Target ISAR imaging method and system based on deep learning time-frequency analysis

Abstract

The present invention provides a target ISAR imaging method, system, storage medium, and electronic device based on deep learning time-frequency analysis, relating to the field of radar signal processing. The present invention includes obtaining target reflection echo data received by a radar; preprocessing each echo data to obtain a corresponding one-dimensional range image; performing motion compensation on each one-dimensional range image to obtain a corresponding pulse-range data matrix; performing an SPWVD transform on the data matrix along the pulse dimension to obtain a corresponding time-range-Doppler stereogram to generate an image set; selecting the best-focused image in the image set based on a minimum entropy criterion and using it as a low-resolution first target ISAR image; and using the first target ISAR image as input to a pretrained DenseU-Net network model to output a high-resolution second target ISAR image. By combining a time-frequency analysis algorithm based on SPWVD transform with a deep learning algorithm based on the DenseU-Net network model, the resolution of maneuvering target ISAR imaging is greatly improved.

Description

Technical Field

[0001] The present invention relates to the field of radar signal processing, and in particular to a target ISAR imaging method, system, storage medium and electronic equipment based on deep learning time-frequency analysis. Background Art

[0002] Inverse-Synthetic-Aperture-Radar (ISAR) can achieve high-resolution imaging of moving targets. Related technologies include traditional and improved algorithms for TSAR imaging, primarily the Range-Doppler (RD) algorithm and algorithms based on time-frequency analysis.

[0003] The RD algorithm can obtain relatively clear images of steadily moving targets. However, the rotation of a maneuvering target generally includes acceleration, and this acceleration causes the Doppler frequency of the scattering point echo to vary time-varying, resulting in low resolution, defocusing, and smearing in the target image obtained by the RD algorithm.

[0004] Time-frequency analysis is a signal processing method that combines time and frequency. It can intuitively process and analyze non-stationary signals and is widely used to overcome the effects of target maneuvers on imaging. Typical time-frequency analysis methods include short-time Fourier transform (STFT), Wigner distribution (WVD), smoothed pseudo-Wigner distribution (SPWVD), and some improved algorithms, such as combining SPWVD with WVD to further reduce cross-term interference. Although the time-frequency algorithms listed above can achieve relatively good imaging results, the complexity and uncertainty of maneuvering target motion can still lead to defocusing or even failure to image. Summary of the Invention

[0005] (1) Technical problems solved

[0006] In response to the shortcomings of the existing technology, the present invention provides a target ISAR imaging method, system, storage medium and electronic equipment based on deep learning time-frequency analysis, which solves the technical problem of high-resolution imaging of maneuvering targets.

[0007] (2) Technical solution

[0008] To achieve the above objectives, the present invention is implemented through the following technical solutions:

[0009] A target ISAR imaging method based on deep learning time-frequency analysis, comprising:

[0010] Obtain target reflection echo data received by radar;

[0011] Preprocess each echo data to obtain the corresponding one-dimensional range image;

[0012] After performing motion compensation on each of the one-dimensional range images, a corresponding pulse-range data matrix is ​​obtained;

[0013] Performing SPWVD transformation on each of the pulse-distance data matrices to obtain a corresponding time-range-Doppler stereogram to generate an image set;

[0014] In the image set, the best focused image is selected based on a minimum entropy criterion and used as a first target ISAR image with low resolution;

[0015] The first target ISAR image is used as input to a pre-trained DenseU-Net network model to output a high-resolution second target ISAR image.

[0016] Preferably, the SPWVD transformation refers to adjusting two window functions in the time domain and frequency domain respectively to obtain the optimal time-frequency distribution, and the calculation formula is:

[0017]

[0018] Wherein, SPWVD(t, f) is the smoothed pseudo-Wigner-Ville distribution of the pulse-distance data matrix that varies with time t and frequency f; g(ξ) is the window function that suppresses the cross-terms in the time domain, and ξ is the time domain integral variable; h(τ) is the window function that suppresses the cross-terms in the frequency domain, and τ is the frequency domain integral variable; is the pulse-distance data matrix containing P single signal components, z i and z y′ Both are single signal components; e is a mathematical constant, and j is an imaginary unit.

