based on the idea of the present application are still within the protection scope of the present application.

[0035] REFERENCE Figure 1 The implementation steps of the present embodiment include the following:

[0036] Step one, establish a sparse observation model under echo missing condition.

[0037] 1.1) Assume that the radar transmits a linear frequency modulation pulse signal, the target is represented by H scattering points, and the dechirped echo signal s received by the radar is obtained r (f r ,m):

[0038]

[0039] Where σ h is the backscattering coefficient of the hth scattering point, rect(·) is a rectangular window function, is the distance frequency, R h (t m ) is the distance from the hth scattering point to the radar in the mth echo, m = 1, 2,..., M, M represents the total number of pulses, B is the bandwidth of the transmitted signal, f c is the center frequency, r m = r R (t m )-R ref (t m ) is the target translation component, R ref (t m ) is the reference distance varying with slow time, (x h , y h ) is the starting coordinate of the scattering point h, is the random phase error of the change between echoes caused by system error, is Gaussian white noise;

[0040] 1.2) According to the echo signal s r (fr m) Constructing the translational matrix F(θ):

[0041]

[0042] where, is the translational matrix the element in the nth row, the lth column, θ = {r1,..., r L , φ1,..., φ L} represents the translational parameters, l = 1,..., L, L represents the echo number, 0 < L < M, f n = nB / N, n = 1,..., N, N represents the number of sampling points, r l represents the envelope offset of the lth column echo, represents the total phase error between the lth column echoes;

[0043] 1.3) Let the ISAR image size be U x V, and the image element be i h (u, v), u ∈ [1, U], v ∈ [1, V];

[0044] 1.4) Perform Fourier transform on the ISAR image in the range direction and the azimuth direction, and add the translational error F n,l (θ) to obtain the echo signal s r (n, l) containing the translational error:

[0045]

[0046] where d is the azimuth direction missing vector, which represents the vector of length L obtained by randomly down-sampling the original vector of length Q in the case of sparse observation, d l is the lth element in d;

[0047] 1.5) Take s r (n, l) as the element in the nth row, the lth column of the matrix to construct the sparse observation model S containing the translational error under the echo missing condition:

[0048] S = F(θ) ⊙ (D r XD a Φ a ) + Z

[0049] where, is the range dictionary, and the element in the nth row, the uth column is

[0050] is the Doppler dictionary, and the element in the vth row, the mth column is

[0051] denotes the position observation matrix, which is obtained by removing I M×M specific M-L columns from M×M denotes the identity matrix, and denotes the Hadamard product.

[0052] denotes the ideal two-dimensional image corresponding to the target, is noise.

[0053] In this embodiment, the size of the ISAR image is set to P = 128 and Q = 256, but is not limited thereto.

[0054] Step two, according to the sparse observation model S under echo loss, a sparse ISAR translation compensation and imaging optimization objective function based on L1 norm optimization is constructed.

[0055] 2.1) The conjugate of the translation matrix F(θ) is taken to obtain the phase compensation matrix E(θ) = (F(θ)) * The real echo data S is phase compensated through the matrix E(θ) ⊙ S.

[0056] 2.2) The imaging result X is subjected to distance and azimuth Fourier transform to obtain the echo result, i.e., D r X D a Φ a ;

[0057] 2.3) The difference between steps 2.1) and 2.2) is taken, and the square of the F norm of the difference value is taken to obtain the optimization objective function J0(X, θ):

[0058]

[0059] where ||·||F denotes the matrix F norm. F

[0060] 2.4) A sparse constraint term ||X||1 is added to the optimization objective function J0(X, θ) to obtain the sparse ISAR translation compensation and imaging optimization objective function J1(X, θ):

[0061]

[0062] where ||·||1 denotes the l1 norm, and λ is a regularization coefficient.

[0063] Step three, the optimization objective function J1(X, θ) is iteratively solved according to the TMC-EADMM algorithm to obtain the iteration formula at the current iteration time t, i.e., the ISAR image X (t) and the estimated translation parameter θ (t) are updated.

[0064] ​3.1) Fix the phase compensation term E(θ) in J1(X,θ) to obtain the updated ISAR image X. (t) The expression:

[0065]

[0066] in, For distance dictionary, For Doppler dictionaries, This represents the azimuth observation matrix, and ⊙ represents the Hadamard product. The ideal two-dimensional image corresponding to the target, θ( t-1 S represents the translational parameter estimated in the (t-1)th time. (t-1) It means after E(θ) (t-1) The t-th echo after compensation, where λ is the regularization coefficient;

[0067] 3.2) Use the EADMM algorithm on X (t) Perform iterative solution:

[0068] 3.2.1) Based on the input echo signal S (t-1) Slack variables in the (b-1)th iteration and Update ISAR image

[0069]

[0070] in,(·) H Indicates conjugate transpose;

[0071] 3.2.2) Based on the parameters of the (b-1)th iteration and the ISAR image of the b-th iteration Update Lagrange multipliers

[0072]

