MIMO radar three-dimensional high-resolution imaging method based on cascade neural network

Abstract

The invention discloses an MIMO radar three-dimensional high-resolution imaging method based on a cascade neural network. The method comprises the following steps: constructing a T-ALISTA network training data set; the method comprises the following steps of: initializing and training a T-ALISTA network; constructing a training data set to train the IT-Net; processing the radar echo data by using the trained T-ALISTA to obtain a low-quality target image; and carrying out maximum value normalization processing and conversion processing from a complex value image to a real value image on a low-quality target image # imgabs0 # output by the T-ALISTA to obtain an input image # imgabs1 # of the IT-Net. The method is used for realizing rapid, steady and high-resolution three-dimensional imaging of an aerial moving target by the MIMO radar under a system error condition; and rich and key feature information is provided for early warning detection, classification identification and the like of the target.

Description

Technical Field

[0001] The present invention relates to the field of radar technology, and in particular to a three-dimensional high-resolution imaging method of a multiple-input multiple-output (MIMO) radar based on a cascade neural network. Background Art

[0002] Three-dimensional imaging of aerial moving targets is one of the important research directions of radar technology today. The information such as target shape, size and structure extracted from the imaging results can provide important basis for target detection, early warning, classification and identification, etc., and plays an important role in both military and civilian fields. Due to its advantages such as single-shot imaging and no need for complex motion compensation, multiple-input multiple-output (MIMO) radar has become an important technical means for three-dimensional imaging of aerial targets. In order to reduce the number of array elements and improve the imaging resolution, the sparse high-resolution imaging method of MIMO radar based on sparse recovery (SR) has been widely studied by relevant institutions and experts and scholars at home and abroad, and has made great progress.

[0003] However, most SR algorithms contain parameters that need to be optimized, which are difficult to set accurately in practice, affecting the imaging performance of MIMO radar. In addition, SR algorithms usually require multiple iterations to achieve convergence, with high computational complexity, and cannot meet the real-time requirements of moving target imaging. In essence, existing MIMO radar sparse high-resolution imaging methods are all based on model-driven implementation, which are often limited by speed and accuracy in practical applications. In recent years, data-driven intelligent methods represented by deep neural networks (DNNs) have developed rapidly, providing new ideas for MIMO radar aerial target three-dimensional imaging. Through training, DNNs can accurately mine the complex relationships and inherent laws in the data to achieve high-quality imaging of targets. Moreover, the trained DNN only needs one forward propagation when applied, without iterative optimization and back propagation, and has high computational efficiency. Combining model-driven and data-driven algorithms, based on the intelligent SR (ISR) algorithm, the optimal parameters of the SR algorithm are obtained through training and learning, which improves the convergence speed and accuracy of the algorithm, and can better solve the problems encountered by existing MIMO radar sparse high-resolution imaging methods in practical applications. However, the performance of existing ISR imaging algorithms is poor under system error conditions, and the computational complexity needs to be further reduced. Summary of the invention

[0004] The present invention provides a MIMO radar three-dimensional high-resolution imaging method based on a cascade neural network, which is characterized by comprising the following steps:

[0005] Step 1: Build the T-ALISTA network training data set;

[0006] The specific steps include:

[0007] Step 1: According to the actual detection needs, set the number of transmitting array elements M, the number of receiving array elements N, the transmitting array element interval dt, the receiving array element interval dr, and the carrier frequency f of the MIMO radar. c , signal bandwidth B, number of sub-pulses L and other parameters;

[0008] Step 2: Construct a MIMO radar three-dimensional imaging coordinate system, where o is the origin of the coordinate system, the positive direction of the x-axis points to the east, the positive direction of the y-axis points to the north, and the positive direction of the z-axis points to the sky. The transmitting array and the receiving array are perpendicular to each other. In this array, the transmitting array and the receiving array are uniform linear arrays composed of M array elements and N array elements respectively. The unit vector from the reference point O to the Pth target can be expressed as (x p ,y p ,z p ), where x p -y p -z p represents the xyz coordinates of the pth target relative to the reference point O; according to the possible positions of the targets, the MIMO radar 3D imaging space range is divided into I along the x, y and z directions respectively. x ,I y and I z grid points, constructing a first-dimensional imaging dictionary F1, a second-dimensional imaging dictionary F2 and a third-dimensional imaging dictionary F3;

