A Computational Imaging Method for Phase-Free Frequency Diversity Based on VAE-GAN

Abstract

The present invention discloses a computational imaging method for non-phase frequency diversity based on VAE-GAN, comprising the following steps: S1, constructing a mathematical model for near-field imaging of a metasurface antenna; S2, based on the mathematical model for near-field imaging of a metasurface antenna, and by combining deep neural network and compressive sensing technology, constructing a PFDCI-Net imaging network; S3, designing a network training algorithm for the PFDCI-Net imaging network, and optimizing the PFDCI-Net imaging network to minimize the loss of the PFDCI-Net imaging network; S4, using the target FMNIST data and the target MNIST dataset to train the PFDCI-Net imaging network to obtain the scattering coefficients for reconstructing the target scene. The computational imaging method proposed by the present invention completely avoids the errors caused by phase retrieval, reduces the computational complexity of the frequency diversity CI reconstruction problem, and improves the imaging accuracy and efficiency.

Description

Technical Field

[0001] The present invention relates to the field of computational imaging, and particularly to a computational imaging method based on VAE-GAN for non-phase frequency diversity. Background Art

[0002] Computational Imaging (CI) is a modern imaging method that shifts the focus of imaging system design from system hardware to backend image processing and software. It often achieves the imaging performance required by the imaging system through the complexity of hardware antenna design, acquisition rate, and the combination of the two. Great progress has been made in the application of frequency diversity imaging and phase retrieval technology in the field of computational imaging.

[0003] Generally speaking, the imaging performance depends on the spatial and frequency orthogonality of the antenna measurement mode. The key features of the metasurface antenna system are mainly related to the feeding structure, radiation mechanism, physical structure of the radiator, and quality factor, etc. These complex factors make it computationally difficult to directly analyze and calculate the radiation pattern of the metasurface antenna. In actual imaging applications, the radiation field distribution is directly measured through near-field grid scanning technology. The measurement matrix used is characterized by near-field grid scanning in experiments. This characterization requires precise knowledge of the positions and orientations of the transmitter and receiver. Any difference between the modeled position and the actual position will introduce phase errors, thereby reducing the quality of image reconstruction. System errors, including misalignment between the transmitter and receiver apertures, mainly introduce phase errors into the system, and antenna modulation errors will further cause phase errors. Previously, traditional near-field computational imaging compensated for phase errors through compressive sensing (CS) and phase retrieval techniques, and combined compressive sensing technology and deep neural networks to solve the actual system phase errors. Due to the typical non-convex and ill-posed characteristics of phase retrieval, accurate phase measurement has become increasingly difficult, requiring more measurement results and longer calculation times. Summary of the Invention

[0004] To solve the technical problems existing in the background art, the present invention proposes a computational imaging method based on VAE-GAN for non-phase frequency diversity.

[0005] The present invention proposes a computational imaging method based on VAE-GAN for non-phase frequency diversity, and the method includes the following steps:

[0006] S1. Construct a mathematical model for near-field imaging of the metasurface antenna;

[0007] S2. Based on the mathematical model for near-field imaging of the metasurface antenna, construct a PFDCI-Net imaging network by combining deep neural network and compressive sensing technology;

[0008] S3. Design a network training algorithm for the PFDCI-Net imaging network and optimize the PFDCI-Net imaging network to minimize the loss of the PFDCI-Net imaging network.

[0009] S4. Use the target FMNIST data and the target MNIST dataset to train the PFDCI-Net imaging network and obtain the scattering coefficients for reconstructing the target scene.

[0010] Preferably, in step S1, a mathematical model for near-field imaging of a metasurface antenna is constructed as follows:

[0011] S11. The probe of the metasurface antenna receives the echo measurement value g scattered by the target of the scene to be detected; among them, the echo measurement value g scattered by the target of the scene includes all the backscattering components of the target of the scene, and the echo measurement value g scattered by the target of the scene comes from the incident field scattered by the object in the scene.