[0073] 3.2.3) Based on the Lagrange multipliers of the b-th iteration ISAR images of [and] Update auxiliary variables

[0074]

[0075] Among them, S λ / ρ (·) represents a soft thresholding function with parameter λ / ρ;

[0076] 3.2.4) Regarding parameters and Perform relaxation calculations to obtain slack variables. and

[0077]

[0078] where ρ is the initialization parameter iteration step size, and γ is the relaxation factor;

[0079] 3.3) The ISAR image X (t) is obtained in the tth iteration (t) The expression of the estimation of the translational parameters θ

[0080]

[0081] where θ (t) ={r1,…,r L ,φ1,…,φ L}, E(θ) = (F(θ)) * , F(θ) is the translational matrix, (·) * represents the conjugate operation;

[0082] 3.4) The term (t) in θ is expanded, and the terms irrelevant to θ (t) in the expression of θ (t) are removed, to obtain the following simplified expression of θ

[0083]

[0084] where Re{·} represents the real part operation, E n,l (θ) is the phase compensation matrix , f n =nB / N, n = 1,…,N, N represents the number of sampling points, r l is the target translational component of the lth echo, φ l represents the total phase error between the lth column of echoes, l = 1,…,L, L represents the number of echoes;

[0085] 3.5) The solution of θ (t) is obtained:

[0086] 3.5.1) Discretize the scene into I parts with a interval of ρ r / N S , where ρ r represents the distance resolution, and N S represents the number of discrete parts, so that r l ≈r l (i), r l (i) = iρ r / NS , i = -I / 2,..., I / 2-1, by exhaustive search

[0087]

[0088] 3.5.2) According to the translational component estimation value get the estimate of the total phase error between echoes

[0089]

[0090] where phase(·) represents the phase extraction operation;

[0091] 3.5.3) According to and get the translational parameter estimation value

[0092] 3.6) According to the obtained translational parameter estimation value θ (t) construct E(θ) and compensate the echo to get the t-th echo signal S (t) :

[0093] S (t) = E(θ (t) )⊙S (t-1) ;

[0094] 3.7) According to steps 3.2), 3.5) and 3.6), get the iteration step at the current iteration time t of the TMC-EADMM iterative algorithm:

[0095] 3.7.1) Repeat the iteration formula in steps 3.2.1)-3.2.4) and until its iteration number b = B stops iteration, and gets the current updated ISAR image X( t ):

[0096]

[0097] 3.7.2) According to the expressions of and in steps 3.5.1)-3.5.2), get the estimated translational parameter

[0098] 3.8) According to the above steps 3.1)-3.7), get the iteration formula at the current iteration time t:

[0099] 3.8.1) Update the ISAR image X( t ):

[0100] for b=1:B

[0101]

[0102] After the loop, the final output result as the updated ISAR image X (t) , i.e.

[0103] 3.8.2) Estimate the translational parameter θ (t) :

[0104]

[0105] s (t) = E(θ (t) ) ⊙ s (t-1) .

[0106] Step four, construct a sparse ISAR translational compensation and high-resolution imaging integrated network based on super network.

[0107] With reference Figure 2 , the implementation of this step includes the following:

[0108] 4.1) intercept T times of iterations in the TMC-EADMM iterative algorithm, and the iteration formula contained in the tthiteration is (t) and θ (t) correspond to the image reconstruction module and the translational compensation module, respectively;

[0109] The image reconstruction module comprises G stages, and each stage is composed of an image reconstruction unit, a denoising unit, a multiplier updating unit and a relaxation unit in cascade, wherein:

[0110] The image reconstruction unit is configured to update the ISAR image (t-1) according to the echo signal S , the relaxation variable of the g-1thstage, and

[0111]

[0112] wherein, is a distance dictionary, is a Doppler dictionary, denotes an azimuth observation matrix, and ρ is an iterative step size;

[0113] The multiplier updating unit is configured to update the Lagrange multiplier according to the parameters of the g-1thstage and the ISAR image of the g-1thstage

[0114]

[0115] the de-noising unit is configured to calculate a Lagrange multiplier of a gth level according to a gth level ISAR image and a gth level ISAR image update an auxiliary variable

[0116]

[0117] wherein λ is a regularization coefficient, S λ / ρ (·) represents a soft threshold function with a parameter λ / ρ;

[0118] the relaxation unit is configured to perform relaxation calculation according to parameters and to obtain relaxation variables and

[0119]

[0120] wherein γ is a relaxation factor;

[0121] The translational compensation module is composed of a translational parameter estimation unit and a translational phase compensation unit in cascade, wherein:

[0122] The translational parameter estimation unit is configured to obtain a current updated estimated translational parameter θ according to a translational component estimation value and a phase error estimation value wherein:

[0123]

[0124] In the formula, N is the number of sampling points;

[0125] The translational phase compensation unit is configured to construct a phase compensation matrix E(θ (t) ) according to the obtained translational parameter estimation value θ (t) , and compensate the echo S (t) :

[0126] S (t) =E(θ (t) )⊙S (t-1)

[0127] wherein ⊙ represents Hadamard product.