[0019] The calculation formula of the minimum entropy criterion is:

[0020]

[0021] Where ENT is the minimum image entropy in the image set; min is the minimization function; I is the range-Doppler image to be screened; I(m,n)m∈[0,M],n∈[0,N] represents the amplitude intensity of the pixel in the mth row and nth column, and the image size is M·N; S represents the total energy of the image.

[0022] The training process of the DenseU-Net network model includes:

[0023] Establish an ISAR scattering point echo model, set radar parameters and target motion parameters, and use the scattering point model to generate simulated echo data; the scattering point echo model used is:

[0024]

[0025] Where, t is time; N * is the total number of scattering points on the target; For nth * The backscattering field intensity of each scattering point; e is a mathematical constant, j is an imaginary unit; For nth * The coordinates of the scattering points in the target coordinate system; f * is the carrier frequency, c is the speed of light; R0 is the initial distance from the radar to the center point of the target; ω is the target's rotational angular velocity, v is the radial velocity, and a is the radial acceleration;

[0026] The simulated echo data is compressed in range and then motion compensated, and after the compensation is completed, an SPWVD transformation is performed in azimuth, and then a minimum entropy criterion is used to select the best focused image and use it as a low-resolution third target ISAR image;

[0027] According to the point coordinates and motion parameters of the scattering point model, the range unit and Doppler unit position of the scattering point at the imaging moment are calculated to draw an ideal reference target ISAR image corresponding to each of the simulated echo data;

[0028] The third target ISAR image and the ideal reference target ISAR image are used as a piece of training data and put into a training data set, and the training data set is expanded by changing the number of target scattering points and the motion parameters of the target;

[0029] After setting the training parameters, any third target ISAR image in the training data set is used as the input of the DenseU-Net network model, and combined with the corresponding ideal reference target ISAR image, training is performed until convergence to obtain the DenseU-Net network model.

[0030] The Adam optimizer is used to minimize the loss function during the training process of the DenseU-Net network model, wherein the loss function adopts the mean square logarithmic error function.

[0031] The DenseU-Net network model includes an encoder path and a decoder path;

[0032] The encoder path is used to extract shallow features of the input image and reduce the feature map through densely connected blocks; the encoder path includes multiple parts, each part consists of a convolutional layer, a densely connected block and a maximum pooling for downsampling;

[0033] The decoder path is responsible for expanding the feature map and fusing the downsampled image, and then extracting the fused features through the densely connected block; the decoder path includes the same number of parts as the encoder path, each part consisting of a transposed convolution layer, a convolution layer, and a densely connected block;

[0034] The same layers of the encoder path and the decoder path are connected via skip connections;

[0035] The densely connected block structure in the encoder path and the decoder path is the same, and both include four identical components, each of which is composed of a basic convolutional layer, a batch normalization layer, and a rectified linear unit layer arranged in sequence.

[0036] A target ISAR imaging system based on deep learning time-frequency analysis, comprising:

[0037] A data acquisition module is used to obtain target reflection echo data received by the radar;

[0038] The data preprocessing module is used to obtain and preprocess each echo data to obtain the corresponding one-dimensional range image;

[0039] A motion compensation module, configured to obtain a corresponding pulse-range data matrix after performing motion compensation on each of the one-dimensional range images;

[0040] A time-frequency analysis module is used to perform SPWVD transformation on each of the pulse-distance data matrices to obtain a corresponding time-range-Doppler stereogram to generate an image set;

[0041] An image screening module is used to obtain an image with the best focus from the image set based on a minimum entropy criterion and use it as a low-resolution first target ISAR image;

[0042] The image output module is used to obtain the first target ISAR image as the input of the pre-trained DenseU-Net network model to output a high-resolution second target ISAR image.