[0009]

[0010] Among them, the superscript T represents the matrix transpose, and C represents the complex number;

[0011] Step 3: Use the gradient projection algorithm to solve the optimization problem shown in formula (2) to obtain the first to third dimensional optimization matrix corresponding to the first to third dimensional imaging dictionary and

[0012]

[0013] Among them, ||·|| F is the matrix Frobenius norm, R1, R2, and R3 represent the optimal matrices corresponding to F1, F2, and F3 respectively. j R represents the j-th column of R, j F represents the j-th column of F, (·) H represents the conjugate transpose, represents any j-th column;

[0014] Step 4: Let the number of target scattering points P obey [P min ,P max ] in the range of random uniform distribution, where P min and P max The minimum and maximum number of scattering points of the target are set respectively. The target scattering point positions are randomly and uniformly distributed within the three-dimensional imaging space. The ideal three-dimensional images of Q targets are randomly determined. As the label data of T-ALISTA, represents the qth target three-dimensional image, q = 1, 2, ..., Q;

[0015] Step 5: For each target ideal 3D image Randomly set the coding phase of the radar transmission sub-pulse to generate radar echo data Perform matched filtering and reference signal mixing to obtain T-ALISTA input data in Represents the qth radar echo data;

[0016]

[0017] Where t represents time, ξ p represents the amplitude of the pth scattering point, represents the broadband signal transmitted by the mth transmitting antenna, m=1,2,...,M, is the phase modulation signal, rect{·} represents the rectangular function, T is the sub-pulse width, represents the coding phase of the lth sub-pulse of the mth transmitting antenna, l=1,2,...,L,τ m,n,p represents the time delay of the pth scattering point relative to the mth transmitting antenna and the nth receiving antenna;

[0018] Step 6: Combine Q radar data and the target ideal 3D image Randomly divide into groups of size Q train The training data and label set of size Q test =QQ train Test data and label sets;

[0019] Step 2: Initialize and train the T-ALISTA network;

[0020] The specific steps include:

[0021] Step 1: Calculate the conditions that the iteration step size γ and threshold θ must meet when the T-ISTA algorithm converges, and set multiple different sets of γ and θ within the numerical range that meets the convergence conditions;

[0022] Step 2: Process multiple sets of radar data based on different combinations of γ and θ, and the number of iterations of the T-ISTA algorithm is set to K;

[0023] Step 3: By comparing the processing results of the radar data in the previous step, a set of parameters γ0 and θ0 with the smallest error in the three-dimensional imaging results of multiple sets of radar data T-ISTA is obtained as the initial values ​​of γ and θ for each layer in T-ALISTA, that is, {γ 0 ,γ 1 ,...,γ k ,...,γ K-1} are all equal to γ0, {θ 0 ,θ 1 ,...,θ k ,...,θ K-1} are all equal to θ0, where γ k and θ k They represent the iteration step and threshold of the kth layer of T-ALISTA, k=0,1,...,K-1, K represents the number of network layers of T-ALISTA, that is, the number of iterations of the T-ISTA algorithm;

[0024] Step 4: Based on the constructed training data set Define the normalized mean square error as the network loss function, use the back propagation method to solve the optimization problem, and obtain the optimal parameters of T-ALISTA

[0025]

[0026] in, Indicates the use of F1, F2, F3, and As input, Θ A ={γ 1 ,γ 2 ,...,γ k ,...,γ K θ 1 ,θ 2 ,...,θ k ,...,θ K} is the output of the K-th layer network of T-ALISTA with parameters, Θ A are network parameters, is the qth original input image, × o Represents mode-o tensor multiplication;

[0027] Step 3: Build a training data set to train IT-Net;

[0028] The specific steps include:

[0029] Step 1: Take Q target ideal 3D images As a labeled dataset for IT-Net;

[0030] Step 2: Use the trained T-ALISTA network to Processing, maximum normalization and conversion of complex-valued images to real-valued images are performed to obtain the input data set of IT-Net is the qth target image processed by the T-ALISTA network, where the superscript A indicates that the data is obtained based on T-ALISTA;

[0031] Step 3: Q pre-processed images and target ideal 3D image Randomly divide into groups of size Q train The training data and label set of size Q test =QQ train Test data / label set;

[0032] Step 4: Use Kaiming method to initialize IT-Net, define the normalized mean square error between IT-Net's output 3D image and the target ideal 3D image as the network loss function, use the back propagation method to solve the optimization problem, and obtain the optimal parameters of IT-Net.