[0128] 4.2) sequentially connecting the image reconstruction module and the translational compensation module to obtain a t-th layer subnetwork, and then cascading a plurality of subnetworks to obtain a backbone network containing T layers of subnetworks, as shown in Figure 3

[0129] 4.3) designing a hypernetwork module based on a residual network:

[0130] With reference to Figure 4 , the implementation of this step includes the following:

[0131] 4.3.1) constructing a range-doppler imaging unit, using the RD algorithm to image the echo S (t-1) output by the t-th layer backbone network, and taking the modulus of the imaging result to obtain an input image of the hypernetwork feature extraction unit

[0132]

[0133] wherein, is a range dictionary, is a Doppler dictionary, denotes an azimuth observation matrix, and |·| denotes a modulus operation;

[0134] 4.3.2) constructing a feature extraction unit:

[0135] First, seven convolution modules a1, a2, a3, a4, a5, b1, b2, two residual modules r1, r2, and two rectified linear unit ReLU activation layers are set:

[0136] The first convolution module a1 is composed of a 3x3 standard convolution layer with an input dimension of 1 and an output dimension of 32, a batch normalization layer, a ReLU activation layer, and a maximum pooling layer maxpool;

[0137] The second convolution module a2 is composed of a 3x3 standard convolution layer with an input dimension of 32 and an output dimension of 32;

[0138] The third convolution module a3 is composed of a 3x3 standard convolution layer with an input dimension of 32 and an output dimension of 32;

[0139] The fourth convolution module a4 is composed of a 3x3 standard convolution layer with an input dimension of 32 and an output dimension of 64;

[0140] The fifth convolution module a5 is composed of a 3x3 standard convolution layer with an input dimension of 64 and an output dimension of 64;

[0141] The sixth convolution module b1 is composed of a 1x1 standard convolution layer with an input dimension of 32 and an output dimension of 32;

[0142] ​The seventh convolutional module b2 is composed of a 1x1 standard convolutional layer with an input dimension of 32 and an output dimension of 64;

[0143] The first residual module r1 is composed of the second convolutional module a2, a batch normalization layer, a ReLU activation layer, and the third convolutional module a3 in cascade;

[0144] The second residual module r2 is composed of the fourth convolutional module a4, a batch normalization layer, a ReLU activation layer, and the fifth convolutional module a5 in cascade;

[0145] Then, the first residual module r1 is connected in parallel with the sixth convolutional module b1 to obtain a first parallel multi-scale convolutional module, and the second residual module r2 is connected in parallel with the seventh convolutional module b2 to obtain a second parallel multi-scale convolutional module; the first convolutional module a1, the first parallel multi-scale convolutional module, the first rectified linear unit (ReLU) activation layer, the second parallel multi-scale convolutional module, and the second ReLU activation layer are sequentially connected in cascade to form a feature extraction unit;

[0146] The feature extraction unit is used to extract the features of the input image, and the output feature information is represented as:

[0147]

[0148] where O i is the output of the i-th convolutional module a i , and relu(·) represents the ReLU activation function;

[0149] 4.3.3) An optimal parameter extraction unit composed of an average pooling layer avgpool, a fully connected layer W containing 64 nodes, and a sigmoid activation function in cascade is constructed, the input of which is the feature O5 output by the feature extraction unit, and the output is a parameter vector with a length of 3G, which is the internal parameter of the t-th layer subnetwork in the backbone network

[0150]

[0151] where the parameter vector includes the regularization coefficient λ, the penalty factor ρ, and the relaxation factor γ in all stages of the image reconstruction module in the t-th backbone network, i.e. G represents the number of each stage of the image reconstruction module, avgpool(·) represents the average pooling function, and sigmoid(·) represents the sigmoid activation function;

[0152] 4.3.4) The range-Doppler imaging unit, the feature extraction unit, and the optimal parameter extraction unit are sequentially connected in cascade to obtain a super network module;

[0153] 4.4) Combine the backbone network and the corresponding hypernetwork of each layer to obtain the t-th layer sub-combination network:

[0154] 4.4.1) Obtain the optimal parameters of the t-th layer backbone network by passing the output of the (t-1)-th layer backbone network through the t-th layer hypernetwork;

[0155] 4.4.2) Take the optimal parameters and the output of the (t-1)-th layer backbone network as the input of the t-th layer backbone network, and finally obtain the output S of the t-th layer backbone network (t) ;

[0156] 4.5) Cascade multiple sub-combination networks to obtain a hypernetwork-based sparse ISAR translation compensation and imaging integrated network.

[0157] Step five, generate a training set.

[0158] 5.1) Take the scattering points with random distribution of positions, normal distribution of amplitudes, and uniform distribution of phases [0, 2π] as image data X;

[0159] 5.2) Substitute the image X into the sparse observation model S = F(θ) ⊙ (D r XD a Φ a ) + Z to obtain echo data with missing and noise and containing translation errors, which is taken as network input data S, wherein the translation errors include echo envelope offset errors and echo random phase errors, the echo envelope offset errors are uniformly distributed in [-20m, 20m], and the echo random phase errors are Gaussian distributed with parameters (0, π / 2);

[0160] 5.3) Construct echo data b with N samples as a training set;

[0161] In this embodiment, the training set image size is set to but not limited to 128 × 256, the echo missing rate is set to 50%, the echo signal-to-noise ratio range is set to but not limited to 5-15 dB, and the training set sample number N b is set to but not limited to 100.