[0043] A storage medium stores a computer program for target ISAR imaging based on deep learning time-frequency analysis, wherein the computer program enables a computer to execute the target ISAR imaging method as described above.

[0044] An electronic device, comprising:

[0045] One or more processors; a memory; and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, the programs including instructions for executing the target ISAR imaging method as described above.

[0046] (3) Beneficial effects

[0047] The present invention provides a target ISAR imaging method, system, storage medium, and electronic device based on deep learning time-frequency analysis. Compared with the existing technology, it has the following advantages:

[0048] The present invention includes acquiring target reflection echo data received by radar; preprocessing each echo data to obtain a corresponding one-dimensional range image; performing motion compensation on each one-dimensional range image to obtain a corresponding pulse-range data matrix; performing an SPWVD transform on each pulse-range data matrix to obtain a corresponding time-range-Doppler stereogram to generate an image set; selecting the best-focused image from the image set based on a minimum entropy criterion and using it as a low-resolution first target ISAR image; and using the first target ISAR image as input to a pre-trained DenseU-Net network model to output a high-resolution second target ISAR image. By combining a time-frequency analysis algorithm based on the SPWVD transform with a deep learning algorithm based on the DenseU-Net network model, the resolution of ISAR imaging of maneuvering targets is greatly improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0050] Figure 1 A block diagram of a target ISAR imaging method based on deep learning time-frequency analysis provided by an embodiment of the present invention;

[0051] Figure 2 A structural diagram of a DenseU-Net network model provided by an embodiment of the present invention;

[0052] Figure 3 A structural diagram of a densely connected block provided by an embodiment of the present invention;

[0053] Figure 4 A training flowchart of a DenseU-Net network model provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0054] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention are clearly and completely described. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of them. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0055] The embodiments of the present application solve the technical problem of high-resolution imaging of maneuvering targets by providing a target ISAR imaging method, system, storage medium and electronic device based on deep learning time-frequency analysis, thereby meeting the requirements of high-resolution imaging.

[0056] The technical solution in the embodiments of the present application is to solve the above technical problems, and the overall idea is as follows:

[0057] As mentioned in the background technology, the uncertainty of the motion of maneuvering targets may cause the range-Doppler imaging algorithm to be unable to obtain a good target image. Although common time-frequency analysis methods such as STFT, WVD and SPWVD have improved the imaging effect, they still have some problems to a certain extent and fail to meet the requirements of high-precision imaging.

[0058] Against this backdrop, the present invention employs a time-frequency analysis algorithm based on the SPWVD transform. By adjusting two window functions in the time and frequency domains, respectively, the algorithm achieves an optimal time-frequency distribution. This algorithm achieves superior joint time-frequency resolution to that achieved by the STFT, offering superior cross-interference suppression and higher time-frequency concentration. Furthermore, considering that the target image obtained by the SPWVD algorithm may also be defocused, the SPWVD transform is specifically used to process the motion-compensated data to obtain a low-resolution ISAR image of the first target.

[0059] On this basis, to further improve imaging quality, the present invention introduces a deep learning algorithm based on the DenseU-Net network model. Compared to the traditional ResU-Net, DenseU-Net uses densely connected blocks instead of residual connections, achieving superior performance with fewer parameters and computational complexity. The low-resolution ISAR image of the first target acquired using the SPWVD transform is used as input to the pre-trained DenseU-Net network model to obtain the second ISAR image of the target.

[0060] In order to better understand the above technical solution, the above technical solution will be described in detail below with reference to the accompanying drawings and specific implementation methods.