[0012] S12. Construct a scene measurement matrix H; among them, the scene measurement matrix H is a set of radiated electric fields from the transmitting antenna and the receiving probe at each position in the scene.

[0013] S13. By constructing the mapping relationship between the echo measurement value g of the scene target scattering, the scene measurement matrix H and the scene target scattering coefficient obtain the mathematical model for near-field imaging of the metasurface antenna.

[0014] Preferably, in step S13, by constructing the mapping relationship between the echo measurement value g of the scene target scattering, the scene measurement matrix H and the scene target scattering coefficient the specific process is as follows:

[0015] The integral form of the echo measurement value g of the scene target scattering is:

[0016] (10)

[0017] In formula (10), is the echo measurement value of the scene target scattering at different frequencies; V represents the near-field space; represents the magnitude of the radiated electric field of the transmitting antenna at different frequencies in the scene at ; represents the magnitude of the radiated electric field of the receiving probe at different frequencies in the scene at ; represents the scene target scattering coefficient at in the scene; represents the vector pointing to free space;

[0018] Write the formula (10) in the form of a discrete matrix equation, that is, the mathematical model of near-field imaging of the metasurface antenna is as follows:

[0019] (11)

[0020] Write the formula (11) in the form of intensity measurement of the compressed waveform, that is:

[0021] (12)

[0022] Preferably, in step S2, based on the mathematical model of near-field imaging of the metasurface antenna, construct the PFDCI-Net imaging network by combining the deep neural network and the compressed sensing technology. The specific process is as follows:

[0023] S21. Input the echo measurement value scattered by the scene target into the encoder E of the PFDCI-Net imaging network, infer a latent vector z, and learn the relationship between the training sample and the latent vector z;

[0024] S22. Input the latent vector z into the generator G of the PFDCI-Net imaging network to generate fake samples for training;

[0025] S23. By training the discriminator D of the PFDCI-Net imaging network, use the discriminator D to monitor and discriminate the fake samples generated by the generator G and the real samples from the real data.

[0026] Preferably, in step S21, input the echo measurement value scattered by the scene target into the encoder E of the PFDCI-Net imaging network, infer a latent vector z, and learn the relationship between the training sample and the latent vector z. The specific process is as follows:

[0027] Based on the mathematical model of near-field imaging of the metasurface antenna , input the echo measurement value scattered by the scene target into the encoder E. After passing through five fully connected layers, obtain the mean μ and variance δ of the echo measurement value scattered by the scene target, and infer a latent vector z; the encoder E learns the hidden relationship between the training sample x and the latent vector z. Given the training sample x, the conditional probability distribution of the latent vector z is ;

[0028] Among them, the latent vector z contains the contour feature information of the target scene.

[0029] Preferably, in step S22, input the latent vector z into the generator G of the PFDCI-Net imaging network to generate fake samples for training. The specific process is as follows:

[0030] Generate fake samples through the generator G, and the generator G learns the distribution of the training sample x , the prior distribution of the input noise variable , maps the space from the latent vector z to the original scene target as , where are the weights of the generator G; by training the discriminator D, the probability of correctly assigning labels to the fake samples generated by the generator G and the real samples from the real data is maximized.

[0031] Preferably, in step S23, by training the discriminator D of the PFDCI-Net imaging network, the discriminator D is used to monitor and discriminate the fake samples generated by the generator G and the real samples from the real data. The specific process is as follows:

[0032] The sample features are extracted by the translation of the convolutional layer of the discriminator D from the fake samples generated by the generator G or the real samples from the real data. After passing through the Flatten layer, the multi-dimensional data is converted into a one-dimensional sequence, and the extracted sample features are integrated through the fully connected layer to maximize the probability of correctly assigning labels to the fake samples generated by the generator G and the real samples from the real data.