[0162] Step six, train the sparse ISAR translation compensation and high-resolution imaging integrated network.

[0163] 6.1) Define the loss function of the integrated network:

[0164] loss = loss true + βloss constraint

[0165] , wherein β is a loss weight coefficient, losstrue is the loss function for accumulated fidelity term, constraint is the sparsity constraint term, which is expressed as follows:

[0166]

[0167] where T represents the total number of network layers, is the reconstructed ISAR image of the t-th layer of the network, S( t ) is the echo of the t-th layer of the network, is the range dictionary, is the Doppler dictionary, represents the azimuth observation matrix;

[0168] 6.2) Let batch be the size of a single batch, lr be the learning rate during the training of the integrated network, and Θ0 be the network parameters in the training phase of the integrated network: where, represents the parameters of the convolution module with a kernel size of 3x3 in the super network, n c represents the serial number of the convolution module, represents the parameters of the convolution module with a kernel size of 1x1 in the super network, n d represents the serial number of the convolution module, and W represents the parameters of the fully connected layer in the super network;

[0169] 6.3) Each time, select batch size of data from the training set, input into the integrated network to calculate the loss value in each batch

[0170]

[0171] where N batch is the number of samples in each batch, and S represents the input echo data;

[0172] 6.4) Apply the back propagation algorithm to calculate the gradient of the loss function with respect to any parameter in the integrated network According to the solved gradient update the network parameters of the integrated network to obtain the network parameters Θ' of the current training phase:

[0173]

[0174] 6.5) Repeat steps 6.3)-6.4) until the loss function converges, and obtain the trained translation compensation and ISAR imaging integrated network.

[0175] In this embodiment, the size of a single batch batch is set to 8 during the training process, the learning rate lr = 0.005, and the Adam optimizer is used to update the network parameters.

[0176] Step seven, obtaining the ISAR target imaging result.

[0177] The measured space target echo data is input into the trained integrated network, and for different network layers t, the following operations are performed:

[0178] When the network layer t=1, the space target echo data is first input into the first layer super network to obtain the optimal parameters of the first layer backbone network; then the optimal parameters and the initial echo are taken as the input of the first layer backbone network to obtain the output echo S (1) of the first layer backbone network.

[0179] When the network layer 1 (t) .

[0180] When the network layer t=T, the output of the T-1 layer backbone network is first passed through the T layer super network to obtain the optimal parameters of the T layer backbone network; then the optimal parameters and the output of the T-1 layer backbone network are taken as the input of the T layer backbone network to obtain the final output echo S T and the imaging result X T , and the envelope alignment result T is obtained according to the output echo S

[0181] In this embodiment, the echo data of the measured Yak-42 aircraft is used for testing.

[0182] The effects of the present application can be further illustrated by the following simulation experiment:

[0183] I. Simulation experiment conditions

[0184] The software platform of the simulation experiment of the present application is Windows 10 operating system and Pytorch 3.9, and the hardware configuration is Core i9-13900K CPU and NVIDIA GeForce RTX 4090 GPU.

[0185] The simulation experiment of the present application uses point simulation data with random position distribution, amplitude obeying normal distribution and phase obeying [0, 2π] uniform distribution, and the number of images is 100.

[0186] The comparison method of the simulation experiment is to combine the minimum entropy-based envelope alignment method MERA and the sparse ISAR self-focusing imaging method AF-ADN based on CV-ADMMN to obtain the MERA+AF-ADN method, so as to perform translational compensation and imaging on the echo containing translational error.

[0187] II. Simulation content and result analysis

[0188] Simulation 1. Under the above simulation conditions, the measured ISAR echo data containing translational components are compensated for translation by using the present application and the existing MERA+AF-ADN method under the conditions of a loss rate of 50% and a signal-to-noise ratio of 5 dB and 10 dB, respectively, to obtain the corresponding envelope alignment results, as shown in Figure 5 , wherein:

[0189] Figure 5 (a) is the envelope alignment result obtained by the prior art on the measured Yak-42 aircraft data under the conditions of an echo loss rate of 50% and an echo signal-to-noise ratio of 10 dB.

[0190] Figure 5 (b) is the envelope alignment result obtained by the prior art on the measured Yak-42 aircraft data under the conditions of an echo loss rate of 50% and an echo signal-to-noise ratio of 5 dB.

[0191] Figure 5 (c) is the envelope alignment result obtained by the present application on the measured Yak-42 aircraft data under the conditions of an echo loss rate of 50% and an echo signal-to-noise ratio of 10 dB.