[0061] Example 1:

[0062] like Figure 1As shown, an embodiment of the present invention provides a target ISAR imaging method based on deep learning time-frequency analysis, including:

[0063] S1. Obtain target reflection echo data received by radar;

[0064] S2. Preprocess each echo data to obtain the corresponding one-dimensional range image;

[0065] S3, performing motion compensation on each of the one-dimensional range images to obtain a corresponding pulse-range data matrix;

[0066] S4, performing SPWVD transformation on each of the pulse-distance data matrices to obtain a corresponding time-range-Doppler stereogram to generate an image set;

[0067] S5. In the image set, selecting the best-focused image based on a minimum entropy criterion and using it as the first target ISAR image with low resolution;

[0068] S6. Using the first target ISAR image as input to a pre-trained DenseU-Net network model to output a high-resolution second target ISAR image.

[0069] The embodiment of the present invention greatly improves the resolution of ISAR imaging of maneuvering targets by combining a time-frequency analysis algorithm based on SPWVD transform with a deep learning algorithm based on the DenseU-Net network model.

[0070] The following sections describe the various steps of the above solution in detail:

[0071] In step S1, target reflection echo data received by the radar is obtained.

[0072] In step S2, each echo data is preprocessed to obtain a corresponding one-dimensional range image.

[0073] The preprocessing operations in this step include Hilbert transform, downsampling, pulse compression, etc.

[0074] In step S3, after performing motion compensation on each of the one-dimensional range images, a corresponding pulse-range data matrix is ​​obtained.

[0075] The motion compensation operation in this step includes envelope alignment and phase correction using the accumulated cross-correlation method.

[0076] In step S4, SPWVD transformation is performed on each of the pulse-distance data matrices to obtain a corresponding time-range-Doppler stereogram to generate an image set.

[0077] The SPWVD transformation in this step refers to adjusting the two window functions in the time domain and frequency domain respectively to obtain the optimal time-frequency distribution. The calculation formula is:

[0078]

[0079] Wherein, SPWVD(t, f) is the smoothed pseudo-Wigner-Ville distribution of the pulse-distance data matrix that varies with time t and frequency f; g(ξ) is the window function that suppresses the cross-terms in the time domain, and ξ is the time domain integral variable; h(τ) is the window function that suppresses the cross-terms in the frequency domain, and τ is the frequency domain integral variable; is the pulse-distance data matrix containing P single signal components, z i and z i′ Both are single signal components; e is a mathematical constant, and j is an imaginary unit.

[0080] In step S5, the best-focused image in the image set is screened based on a minimum entropy criterion and used as the first target ISAR image with low resolution.

[0081] The calculation formula of the minimum entropy criterion in this step is:

[0082]

[0083] Where ENT is the minimum image entropy in the image set; min is the minimization function; I is the range-Doppler image to be screened; I(m,n)m∈[0,M],n∈[0,N] represents the amplitude intensity of the pixel in the mth row and nth column, and the image size is MN; S represents the total energy of the image.

[0084] In step S6, the first target ISAR image is used as input to a pre-trained DenseU-Net network model to output a high-resolution second target ISAR image.

[0085] like Figure 2 As shown, the DenseU-Net network model in this step includes input, output, encoder, decoder, and skip connections. The DenseU-Net network model uses a six-layer structure to enhance the extraction of deep features in ISAR images. The Dense Block module is designed to have the same number of input and output feature maps, significantly reducing the number of parameters and accelerating training. DenseU-Net is a combination of DenseNet and UNet, replacing the convolutional blocks in UNet with densely connected blocks. The architecture is primarily a U-shaped fully convolutional neural network consisting of an encoder and decoder. This network can learn the feature information contained in ISAR images.

[0086] Figure 2The encoder path and the decoder path are included:

[0087] The encoder path is used to extract shallow features of the input image and reduce the feature map through densely connected blocks (Dense Block); the encoder path includes multiple parts, each of which consists of a convolutional layer, a densely connected block (DenseBlock) and a maximum pooling for downsampling;

[0088] The decoder path is responsible for expanding the feature map and fusing the downsampled image, and then extracting the fused features through a densely connected block. The decoder path includes the same number of parts as the encoder path, each of which consists of a transposed convolution layer, a convolution layer, and a densely connected block.