[0033]

[0034] Among them, Q train is the training dataset size, Indicates is the IT-Net output of the input, Θ U Indicates the network parameters of IT-Net;

[0035] Step 4: Use the trained T-ALISTA to process the radar echo data to obtain a low-quality target image;

[0036] Radar echo data And the 3D imaging dictionaries F1, F2 and F3 are input into the trained K-layer T-ALISTA network to obtain low-quality target images

[0037] The specific steps include:

[0038] Step 1: Perform initialization processing;

[0039] Using 3D imaging dictionaries F1, F2 and F3 to analyze radar echo data Process and output the initial target image

[0040] Step 2: Perform gradient descent processing;

[0041] Based on radar echo data Optimization Matrix and 3D imaging dictionary matrices F1, F2 and F3 and the k-th layer iteration step length γ obtained by T-ALISTA training optimization k , k=0,1,...,K-1, output image of the previous layer Perform gradient descent processing to obtain the original output image of the k+1th layer

[0042]

[0043] Step 3: Perform soft threshold processing;

[0044] The k-th layer threshold θ obtained based on T-ALISTA training optimization k , for the original output image of the k+1th layer Perform soft threshold processing to obtain the k+1th layer output image:

[0045]

[0046] Among them, h θk (x) = xmax(|x|-θ) k ,0) / |x| is the soft threshold function, x is the independent variable of the function;

[0047] Step 4: Repeat steps 2 to 3 for K times to obtain a low-quality target image.

[0048] Step 5: Low-quality target image output by T-ALISTA Perform maximum normalization and conversion from complex-valued image to real-valued image to obtain the input image of IT-Net

[0049] Step 6: Use the trained IT-Net to input the image Processing is performed to obtain high-quality target images;

[0050] Will Input into the trained IT-Net network containing encoder, decoder and generator for processing to obtain high-quality target images

[0051] The specific steps include:

[0052] step1: yes Perform encoding processing to obtain encoder output

[0053] Will Input to the first 3D convolutional neural network (CNN) module of the encoder for processing to obtain the first 3D CNN module output The 3D CNN module consists of a tensor convolution layer, a batch normalization layer, and a ReLU layer. Input to the first MaxPool layer of the encoder for processing to obtain the first MaxPool layer output and the first maximum index result i1; Input to the second 3D CNN module for processing to obtain the output of the second 3D CNN module Will Input to the second MaxPool layer of the encoder for processing to obtain the second MaxPool layer output and the second largest index result i2; Input to the third 3D CNN module for processing to obtain the output of the third 3D CNN module

[0054] step2: yes Perform decoding processing to obtain the decoder output

[0055] Will The input is processed by the third 3D CNN module containing tensor deconvolution layer of the decoder, and the result is similar to Add together to get the output of the first 3D CNN module containing tensor deconvolution layer Will and i2 are input to the second MaxUnpool layer of the decoder for processing, and the result is the same as Add together to get the second MaxUnpool layer output Will The input is processed by the second 3D CNN module containing tensor deconvolution layer of the decoder, and the result is the same as Add together to get the output of the second 3D CNN module with tensor deconvolution layer Will and i1 are input to the first MaxUnpool layer of the decoder for processing, and the result is the same as Add together to get the first MaxUnpool layer output Will The input is processed by the first 3D CNN module containing tensor deconvolution layer of the decoder, and the result is the same as Add together to get

[0056] step3: and Perform channel-dimensional splicing connection and input into the generator to obtain high-quality target images;

[0057] The encoder input With the decoder output The result is input into the 3D CNN module composed of tensor convolution, batch normalization layer and Sigmoid layer for processing to obtain high-quality target images.