[0033] Preferably, in step S3, a network training algorithm is designed for the PFDCI-Net imaging network, and the PFDCI-Net imaging network is optimized to minimize the loss of the PFDCI-Net imaging network, specifically:

[0034] S31. Obtain a training data set containing n training samples x , based on the mathematical model of metasurface antenna imaging , design a network training algorithm for the PFDCI-Net imaging network;

[0035] where, σ i is the scattering coefficient of the i-th scene target in the training data set; g i is the echo measurement value scattered by the i-th scene target in the training data set;

[0036] S32. In the PFDCI-Net imaging network, input the measurement matrix H, the number of iterations T, the echo measurement value g of the scattered scene target, and the scattering coefficient of the scene target , initialize the encoder E, the generator G, and the discriminator D;

[0037] S33. Use the mean square error function MSE to calculate the loss MSE between the fake samples and the real samples as:

[0038] (13)

[0039] In formula (13), represents σ = [ σ 1 , σ 2 , σ 3 , ⋯ , σ n ] The scattering coefficient of the i-th original scene target in denotes the fake sample generated by the generator G;

[0040] S34. Use the KL divergence to calculate the gap between the probability distribution of the training sample x and the probability fitting distribution. The specific formula is:

[0041] (14)

[0042] In formula (14), denotes the probability distribution of the sample x, denotes the probability fitting distribution of the sample x;

[0043] Optimize the objective function , and the specific formula is:

[0044] ℒ ( θ , ϕ ) = ∫ z q ϕ ( z | x ) l o g p θ ( x , z ) q ϕ ( z | x ) = − D KL ( q ϕ ( z | x ) | p ( z ) ) + E z ∼ q [ log p θ ( x | z ) ] (15)

[0045] In formula (15), denotes the output distribution function of the decoder, denotes the joint probability distribution of the training sample x and the latent vector z, denotes the prior distribution function of the latent vector z, denotes the probability distribution that the latent vector z follows the output distribution function, denotes the conditional distribution function;

[0046] S35. Use the Adam algorithm to update the cost functions of the discriminator D and the generator G:

[0047] L =− 1 s ∑ i = 1 s [ log D ( σ i ) + log( 1 − D ( G ( E ( g i )))) ] (16)

[0048] In formula (16), denotes the output of the discriminator D for the scattering coefficient of the scene target, denotes the output of the discriminator D for the fake data generated by the generator G after the target echo data passes through the decoder, where s represents the number of samples extracted.

[0049] The encoder E and the generator G are jointly optimized through the following cost function:

[0050] (17)

[0051] In formula (17), g represents the echo measurement value of the scene target scattered by the probe, H represents the measurement matrix constructed by the transmitting field and the scattering field, denotes the fake sample generated by the generator G, and λ represents the regularization parameter. Represents the prior conditional probability distribution of the latent vector z, represents the probability distribution of the latent vector z;

[0052] The imaging network is alternately trained using the generator G and the discriminator D with the min-max cost function, and the specific formula is:

[0053] ℒ 2 ( E , G ) = min G max D E x ∼ P data ( x ) [ log D ( x ) ] + E z ∼ q ϕ ( z | y ) [ log( 1 − D ( G ( z ))) ] (18)

[0054] In formula (18), represents the data distribution of the training sample x, represents the prior conditional probability distribution of the latent vector z, represents the weight parameter, represents the output of the discriminator D for the training sample x, represents the discriminator D for the generated fake sample output;

[0055] Step 36. Calculate the gradient of the measurement matrix H , update the weight coefficients of the convolutional layer, update the first moment vector and the second moment vector , update the objective function parameter , until the cost function of the training converges, that is, the training cycle ends.