[0089] The same layers of the encoder path and the decoder path are connected by skip connections to improve the network's ability to transfer gradients and improve training efficiency.

[0090] In particular, the densely connected blocks in the encoder path and the decoder path have the same structure, such as Figure 3 As shown, each consists of four identical components, each consisting of a basic convolutional layer, a batch normalization layer, and a rectified linear unit layer, arranged in sequence. To increase the correlation between convolutional layers and better learn features, the output of each convolutional layer is connected to the output of the subsequent convolutional layer. The conventional stacking operation is replaced by addition, effectively solving the problem of DenseBlock convolution layers not being able to be designed too deep and further improving the running speed of the network model. To better capture local features and increase the receptive field of the convolutional layer, the basic convolution is replaced by a dilated convolution (Conv, 3*3).

[0091] In order to ensure the acquisition of good DenseU-Net network architecture parameters, the embodiment of the present invention is based on the ISAR scattering point model and performs simulation under different motion parameters (including different initial angles, motion speeds, accelerations, etc.) to generate echo data and reference image sets. The echo data is motion compensated and SPWVD transformed, and a low-resolution image set is obtained based on the minimum entropy principle. The low-resolution image set and the reference image set are sent to the designed DenseU-Net network model for training. During the training process, the mean square logarithmic error is used as the loss function, the learning rate and batch size are set, and the Adam method is used for optimization. After reaching the preset number of iterations, the training process is completed to obtain the DenseU-Net network architecture parameters.

[0092] Correspondingly, such as Figure 4 As shown in FIG, the training process of the DenseU-Net network model includes:

[0093] S100, establishing an ISAR scattering point echo model, setting radar parameters and target motion parameters, and using the scattering point model to generate simulated echo data; the scattering point echo model used is:

[0094]

[0095] Where, t is time; N * is the total number of scattering points on the target; For nth * The backscattering field intensity of each scattering point; e is a mathematical constant, j is an imaginary unit; For nth * The coordinates of the scattering points in the target coordinate system; f * is the carrier frequency, c is the speed of light; R0 is the initial distance from the radar to the center point of the target; ω is the target's rotational angular velocity, v is the radial velocity, and a is the radial acceleration;

[0096] S200, performing motion compensation on the simulated echo data after range compression, performing SPWVD transformation on the azimuth after compensation, and then selecting the best focused image using the minimum entropy criterion as the low-resolution third target ISAR image;

[0097] S300, calculating the range unit and Doppler unit position of the scattering point at the imaging moment based on the point coordinates and motion parameters of the scattering point model, so as to draw an ideal reference target ISAR image corresponding to each of the simulated echo data;

[0098] S400, taking the third target ISAR image and the ideal reference target ISAR image as a piece of training data and putting them into a training data set, and expanding the training data set by changing the number of target scattering points and the target motion parameters;

[0099] S500: After setting the training parameters (total number of samples, epochs, batch size, number of iterations, and learning rate), any third target ISAR image in the training data set is used as input to the DenseU-Net network model. The model is trained in combination with the corresponding ideal reference target ISAR image until convergence, thereby obtaining the DenseU-Net network model.

[0100] During the training process, the Adam optimizer is used to minimize the loss function during the training of the DenseU-Net network model, wherein the loss function adopts the mean square logarithmic error (MSLE) function, which is expressed as:

[0101]

[0102] Wherein, Y is the output high-resolution fourth target ISAR image, w and h are the width and height of Y respectively, and G represents the corresponding ideal reference target ISAR image.

[0103] After training, the first target ISAR image is used as input to the DenseU-Net network model to obtain a high-resolution second target ISAR image. This demonstrates the ISAR image autofocus algorithm, combining the SPWVD time-frequency analysis algorithm with the deep learning DenseU-Net, significantly improving the imaging accuracy of ISAR images.