[0058] The present invention is used to realize fast, robust, high-resolution three-dimensional imaging of aerial moving targets by MIMO radar under system error conditions, and can provide rich and key feature information for early warning detection, classification and identification of targets. The advantages of the present invention are as follows:

[0059] 1) A cascade network for MIMO radar 3D high-resolution imaging is proposed, which is mainly composed of a tensor ISR network and an image transform network (IT-Net). The tensor ISR network processes the radar echo data to obtain a low-quality image, which is then input into the IT-Net for processing after preprocessing to obtain a high-quality image.

[0060] 2) Based on the tensor-based iterative soft-thresholding algorithm (T-ISTA), a tensor ISR network T-ALISTA was constructed. Its optimal parameters were obtained through training, which can obtain target imaging results with faster speed and accuracy.

[0061] 3) IT-Net was constructed based on the three-dimensional U-Net, which performed nonlinear transformation on the preprocessed target three-dimensional image. It can extract the high-dimensional features of the input low-quality image through the encoding path and obtain the target three-dimensional high-quality image through the decoding path and generator. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 It is a processing framework for MIMO radar imaging methods based on cascade neural networks;

[0063] Figure 2 It is the MIMO radar imaging three-dimensional imaging coordinate system;

[0064] Figure 3 is the constructed tensor ISR network T-ALISTA;

[0065] Figure 4 This is the constructed image transformation network IT-Net. DETAILED DESCRIPTION

[0066] The present invention will be further described below in conjunction with the accompanying drawings.

[0067] The present invention provides a MIMO radar three-dimensional high-resolution imaging method based on a cascade neural network, and its processing framework is as follows: Figure 1 As shown, the specific steps include the following steps.

[0068] Step 1: Build the T-ALISTA network training data set;

[0069] The specific steps include:

[0070] Step 1: According to the actual detection needs, set the number of transmitting array elements M, the number of receiving array elements N, the transmitting array element interval dt, the receiving array element interval dr, and the carrier frequency f of the MIMO radar. c , signal bandwidth B, number of sub-pulses L and other parameters;

[0071] Step 2: Build Figure 2 In the MIMO radar three-dimensional imaging coordinate system shown in the figure, o is the origin of the coordinate system, the positive direction of the x-axis points to the east, the positive direction of the y-axis points to the north, and the positive direction of the z-axis points to the sky. In the figure, the transmitting array and the receiving array are perpendicular to each other. In this array, the transmitting array and the receiving array are uniform linear arrays composed of M array elements and N array elements respectively. The unit vector from the reference point O to the Pth target can be expressed as (x p ,y p ,z p ), where x p -y p -z p represents the xyz coordinates of the pth target relative to the reference point O. According to the possible positions of the targets, the MIMO radar 3D imaging space is divided into I and x ,I y and I z grid points, constructing a first-dimensional imaging dictionary F1, a second-dimensional imaging dictionary F2 and a third-dimensional imaging dictionary F3;

[0072]

[0073] Among them, the superscript T represents matrix transpose, and C represents complex number.

[0074] Step 3: Use the gradient projection algorithm known in the art to solve the optimization problem shown in formula (2) to obtain the first to third dimensional optimization matrix corresponding to the first to third dimensional imaging dictionary and

[0075]

[0076] Among them, ||·|| F is the matrix Frobenius norm, R1, R2, and R3 represent the optimal matrices corresponding to F1, F2, and F3 respectively. j R represents the j-th column of R, j F represents the j-th column of F, (·) H represents the conjugate transpose, represents any j-th column.