[0056] Preferably, in step S4, the PFDCI-Net imaging network is trained using the target FMNIST data and the target MNIST dataset to obtain the scattering coefficients for reconstructing the target scene. The specific process is as follows:

[0057] S41. Obtain the training set and the test set , set the maximum number of iterations T for training the PFDCI-Net imaging network, and initialize the weight parameters W of the encoder E, generator G, and discriminator D in the PFDCI-Net imaging network;

[0058] S42. In each iteration, s scene target scattering coefficients are extracted from the training set , and according to calculate the echo measurement values of the scene target scattering corresponding to the s scene target scattering coefficients, and input the echo measurement values of the scene target scattering into the PFDCI-Net imaging network. Using the MSE function and the KL divergence as the cost function of the PFDCI-Net imaging network, train the weight parameters W of the encoder E, generator G, and discriminator D in the PFDCI-Net imaging network;

[0059] S43. After T iterations, the cost function of the PFDCI-Net imaging network gradually converges, and the value of the cost function tends to a minimum value, indicating that the training of the PFDCI-Net imaging network is completed;

[0060] S44. Input the test set into the trained near-field PFDCI-Net imaging network to obtain the scattering coefficients of the reconstructed target scene , achieving high-fidelity restoration of the original target information.

[0061] A PFDCI-Net imaging network, applied to the computational imaging method described above, is composed of an encoder E, a generator G, and a discriminator D;

[0062] The encoder E is composed of three serially connected fully connected layers plus two juxtaposed five-layer fully connected layers, and each fully connected layer contains N neurons;

[0063] The generator G is composed of five serially connected fully connected layers;

[0064] The discriminator D is composed of a convolutional layer, a Flatten layer, and a fully connected layer.

[0065] A computational imaging method based on VAE-GAN with phaseless frequency diversity proposed by the present invention models the mathematical principle of metasurface antenna imaging; combines deep neural network and compressive sensing technology to construct a phaseless frequency-diverse computational imaging network (PFDCI-Net) to reconstruct the receiving matrix; designs a PFDCI-Net training algorithm according to the PFDCI-Net imaging network, and trains the echo signal test data set and the scene target training data set; uses the target FMNIST data and the target MNIST data set to train the PFDCI-Net imaging network to obtain the scattering coefficients of the reconstructed target scene.

[0066] The computational imaging method proposed by the present invention uses the spatial radiation field generated by the metasurface antenna to observe the scene, combines deep neural network and compressive sensing technology to achieve phaseless frequency-diverse scene imaging, thus completely avoiding the errors caused by phase recovery, reducing the computational complexity of the frequency-diverse CI reconstruction problem, and improving the imaging accuracy and efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Figure 1 is a flowchart of the computational imaging method proposed by the present invention;

[0068] Figure 2It is the PFDCI-Net imaging network model diagram of the computational imaging method proposed by the present invention;

[0069] Figure 3 It is the training flow chart of the PFDCI-Net imaging network of the computational imaging method proposed by the present invention;

[0070] Figure 4 It is the FDCI network reconstruction result diagram of different scenario targets in the first embodiment of the computational imaging method proposed by the present invention;

[0071] Figure 5 It is the reconstruction result diagram of the PFDCI network of MSACI-FMNIST at different scenario information sampling rates in the first embodiment of the computational imaging method proposed by the present invention;

[0072] Figure 6 It is the reconstruction result diagram of the PFDCI network in two imaging algorithms of MSACI-MNIST at different scenario information sampling rates in the first embodiment of the computational imaging method proposed by the present invention;

[0073] Figure 7 It is the PSNR and SSIM change curves of MSACI-MNIST at different scenario information sampling rates in the first embodiment of the computational imaging method proposed by the present invention;

[0074] Figure 8 It is the reconstruction result diagram of the PFDCI network at different signal-to-noise ratios in the first embodiment of the computational imaging method proposed by the present invention;

[0075] Figure 9 It is the PSNR and SSIM change curves of PFDCI-MNIST and PFDCI-FMNIST at different signal-to-noise ratios in the first embodiment of the computational imaging method proposed by the present invention. Detailed implementation manners

[0076] Refer to Figure 1 , the embodiment of the present invention provides a computational imaging method based on VAE-GAN for non-phase frequency diversity, and its specific steps include:

[0077] S1. Construct a mathematical model for near-field imaging of a metasurface antenna.