[0192] Figure 5 (d) is the envelope alignment result obtained by the present application on the measured Yak-42 aircraft data under the conditions of an echo loss rate of 50% and an echo signal-to-noise ratio of 5 dB.

[0193] It can be seen from Figure 5 that the envelope alignment result obtained by the comparison method will appear envelope jump, which will affect the subsequent imaging result, while the present application realizes envelope alignment under different echo signal-to-noise ratio scenarios compared with the prior art, and does not appear jump.

[0194] Simulation 2. Under the above simulation conditions, the measured ISAR echo data containing translational components are imaged by using the present application and the existing MERA+AF-ADN method under the conditions of a loss rate of 50% and a signal-to-noise ratio of 5 dB and 10 dB, respectively, to obtain the corresponding ISAR imaging results, as shown in Figure 6 , wherein:

[0195] Figure 6(a) is the imaging result of prior art on measured Yak-42 aircraft data under the condition of echo missing rate of 50% and echo signal-to-noise ratio of 10dB.

[0196] Figure 6 (b) is the imaging result of prior art on measured Yak-42 aircraft data under the condition of echo missing rate of 50% and echo signal-to-noise ratio of 5dB.

[0197] Figure 6 (c) is the imaging result of the application on measured Yak-42 aircraft data under the condition of echo missing rate of 50% and echo signal-to-noise ratio of 10dB.

[0198] Figure 6 (d) is the imaging result of the application on measured Yak-42 aircraft data under the condition of echo missing rate of 50% and echo signal-to-noise ratio of 5dB.

[0199] It can be seen that the ISAR image obtained by the comparison method is severely azimuth defocused, while the application obtains an ISAR image with good focusing effect under different echo signal-to-noise ratios, and the target contour is complete and the background is clean. Figure 6

[0200] The imaging results in (a) and (b) are calculated respectively to obtain three imaging evaluation indexes of reconstruction mean square error, image entropy and running time, and the results are shown in Table 1, Figure 6

[0201] Table 1 Algorithm performance index of measured data

[0202]

[0203] The reconstruction mean square error and the image entropy in Table 1 are defined as follows:

[0204] The reconstruction mean square error is a method for measuring the reconstruction effect of the translational compensation ISAR image, and the smaller the value is, the better the image quality is, and is defined as:

[0205]

[0206] Wherein, N represents the number of samples, |·| represents the modulus operation, is the imaging result of the network, X n is the label image, M is the number of complete echoes, and L is the number of echoes after missing.

[0207] The image entropy is a method for measuring the average information amount of the image, and the smaller the value is, the better the image quality is, and is defined as:

[0208]

[0209] Wherein,​​ networked imaging results the element in the u-th row and the v-th column of the matrix, representing the total energy of the image.

[0210] As can be seen from Table 1, in the case of completing training, the translational compensation and imaging integrated network of the present application has smaller reconstruction mean square error and image entropy under different echo signal-to-noise ratios, and shorter running time, indicating that the imaging quality of the present application is better.

[0211] In summary, the envelope alignment and imaging results and imaging evaluation indexes of the present application under different echo signal-to-noise ratios are all better than those of the prior art, verifying that the present application can improve the precision of translational compensation and the quality of ISAR imaging of the network under low signal-to-noise ratio conditions, and at the same time, improve the robustness to echo signal-to-noise ratio, and reduce the time and space complexity.

[0212] It should be noted that the serial numbers of the above steps are for more clearly describing the implementation schemes of the present application, and the serial number order is not limited.

Claims

1. A method for integrated translational compensation and imaging of sparse ISAR based on hypernetworks, characterized in that, Includes the following steps: (1) Based on the translation matrix F(θ) that produces the translation error of the echo and the sparse observation matrix Φ a By performing range-to-Fourier transform on the ISAR image D r and orientation to Fourier transform D a Establish a sparse observation model S under echo loss: S<F(θ)⊙(D r XD a Φ a )+Z Where θ represents the translational parameter, X represents the ISAR image to be solved, Z represents noise, and ⊙ represents the Hadmar product; (2) Based on the sparse observation model S under the condition of echo loss, construct the objective function J1(X,θ) for sparse ISAR translational compensation and imaging optimization based on L1 norm optimization: Where E(θ)=(F(θ)) * ,(·) * Denotes the conjugate operation, ||·|| F Let ||·||1 represent the F-norm and 1-norm of the matrix, respectively, and λ be the weight coefficients; (3) Solve the optimization objective function J1(X,θ) iteratively according to the TMC-EADMM algorithm to obtain the iterative formula at the current iteration number t, that is, update the ISAR image X. (t) And estimate the translational parameter θ (t) : Among them, S (t) It means after E(θ) (t) The t-th echo after compensation, S (t) =E(θ) (t) )⊙S (t-1) X (t) Let θ represent the ISAR image reconstructed in the t-th iteration. (t) Let D represent the translational parameter estimated in the t-th iteration. r and D a Φ represents the distance dictionary and the location dictionary, respectively. a Represents a sparse observation matrix; (4) According to the iterative formula X (t) and θ (t) Constructing a sparse ISAR translational compensation and imaging integrated network based on a supernetwork: 4a) Extract T iterations from the iterative algorithm, and extract the iterative formula X contained in the t-th iteration. (t) and θ (t) This corresponds to the image reconstruction module and the translation compensation module; 4b) The image reconstruction module and the translation compensation module are connected sequentially to obtain the t-th layer subnetwork. Then, multiple subnetworks are cascaded to obtain a backbone network containing T layers of subnetworks. 4c) Design a supernetwork based on residual networks, extract features of ISAR images with different signal-to-noise ratios through the supernetwork, and generate optimal parameters such as regularization coefficient λ, penalty factor ρ and relaxation factor γ for each layer of the backbone network based on these features. 4d) Combine the backbone network and the corresponding supernetworks of each layer to form an integrated translational compensation and ISAR imaging network; (5) Randomly generate N b Given a scattering point X whose amplitude follows a normal distribution and whose phase follows a uniform distribution, different ISAR scenes are obtained by setting different signal-to-noise ratios, and then N is generated. b Echo data from different scenarios Use it as the training set; (6) Input the training set into the integrated translational compensation and ISAR imaging network, and train it using the gradient descent method to obtain the trained integrated translational compensation and ISAR imaging network. (7) Input the measured Yak-42 data into the trained translational compensation and imaging integrated network, and obtain the final ISAR imaging results through network forward propagation.