[0077] Step 4: Let the number of target scattering points P obey [P min ,P max ] in the range of random uniform distribution, where P min and P max The minimum and maximum number of scattering points of the target are set respectively. The target scattering point positions are randomly and uniformly distributed within the three-dimensional imaging space. The ideal three-dimensional images of Q targets are randomly determined. As the label data of T-ALISTA, represents the qth target three-dimensional image, q = 1, 2, ..., Q;

[0078] Step 5: For each target ideal 3D image Randomly set the coding phase of the radar transmission sub-pulse to generate radar echo data Perform matched filtering and reference signal mixing processing (“matched filtering and reference signal mixing processing” are technical means well known to those skilled in the art) to obtain the input data of T-ALISTA in Represents the qth radar echo data;

[0079]

[0080] Where t represents time, ξ p represents the amplitude of the pth scattering point, represents the broadband signal transmitted by the mth transmitting antenna, m=1,2,...,M, is the phase modulation signal, rect{·} represents the rectangular function, T is the sub-pulse width, represents the coding phase of the lth sub-pulse of the mth transmitting antenna, l=1,2,...,L,τ m,n,p It represents the time delay of the p-th scattering point relative to the m-th transmitting antenna and the n-th receiving antenna.

[0081] Step 6: Combine Q radar data and the target ideal 3D image Randomly divide into groups of size Q trainThe training data and label set of size Q test =QQ train The test data and label set.

[0082] Step 2: Initialize and train the T-ALISTA network;

[0083] The specific steps include:

[0084] Step 1: Calculate the conditions that the iterative step size γ and threshold θ must meet when the T-ISTA algorithm converges (A. Beck and M. Teboulle, "AFast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems," SIAM Journal on Imaging Sciences, 2009, 2(1), 183-202), and set multiple different sets of γ and θ within the numerical range that meets the convergence conditions;

[0085] Step 2: Process multiple sets of radar data based on different combinations of γ and θ, and the number of iterations of the T-ISTA algorithm is set to K;

[0086] Step 3: By comparing the processing results of the radar data in the previous step, a set of parameters γ0 and θ0 with the smallest error in the three-dimensional imaging results of multiple sets of radar data T-ISTA is obtained as the initial values ​​of γ and θ for each layer in T-ALISTA, that is, {γ 0 ,γ 1 ,...,γ k ,...,γ K-1} are all equal to γ0, {θ 0 ,θ 1 ,...,θ k ,...,θ K-1} are all equal to θ0, where γ k and θ k They represent the iteration step and threshold of the kth layer (k=0, 1, ..., K-1) of T-ALISTA respectively, and K represents the number of network layers of T-ALISTA (i.e., the number of iterations of the T-ISTA algorithm);

[0087] Step 4: Based on the constructed training data set Define the normalized mean square error as the network loss function, and use the well-known backpropagation method in this field (Ian Goodfellow et al. Deep Learning [M]. Beijing: People's Posts and Telecommunications Press, 2021) to solve the optimization problem and obtain the optimal parameters of T-ALISTA

[0088]

[0089] in, Indicates the use of F1, F2, F3, and As input, Θ A ={γ 1 ,γ 2 ,...,γ k ,...,γ K θ 1 ,θ 2 ,...,θ k ,...,θ K} is the output of the K-th layer network of T-ALISTA with parameters, Θ A are network parameters, is the qth original input image, × o Represents mode-o tensor multiplication.

[0090] Step 3: Build a training data set to train IT-Net;

[0091] The specific steps include:

[0092] Step 1: Take Q target ideal 3D images As a labeled dataset for IT-Net;

[0093] Step 2: Use the trained T-ALISTA network to Processing, maximum normalization processing and conversion processing from complex-valued image to real-valued image (this technology is well known to those skilled in the art and will not be repeated here) are performed to obtain the input data set of IT-Net is the qth target image processed by the T-ALISTA network, where the superscript A indicates that the data is obtained based on T-ALISTA;

[0094] Step 3: Q pre-processed images and target ideal 3D image Randomly divide into groups of size Q train The training data and label set of size Q test =QQ train The test data / label set.

[0095] Step 4: Use the well-known Kaiming method in the field (K. He, X. Zhang, S. Ren, and J. Sun, "Delving Deep into Rectifiers: Surpassing Human-Level Performance on Image Net Classification," 2015 IEEE International Conference on Computer Vision (ICCV), Santiago, Chile, Dec. 2015, pp. 1026-1034) to initialize IT-Net, define the normalized mean square error between the output 3D image of IT-Net and the target ideal 3D image as the network loss function, use the back propagation method to solve the optimization problem, and obtain the optimal parameters of IT-Net

[0096]

[0097] Among them, Q train is the training dataset size, Indicates is the IT-Net output of the input, Θ U Indicates the network parameters of IT-Net.