[0078] Specifically, in step S1, the process of constructing a mathematical model for near-field imaging of a metasurface antenna is as follows:

[0079] S11. The probe of the metasurface antenna receives the echo measurement value g scattered by the target in the scene to be detected; among them, the echo measurement value g scattered by the target in the scene includes all the backscattering components of the target in the scene, and the echo measurement value g scattered by the target in the scene comes from the incident field scattered by the object in the scene.

[0080] S12. Construct a scene measurement matrix H, where the scene measurement matrix H is a set of radiated electric fields from the transmitting antenna and the receiving probe at each position in the scene.

[0081] S13. Obtain the mathematical model of the near-field imaging of the metasurface antenna by constructing the mapping relationship between the echo measurement value g of the scene target scattering, the scene measurement matrix H, and the scene target scattering coefficient therebetween.

[0082] Specifically, in step S13, by constructing the mapping relationship between the echo measurement value g of the scene target scattering, the scene measurement matrix H, and the scene target scattering coefficient therebetween, the specific process is as follows:

[0083] The integral form of the echo measurement value g of the scene target scattering is:

[0084] (19)

[0085] In formula (19), is the echo measurement value of the scene target scattering at different frequencies; V represents the near-field space; represents the magnitude of the radiated electric field of the transmitting antenna at different frequencies in the scene at ; represents the magnitude of the radiated electric field of the receiving probe at different frequencies in the scene at ; represents the scene target scattering coefficient at in the scene; ; represents the vector pointing to free space.

[0086] Due to the diffraction and bandwidth constraints of the system, rewrite formula (19) in the form of a discrete matrix equation, that is, the mathematical model of the near-field imaging of the metasurface antenna is:

[0087] (20)

[0088] That is

[0089] [ g 1 g 2 g 3 ⋮ g M ] = [ h 11 h 12 h 13 ⋯ h 1 N h 21 h 22 h 23 … h 2 N h 31 h 32 h 33 ⋯ h 3 N ⋮ ⋮ ⋮ ⋱ ⋮ h M 1 h M 2 h M 3 ⋯ h MN ] * [ σ 1 σ 2 σ 3 ⋮ σ M ] + [ n 1 n 2 n 3 ⋮ n M ] (21)

[0090] In formula (21), the M-dimensional vector g = [ g 1 g 2 ⋯ g M ] T represents the echo measurement value of the scene target scattering received by the probe, M represents the number of spatial effective radiation patterns of the metasurface antenna, N represents the number of discrete units to be measured in the imaging scene, and the M-dimensional vector σ = [ σ 1 σ 2 ⋯ σ M ] T represents the scene target scattering coefficient to be measured in the discrete scene space, and the M-dimensional vector n = [ n 1 n 2 ⋯ n M ] T Denote the additive noise term provided for generality, Denote the measurement matrix constructed by the transmitting field and the scattering field, whose physical meaning represents the product of the magnitudes of the radiated electric fields at the transmitting antenna and the receiving probe in the scene space.

[0091] To expand the frequency difference range of computational imaging, Equation (20) is written in the form of intensity measurement of the compressed waveform, i.e.:

[0092] (22)

[0093] Refer to Figure 2 , S2. Based on the mathematical model of near-field imaging of the metasurface antenna, and construct the PFDCI-Net imaging network by combining deep neural network and compressive sensing technology.

[0094] Specifically, step S2. Based on the mathematical model of near-field imaging of the metasurface antenna, and construct the PFDCI-Net imaging network by combining deep neural network and compressive sensing technology. The specific process is as follows:

[0095] S21. Input the echo measurement value scattered by the scene target into the encoder E of the PFDCI-Net imaging network, infer a latent vector z, and learn the relationship between the training sample and the latent vector z.