[0104] Example 2:

[0105] An embodiment of the present invention provides a target ISAR imaging system based on deep learning time-frequency analysis, including:

[0106] A data acquisition module is used to obtain target reflection echo data received by the radar;

[0107] The data preprocessing module is used to obtain and preprocess each echo data to obtain the corresponding one-dimensional range image;

[0108] A motion compensation module, configured to obtain a corresponding pulse-range data matrix after performing motion compensation on each of the one-dimensional range images;

[0109] A time-frequency analysis module is used to perform SPWVD transformation on each of the pulse-distance data matrices to obtain a corresponding time-range-Doppler stereogram to generate an image set;

[0110] An image screening module is used to obtain an image with the best focus from the image set based on a minimum entropy criterion and use it as a low-resolution first target ISAR image;

[0111] The image output module is used to obtain the first target ISAR image as the input of the pre-trained DenseU-Net network model to output a high-resolution second target ISAR image.

[0112] Example 3:

[0113] An embodiment of the present invention provides a storage medium storing a computer program for target ISAR imaging based on deep learning time-frequency analysis, wherein the computer program enables a computer to execute the target ISAR imaging method as described in Example 1.

[0114] Example 4:

[0115] An embodiment of the present invention provides an electronic device, including:

[0116] One or more processors; a memory; and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, the programs including instructions for executing the target ISAR imaging method as described above.

[0117] It can be understood that the target ISAR imaging system, storage medium, and electronic device based on deep learning time-frequency analysis provided in the embodiments of the present invention correspond to the target ISAR imaging method based on deep learning time-frequency analysis provided in the embodiments of the present invention. The explanations, examples, and beneficial effects of the relevant contents can refer to the corresponding parts in the target ISAR imaging method, and will not be repeated here.

[0118] In summary, compared with the existing technology, the present invention has the following beneficial effects:

[0119] The embodiments of the present invention solve the problem of high-resolution imaging of maneuvering targets and can achieve higher resolution than traditional time-frequency analysis algorithms. The use of the DenseU-Net network further improves imaging accuracy, and the network has a certain noise resistance capability.

[0120] It should be noted that, in this document, relational terms such as first and second, etc., are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the terms "comprises," "comprising," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or device comprising a series of elements includes not only those elements, but also other elements not explicitly listed, or elements inherent to such process, method, article, or device. In the absence of further limitations, an element defined by the phrase "comprising a..." does not exclude the presence of additional identical elements in the process, method, article, or device comprising the element.

[0121] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims

1. A target ISAR imaging method based on deep learning time-frequency analysis, characterized in that: include: Obtain target reflection echo data received by radar; Preprocess each echo data to obtain the corresponding one-dimensional range image; After performing motion compensation on each of the one-dimensional range images, a corresponding pulse-range data matrix is ​​obtained; Performing SPWVD transformation on each of the pulse-range data matrices along the pulse dimension to obtain a corresponding time-range-Doppler stereogram to generate an image set; In the image set, the best focused image is selected based on a minimum entropy criterion and used as a first target ISAR image with low resolution; The first target ISAR image is used as input to a pre-trained DenseU-Net network model to output a high-resolution second target ISAR image.

2. The target ISAR imaging method according to claim 1, wherein: The SPWVD transform is to adjust two window functions in the time domain and frequency domain respectively to obtain the optimal time-frequency distribution. The calculation formula is: Wherein, SPWVD(t, f) is the smoothed pseudo-Wigner-Ville distribution of the pulse-distance data matrix that varies with time t and frequency f; g(ξ) is the window function that suppresses the cross-terms in the time domain, and ξ is the time domain integral variable; h(τ) is the window function that suppresses the cross-terms in the frequency domain, and τ is the frequency domain integral variable; is a pulse-range data matrix containing P single signal components, z i and z i′ Both are single signal components; e is a mathematical constant, and j is an imaginary unit.