2. The method according to claim 1, characterized in that, In step (1), a sparse observation model S is established under the condition of echo loss, as follows: 1a) Assuming the radar transmits a linear frequency modulated pulse signal, and the target is represented by H scattering points, the radar receives the demodulated echo signal s. r (f r ,m): Where, σ h Let be the backscattering coefficient at the h-th scattering point, and rect(·) be a rectangular window function. R is the distance frequency. h (t m ) represents the distance from the h-th scattering point in the m-th echo to the radar, where m = 1, 2, ..., M, M represents the total number of pulses, B is the transmit signal bandwidth, and f c For the center frequency, r m =r R (t m )-R ref (t m R represents the target translational component. ref (t m (x) represents the reference distance that varies with slow time. h ,y h () represents the initial coordinates of the scattering point h. Let ε(f) be the random phase error caused by the variation between echoes due to systematic errors. r (m) represents Gaussian white noise; 1b) Based on the echo signal s received by the radar r (f r Construct the translation matrix F(θ) for m): in, It is a translation matrix The element in the nth row and lth column, θ = {r1, ..., r L ,φ1,…,φ L } represents the translational parameters, l = 1,...,L, where L represents the echo number, 0 <L<M,f n = nB / N, n = 1, ..., N, where N represents the number of sampling points, r l This represents the envelope offset of the l-th echo. This represents the total phase error between the echoes of the l-th column; 1c) Let the ISAR image size be U×V, and the elements in the image be i. h (u,v), u∈[1,U], v∈[1,V]; 1d) Perform range and azimuth Fourier transforms on the ISAR image and add translational error F. n,l (θ), to obtain the echo signal s containing translational error. r (n,l): Where d is the azimuth loss vector, representing a vector of length L obtained by randomly downsampling the original vector of length Q under sparse observation conditions. l Let be the l-th element in d; 1e) will s r (n,l) is a matrix The elements in the nth row and lth column are used to construct a sparse observation model S with translational errors under the condition of echo loss: S<F(θ)⊙(D r XD a Φ a )+Z in, Let be a distance dictionary, and let the element in the nth row and uth column be... For a Doppler dictionary, the element in row v and column m is... This represents the azimuth observation matrix, which is obtained by removing I. M×M Obtained from a specific ML column, I M×M The symbol represents the identity matrix, and ⊙ represents the Hadamard product. This represents the ideal two-dimensional image corresponding to the target. It is noise.