[0098] Step 4: Use the trained T-ALISTA to process the radar echo data to obtain a low-quality target image;

[0099] like Figure 3 As shown, the radar echo data And the 3D imaging dictionaries F1, F2 and F3 are input into the trained K-layer T-ALISTA network to obtain low-quality target images

[0100] The specific steps include:

[0101] Step 1: Perform initialization processing;

[0102] Using 3D imaging dictionaries F1, F2 and F3 to analyze radar echo data Process and output the initial target image

[0103] Step 2: Perform gradient descent processing;

[0104] Based on radar echo data Optimization Matrix and The three-dimensional imaging dictionary matrices F1, F2 and F3 and the k-th layer (k = 0, 1, ..., K-1) iteration step length γ obtained by T-ALISTA training optimization k , output image of the previous layer Perform gradient descent processing to obtain the original output image of the k+1th layer

[0105]

[0106] Step 3: Perform soft threshold processing;

[0107] The k-th layer threshold θ obtained based on T-ALISTA training optimization k , for the original output image of the k+1th layer Perform soft threshold processing to obtain the k+1th layer output image;

[0108]

[0109] in, is the soft threshold function, and x is the independent variable of the function.

[0110] Step 4: Repeat steps 2 to 3 for K times to obtain a low-quality target image.

[0111] Step 5: Low-quality target image output by T-ALISTA Perform maximum normalization and conversion from complex-valued image to real-valued image to obtain the input image of IT-Net

[0112] Step 6: Use the trained IT-Net to input the image Processing is performed to obtain high-quality target images;

[0113] like Figure 4 As shown, Input into the trained IT-Net network containing encoder, decoder and generator for processing to obtain high-quality target images

[0114] The specific steps include:

[0115] step1: yes Perform encoding processing to obtain encoder output

[0116] Will Input to the first 3D Convolutional Neural Network (CNN) module of the encoder for processing to obtain the first 3D CNN module output The three-dimensional CNN module is composed of a tensor convolution layer, a batch normalization layer, and a ReLU layer (this structure is well known to those skilled in the art); Input to the first MaxPool layer of the encoder for processing to obtain the first MaxPool layer output and the first maximum index result i1; Input to the second 3D CNN module for processing to obtain the output of the second 3D CNN module Will Input to the second MaxPool layer of the encoder for processing to obtain the second MaxPool layer output and the second largest index result i2; Input to the third 3D CNN module for processing to obtain the output of the third 3D CNN module

[0117] step2: yes Perform decoding processing to obtain the decoder output

[0118] Will The input is processed by the third 3D CNN module containing tensor deconvolution layer of the decoder, and the result is similar to Add together to get the output of the first 3D CNN module containing tensor deconvolution layer Will and i2 are input to the second MaxUnpool layer of the decoder for processing, and the result is the same as Add together to get the second MaxUnpool layer output Will The input is processed by the second 3D CNN module containing tensor deconvolution layer of the decoder, and the result is the same as Add together to get the output of the second 3D CNN module with tensor deconvolution layer Will and i1 are input to the first MaxUnpool layer of the decoder for processing, and the result is the same as Add together to get the first MaxUnpool layer output Will The input is processed by the first 3D CNN module containing tensor deconvolution layer of the decoder, and the result is the same as Add together to get

[0119] step3: and Perform channel-dimensional splicing connection (the splicing method is well known to those skilled in the art), and input it into the generator to obtain a high-quality target image;

[0120] The encoder input With the decoder output The result is input into the 3D CNN module composed of tensor convolution, batch normalization layer and Sigmoid layer for processing to obtain high-quality target images.