3. The target ISAR imaging method according to claim 1, wherein: The calculation formula of the minimum entropy criterion is: Where ENT is the minimum image entropy in the image set; min is the minimization function; I is the range-Doppler image to be screened; I(m,n)m∈[0,M],n∈[0,N] represents the amplitude intensity of the pixel in the mth row and nth column, and the image size is M·N; S represents the total energy of the image.

4. The target ISAR imaging method according to claim 1, wherein: The training process of the DenseU-Net network model includes: Establish an ISAR scattering point echo model, set radar parameters and target motion parameters, and use the scattering point model to generate simulated echo data; the scattering point echo model used is: Where, t is time; N * is the total number of scattering points on the target; For nth * The backscattering field intensity of each scattering point; e is a mathematical constant, j is an imaginary unit; For nth * The coordinates of the scattering points in the target coordinate system; f * is the carrier frequency, c is the speed of light; R0 is the initial distance from the radar to the center point of the target; ω is the target's rotational angular velocity, v is the radial velocity, and a is the radial acceleration; The simulated echo data is compressed in range and then motion compensated, and after the compensation is completed, an SPWVD transformation is performed in azimuth, and then a minimum entropy criterion is used to select the best focused image and use it as a low-resolution third target ISAR image; According to the point coordinates and motion parameters of the scattering point model, the range unit and Doppler unit position of the scattering point at the imaging moment are calculated to draw an ideal reference target ISAR image corresponding to each of the simulated echo data; The third target ISAR image and the ideal reference target ISAR image are used as a piece of training data and put into a training data set, and the training data set is expanded by changing the number of target scattering points and the motion parameters of the target; After setting the training parameters, any third target ISAR image in the training data set is used as the input of the DenseU-Net network model, and combined with the corresponding ideal reference target ISAR image, training is performed until convergence to obtain the DenseU-Net network model.

5. The target ISAR imaging method according to claim 4, wherein: The Adam optimizer is used to minimize the loss function during the training process of the DenseU-Net network model, wherein the loss function adopts the mean square logarithmic error function.

6. The target ISAR imaging method according to any one of claims 1 to 5, characterized in that: The DenseU-Net network model includes an encoder path and a decoder path; The encoder path is used to extract shallow features of the input image and reduce the feature map through densely connected blocks; the encoder path includes multiple parts, each part consists of a convolutional layer, a densely connected block and a maximum pooling for downsampling; The decoder path is responsible for expanding the feature map and fusing the downsampled image, and then extracting the fused features through the densely connected block; the decoder path includes the same number of parts as the encoder path, each part consisting of a transposed convolution layer, a convolution layer, and a densely connected block; The same layers of the encoder path and the decoder path are connected via skip connections; The densely connected block structure in the encoder path and the decoder path is the same, and both include four identical components, each of which is composed of a basic convolutional layer, a batch normalization layer, and a rectified linear unit layer arranged in sequence.

7. A target ISAR imaging system based on deep learning time-frequency analysis, characterized in that: include: A data acquisition module is used to obtain target reflection echo data received by the radar; The data preprocessing module is used to obtain and preprocess each echo data to obtain the corresponding one-dimensional range image; A motion compensation module, configured to obtain a corresponding pulse-range data matrix after performing motion compensation on each of the one-dimensional range images; a time-frequency analysis module for performing SPWVD transformation on each of the pulse-range data matrices to obtain a corresponding time-range-Doppler stereogram to generate an image set; An image screening module is used to obtain an image with the best focus from the image set based on a minimum entropy criterion and use it as a low-resolution first target ISAR image; The image output module is used to obtain the first target ISAR image as the input of the pre-trained DenseU-Net network model to output a high-resolution second target ISAR image.

8. A storage medium, characterized in that: The computer program for target ISAR imaging based on deep learning time-frequency analysis is stored therein, wherein the computer program enables a computer to execute the target ISAR imaging method according to any one of claims 1 to 6.

9. An electronic device, characterized in that: include: one or more processors; Memory; and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, and the programs include instructions for executing the target ISAR imaging method according to any one of claims 1 to 6.

Images