3. The method according to claim 2, characterized in that, In step (3), the objective function J1(X,θ) is iteratively solved using the TMC-EADMM algorithm, as follows: 3a) Fix the phase compensation term E(θ) in J1(X,θ) to obtain the ISAR image optimization objective function X. (t) : in, For distance dictionary, For Doppler dictionaries, This represents the azimuth observation matrix, and ⊙ represents the Hadamard product. θ represents the ideal two-dimensional image corresponding to the target. (t-1) S represents the translational parameter estimated in the (t-1)th time. (t-1) It means after E(θ) (t-1) The t-th echo after compensation, where λ is the regularization coefficient; 3b) Use the EADMM algorithm on X (t) Perform iterative solution: 3b1) Based on the input echo signal S (t-1) Slack variables in the (b-1)th iteration and Update ISAR image 3b2) Based on the parameters of the (b-1)th iteration and the ISAR image of the b-th iteration Update Lagrange multipliers 3b3) Based on the Lagrange multipliers of the b-th iteration and ISAR images Update auxiliary variables 3b4) For parameters and Perform relaxation calculations to obtain slack variables. and Where ρ is the initialization parameter iteration step size, γ is the relaxation factor, and S λ / ρ (·) represents a soft thresholding function with parameter λ / ρ; 3c) The ISAR image X obtained in the t-th iteration (t) By fixing the terms related to translational motion in J1(X,θ), we obtain the objective function θ for optimizing sparse ISAR translational parameters. (t) : Where, θ (t) ={r1,…,r L ,φ1,…,φ L }, E(θ)=(F(θ)) * F(θ) is the translation matrix, (·) * Indicates the conjugate operation; 3d) The objective function θ (t) In Expand the terms and remove θ. (t) The terms in the expression that are independent of θ are then obtained as θ. (t) The following simplified form: Where Re{·} denotes the real part extraction operation. f n = nB / N, n = 1, ..., N, where N represents the number of sampling points, r l Let φ be the target translational component of the l-th echo. l This represents the total phase error between the echoes of the l-th column, where l = 1, ..., L, and L represents the number of echoes. 3e) for θ (t) Solve the following: 3e1) with ρ r / N S The scene is discretized into I parts at intervals, where ρ r N represents the distance resolution. S Let r represent the number of discrete parts, such that r l ≈r l (i), r l (i)=iρ r / N S Let i = -I / 2, ..., I / 2-1. The estimated values ​​of the translational components are obtained by iterating through the search. 3e2) Based on the estimated values ​​of translational components The estimated value of the total phase error between echoes is obtained. Where phase(·) represents the phase extraction operation; 3e3) According to and Obtain the estimated translational parameters 3f) Based on the obtained translational parameter estimate θ (t) Construct E(θ) and compensate for the echo to obtain the t-th echo signal S. (t) : S (t) =E(θ (t) )⊙S (t-1) ; 3g) Based on 3b), 3e), and 3f), we obtain the iterative formula at time t for the current iteration number: 3g1) Repeat the iterative formula of the EADMM algorithm until the iteration number b = B, then stop the iteration to obtain the currently updated ISAR image: The ISAR image in the b-th iteration of the EADMM algorithm is: 3g2) According to and The expression yields the estimated translational parameters after the current update.

4. The method according to claim 3, characterized in that, The image reconstruction module and translation compensation module in step 4a) have the following structure: The image reconstruction module comprises G layers, each layer consisting of four cascaded units: an image reconstruction unit, a denoising unit, a multiplier update unit, and a relaxation unit. This image reconstruction unit is used to reconstruct the image based on the echo signal S. (t-1) slack variables of the (g-1)th level and Update ISAR image in, For distance dictionary, For Doppler dictionaries, This represents the azimuth observation matrix, where ρ is the iteration step size; This multiplier update unit is used to update the parameters of the (g-1)th level. and ISAR images of the g-1th layer Update Lagrange multipliers This denoising unit is used to denoise the Lagrange multipliers of the g-th order. and the ISAR image of the g-th layer Update auxiliary variables Where λ is the regularization coefficient, S λ / ρ (·) represents a soft thresholding function with parameter λ / ρ; This relaxation unit is used to adjust according to parameters. and Perform relaxation calculations to obtain slack variables. and Where γ is the relaxation factor; The translational compensation module consists of two cascaded units: a translational parameter estimation unit and a translational phase compensation unit. The translational parameter estimation unit is used to calculate the estimated values ​​of the translational components. and phase error estimate Obtain the estimated translational parameters after the current update. in: In the formula, f n = nB / N, where n = 1, ..., N, and N represents the number of sampling points; This translational phase compensation unit is used to calculate the estimated translational parameters θ. (t) Construct the phase compensation matrix E(θ) (t) ), and compensate for the echo S (t) : S (t) =E(θ (t) )⊙S (t-1) Here, ⊙ represents the Hadema product.

5. The method according to claim 1, characterized in that, In step 4c), a supernetwork based on the residual network is designed and implemented as follows: 4c1) Construct a range-Doppler imaging unit and use the RD algorithm to analyze the echo S output by the t-th layer network. (t-1) Imaging is performed, and the image is moduloed to obtain the input image for the hypernetwork feature extraction unit. in, For distance dictionary, For Doppler dictionaries, represents the azimuth observation matrix, and |·| represents the modulo operation; 4c2) Set up 7 convolutional modules a1, a2, a3, a4, a5, b1, b2, two residual modules r1, r2, and two ReLU activation layers: The first convolutional module a1 consists of a cascaded 3×3 standard convolutional layer with an input dimension of 1 and an output dimension of 32, a batch normalization layer, a ReLU activation layer, and a maxpooling layer. The second convolutional module a2 consists of a 3×3 standard convolutional layer with an input dimension of 32 and an output dimension of 32; The third convolutional module a3 consists of a 3×3 standard convolutional layer with an input dimension of 32 and an output dimension of 32; The fourth convolutional module a4 consists of a 3×3 standard convolutional layer with an input dimension of 32 and an output dimension of 64. The fifth convolutional module a5 consists of a 3×3 standard convolutional layer with an input dimension of 64 and an output dimension of 64. The sixth convolutional module b1 consists of a 1×1 standard convolutional layer with an input dimension of 32 and an output dimension of 32; The seventh convolutional module b2 consists of a 1×1 standard convolutional layer with an input dimension of 32 and an output dimension of 64; The first residual module r1 is composed of a second convolutional module a2, a batch normalization layer, a ReLU activation layer, and a third convolutional module a3 cascaded together. The second residual module r2 is composed of a fourth convolutional module a4, a batch normalization layer, a ReLU activation layer, and a fifth convolutional module a5 cascaded together. Next, the first residual module r1 is connected in parallel with the sixth convolutional module b1 to obtain the first parallel multi-scale convolutional module, and the second residual module r2 is connected in parallel with the seventh convolutional module b2 to obtain the second parallel multi-scale convolutional module. Then, the first convolutional module a1, the first parallel multi-scale convolutional module, the first rectified linear unit ReLU activation layer, the second parallel multi-scale convolutional module, and the second rectified linear unit activation layer are cascaded in sequence to form a feature extraction unit. This feature extraction unit is used to extract features from the input image, and its output feature information is represented as follows: Among them O i For the i-th convolutional module a i The output of , relu(·) represents the ReLU activation function.

6. The method according to claim 5, characterized in that, In step 4c), the optimal parameters such as the regularization coefficient λ, penalty factor ρ, and relaxation factor γ are generated for each layer of the backbone network based on the features extracted from ISAR images with different signal-to-noise ratios, as follows: An optimal parameter extraction unit is constructed, consisting of an average pooling layer (avgpool), a fully connected layer W with 64 nodes, and a cascaded sigmoid activation function. Its input is the feature O5 output by the feature extraction unit, and its output parameter vector of length 3G serves as the internal parameters of the t-th layer subnetwork in the backbone network. Where G represents the number of layers in each level of the image reconstruction module, and the parameter vector... This includes the regularization coefficient λ, penalty factor ρ, and relaxation factor γ in all layers of the image reconstruction module in the t-th backbone network, i.e. avgpool(·) represents the average pooling function, and sigmoid(·) represents the sigmoid activation function.

7. The method according to claim 1, characterized in that, In step 4d), the backbone network and the corresponding supernetworks of each layer are combined to achieve the following: First, the output of the (t-1)th layer backbone network is passed through the t-th layer supernetwork to obtain the optimal parameters of the t-th layer backbone network. Then, these optimal parameters and the output of the (t-1)th layer backbone network are used as the input of the t-th layer backbone network to finally obtain the output S of the t-th layer backbone network. (t) .

8. The method according to claim 1, characterized in that, Step (6) inputs the training set into the integrated translational compensation and ISAR imaging network, and trains it using gradient descent, as follows: 6a) Constructing an integrated loss function for sparse ISAR translational compensation and imaging: loss=loss true +βloss constraint Where β is the loss weight coefficient, loss true For cumulative fidelity, loss constraint The sparse constraint term is expressed as follows: In the formula, T represents the total number of network layers. S is the ISAR image reconstructed from the t-th layer of the network. (t) For the echo of the t-th layer of the network, For distance dictionary, For Doppler dictionaries, Represents the azimuth observation matrix; 6b) Each time, select data of batch size from the training set and input it into the integrated translational compensation and ISAR imaging network to calculate the loss value in each batch. Where, N batch The number of samples in each batch, S represents the input echo data; 6c) Calculate the gradient of the loss function with respect to any parameter in the sparse ISAR high-resolution imaging network using the backpropagation algorithm. Based on the gradient obtained from the solution Update the network parameters of the integrated translational compensation and ISAR imaging network to obtain the network parameters Θ′ for the current training phase: Where Θ0 represents the network parameters during the training phase of the sparse ISAR high-resolution imaging network, and lr represents the learning rate during training. 6d) Repeat steps 6b)-6c) until the loss function converges, and obtain the final trained network parameters, thus obtaining the trained integrated translational compensation and ISAR imaging network.

9. The method according to claim 1, characterized in that, In step (7), the measured Yak-42 data is input into the trained translational compensation and imaging integrated network for forward propagation, as follows: When the network layer number t=1, the initial echo is first input into the first layer supernetwork to obtain the optimal parameters of the first layer backbone network. Then, these optimal parameters and the initial echo are used as the input to the first layer backbone network to obtain the output echo S of the first layer backbone network. (1) ; When the number of network layers \(1 < t < T\), first pass the output of the \((t - 1)\)-th layer backbone network through the \(t\)-th layer hypernetwork to obtain the optimal parameters of the \(t\)-th layer backbone network, and then use these optimal parameters and the output of the \((t - 1)\)-th layer backbone network as the input of the \(t\)-th layer backbone network to obtain the output echo \(S\) of the \(t\)-th layer backbone network (t) ; When the number of network layers t = T, the output of the (T-1)th layer backbone network is first passed through the Tth layer supernetwork to obtain the optimal parameters of the Tth layer backbone network. Then, these optimal parameters and the output of the (T-1)th layer backbone network are used as the input of the Tth layer backbone network to obtain the final imaging result X. (T) .

Images