Claims

1. A MIMO radar three-dimensional high-resolution imaging method based on a cascade neural network, characterized in that: The specific steps include: Step 1: Build the T-ALISTA network training data set; The specific steps include: Step 1: According to the actual detection needs, set the number of transmitting array elements M, the number of receiving array elements N, the transmitting array element interval dt, the receiving array element interval dr, and the carrier frequency f of the MIMO radar. c , signal bandwidth B, number of sub-pulses L and other parameters; Step 2: Construct a MIMO radar three-dimensional imaging coordinate system, where o is the origin of the coordinate system, the positive direction of the x-axis points to the east, the positive direction of the y-axis points to the north, and the positive direction of the z-axis points to the sky. The transmitting array and the receiving array are perpendicular to each other. In this array, the transmitting array and the receiving array are uniform linear arrays composed of M array elements and N array elements respectively. The unit vector from the reference point O to the Pth target can be expressed as (x p ,y p ,z p ), where x p -y p -z p represents the xyz coordinates of the pth target relative to the reference point O; according to the possible positions of the targets, the MIMO radar 3D imaging space range is divided into I along the x, y and z directions respectively. x ,I y and I z grid points, constructing a first-dimensional imaging dictionary F1, a second-dimensional imaging dictionary F2 and a third-dimensional imaging dictionary F3; Among them, the superscript T represents the matrix transpose, and C represents the complex number; Step 3: Use the gradient projection algorithm to solve the optimization problem shown in formula (2) to obtain the first to third dimensional optimization matrix corresponding to the first to third dimensional imaging dictionary and Among them, ||·|| F is the matrix Frobenius norm, R1, R2, and R3 represent the optimal matrices corresponding to F1, F2, and F3 respectively. j R represents the j-th column of R, j F represents the j-th column of F, (·) H represents the conjugate transpose, represents any j-th column; Step 4: Let the number of target scattering points P obey [P min ,P max ] in the range of random uniform distribution, where P min and P max The minimum and maximum number of scattering points of the target are set respectively. The target scattering point positions are randomly and uniformly distributed within the three-dimensional imaging space. The ideal three-dimensional images of Q targets are randomly determined. As the label data of T-ALISTA, represents the qth target three-dimensional image, q = 1, 2, ..., Q; Step 5: For each target ideal 3D image Randomly set the coding phase of the radar transmission sub-pulse to generate radar echo data Perform matched filtering and reference signal mixing to obtain T-ALISTA input data in Represents the qth radar echo data; Where t represents time, ξ p represents the amplitude of the pth scattering point, represents the broadband signal transmitted by the mth transmitting antenna, m=1,2,...,M, is the phase modulation signal, rect{·} represents the rectangular function, T is the sub-pulse width, represents the coding phase of the lth sub-pulse of the mth transmitting antenna, l=1,2,...,L,τ m,n,p represents the time delay of the pth scattering point relative to the mth transmitting antenna and the nth receiving antenna; Step 6: Combine Q radar data and the target ideal 3D image Randomly divide into groups of size Q train The training data and label set of size Q test =QQ train Test data and label sets; Step 2: Initialize and train the T-ALISTA network; The specific steps include: Step 1: Calculate the conditions that the iteration step size γ and threshold θ must meet when the T-ISTA algorithm converges, and set multiple different sets of γ and θ within the numerical range that meets the convergence conditions; Step 2: Process multiple sets of radar data based on different combinations of γ and θ, and the number of iterations of the T-ISTA algorithm is set to K; Step 3: By comparing the processing results of the radar data in the previous step, a set of parameters γ0 and θ0 with the smallest error in the three-dimensional imaging results of multiple sets of radar data T-ISTA is obtained as the initial values ​​of γ and θ for each layer in T-ALISTA, that is, {γ 0 ,γ 1 ,...,γ k ,...,γ K-1 } are all equal to γ0, {θ 0 ,θ 1 ,...,θ k ,...,θ K-1 } are all equal to θ0, where γ k and θ k They represent the iteration step and threshold of the kth layer of T-ALISTA, k=0,1,...,K-1, K represents the number of network layers of T-ALISTA, that is, the number of iterations of the T-ISTA algorithm; Step 4: Based on the constructed training data set Define the normalized mean square error as the network loss function, use the back propagation method to solve the optimization problem, and obtain the optimal parameters of T-ALISTA in, Indicates the use of F1, F2, F3, and As input, Θ A ={γ 1 ,γ 2 ,...,γ k ,...,γ K θ 1 ,θ 2 ,...,θ k ,...,θ K } is the output of the K-th layer network of T-ALISTA with parameters, Θ A are network parameters, is the qth original input image, × o Represents mode-o tensor multiplication; Step 3: Build a training data set to train IT-Net; The specific steps include: Step 1: Take Q target ideal 3D images As a labeled dataset for IT-Net; Step 2: Use the trained T-ALISTA network to Processing, maximum normalization and conversion of complex-valued images to real-valued images are performed to obtain the input data set of IT-Net is the qth target image processed by the T-ALISTA network, where the superscript A indicates that the data is obtained based on T-ALISTA; Step 3: Q pre-processed images and target ideal 3D image Randomly divide into groups of size Q train The training data and label set of size Q test =QQ train Test data / label set; Step 4: Use Kaiming method to initialize IT-Net, define the normalized mean square error between IT-Net's output 3D image and the target ideal 3D image as the network loss function, use the back propagation method to solve the optimization problem, and obtain the optimal parameters of IT-Net. Among them, Q train is the training dataset size, Indicates is the input IT-Net output, Θ U Indicates the network parameters of IT-Net; Step 4: Use the trained T-ALISTA to process the radar echo data to obtain a low-quality target image; Radar echo data And the 3D imaging dictionaries F1, F2 and F3 are input into the trained K-layer T-ALISTA network to obtain low-quality target images The specific steps include: Step 1: Perform initialization processing; Using 3D imaging dictionaries F1, F2 and F3 to analyze radar echo data Process and output the initial target image Step 2: Perform gradient descent processing; Based on radar echo data Optimization Matrix and 3D imaging dictionary matrices F1, F2 and F3 and the k-th layer iteration step length γ obtained by T-ALISTA training optimization k , k=0,1,...,K-1, output image of the previous layer Perform gradient descent processing to obtain the original output image of the k+1th layer Step 3: Perform soft threshold processing; The k-th layer threshold θ obtained based on T-ALISTA training optimization k , for the original output image of the k+1th layer Perform soft threshold processing to obtain the k+1th layer output image: in is the soft threshold function, x is the independent variable of the function; Step 4: Repeat steps 2 to 3 for K times to obtain a low-quality target image. Step 5: Low-quality target image output by T-ALISTA Perform maximum normalization and conversion from complex-valued image to real-valued image to obtain the input image of IT-Net Step 6: Use the trained IT-Net to input the image Processing is performed to obtain high-quality target images; Will Input into the trained IT-Net network containing encoder, decoder and generator for processing to obtain high-quality target images The specific steps include: step1: yes Perform encoding processing to obtain encoder output Will Input to the first 3D convolutional neural network (CNN) module of the encoder for processing to obtain the first 3D CNN module output The 3D CNN module consists of a tensor convolution layer, a batch normalization layer, and a ReLU layer. Input to the first MaxPool layer of the encoder for processing to obtain the first MaxPool layer output and the first maximum index result i1; Input to the second 3D CNN module for processing to obtain the output of the second 3D CNN module Will Input to the second MaxPool layer of the encoder for processing to obtain the second MaxPool layer output and the second largest index result i2; Input to the third 3D CNN module for processing to obtain the output of the third 3D CNN module step2: yes Perform decoding processing to obtain the decoder output Will The input is processed by the third 3D CNN module containing tensor deconvolution layer of the decoder, and the result is similar to Add together to get the output of the first 3D CNN module containing tensor deconvolution layer Will and i2 are input to the second MaxUnpool layer of the decoder for processing, and the result is the same as Add together to get the second MaxUnpool layer output Will The input is processed by the second 3D CNN module containing tensor deconvolution layer of the decoder, and the result is the same as Add together to get the output of the second 3D CNN module with tensor deconvolution layer Will and i1 are input to the first MaxUnpool layer of the decoder for processing, and the result is the same as Add together to get the first MaxUnpool layer output Will The input is processed by the first 3D CNN module containing tensor deconvolution layer of the decoder, and the result is the same as Add together to get step3: and Perform channel-dimensional splicing connection and input into the generator to obtain high-quality target images; The encoder input With the decoder output The result is input into the 3D CNN module composed of tensor convolution, batch normalization layer and Sigmoid layer for processing to obtain high-quality target images.

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