[0096] Specifically, in step S21, input the echo measurement value scattered by the scene target into the encoder E of the PFDCI-Net imaging network, infer a latent vector z, and learn the relationship between the training sample and the latent vector z. The specific process is as follows:

[0097] Based on the mathematical model of metasurface antenna imaging , input the echo measurement value scattered by the scene target into the encoder E. After passing through five fully connected layers, obtain the mean μ and variance δ of the echo measurement value scattered by the scene target, and infer a latent vector z; the encoder E learns the hidden relationship between the training sample x and the latent vector z. When the training sample x is given, the conditional probability distribution of the latent vector z is .

[0098] Among them, the latent vector z contains the contour of the target scene or some other characteristic information.

[0099] S22. Input the latent vector z into the generator G of the PFDCI-Net imaging network to generate fake samples for training.

[0100] Specifically, in step S22, the latent vector z is input into the generator G of the PFDCI-Net imaging network to generate fake samples for training. The specific process is as follows:

[0101] The generator G generates fake samples, and the generator G learns the distribution of the training samples x , the prior distribution of the input noise variable , and the mapping from the latent vector z to the original scene target is , where is the weight of the generator G.

[0102] S23. By training the discriminator D of the PFDCI-Net imaging network, the discriminator D is used to monitor and discriminate between the fake samples generated by the generator G and the real samples from the real data.

[0103] Specifically, in step S23, by training the discriminator D of the PFDCI-Net imaging network, the discriminator D is used to monitor and discriminate between the fake samples generated by the generator G and the real samples from the real data. The specific process is as follows:

[0104] The sample features are extracted from the fake samples generated by the generator G or the real samples from the real data through the translation of the convolutional layer of the discriminator D. After passing through the Flatten layer, the multi-dimensional data is converted into a one-dimensional sequence, and the sample features extracted are integrated through the fully connected layer to maximize the probability of correctly assigning labels to the fake samples generated by the generator G and the real samples from the real data.

[0105] Refer to Figure 3 , S3, design a network training algorithm for the PFDCI-Net imaging network and optimize the PFDCI-Net imaging network to minimize the loss of the PFDCI-Net imaging network.

[0106] Specifically, in step S3, design a network training algorithm for the PFDCI-Net imaging network and optimize the PFDCI-Net imaging network to minimize the loss of the PFDCI-Net imaging network. Specifically:

[0107] S31. Obtain a training data set containing n training samples x , based on the mathematical model of metasurface antenna imaging , design a network training algorithm for the PFDCI-Net imaging network;

[0108] where σ i is the scattering coefficient of the i-th scene target in the training data set; g i is the echo measurement value of the scattering of the i-th scene target in the training data set.

[0109] S32. In the PFDCI-Net imaging network, input the measurement matrix H, the number of iterations T, the echo measurement value g of the scene target scattering, and the scene target scattering coefficient , and initialize the encoder E, the generator G, and the discriminator D.

[0110] S33. Use the mean square error function MSE to calculate the loss MSE between the fake samples and the real samples as:

[0111] (23)

[0112] In formula (23), represents σ = [ σ 1 , σ 2 , σ 3 , ⋯ , σ n ] the i-th original scene target scattering coefficient in , and

[0113] represents the fake sample generated by the generator G. S34. Use the KL divergence

[0114] (24)

[0115] In formula (24), represents the probability distribution of the sample x, represents the probability fitting distribution of the sample x;

[0116] Optimize the objective function as follows:

[0117] ℒ ( θ , ϕ ) = ∫ z q ϕ ( z | x ) l o g p θ ( x , z ) q ϕ ( z | x ) = − D KL ( q ϕ ( z | x ) | p ( z ) ) + E z ∼ q [ log p θ ( x | z ) ] (25)

[0118] In formula (25), represents the output distribution function of the decoder, represents the joint probability distribution of the training sample x and the latent vector z, represents the prior distribution function of the latent vector z, represents the probability distribution that the latent vector z follows the output distribution function, represents the conditional distribution function.

[0119] S35. Use the Adam algorithm to update the cost functions of the discriminator D and the generator G:

[0120] L =− 1 s ∑ i = 1 s [ log D ( σ i ) + log( 1 − D ( G ( E ( g i )))) ] (26)

[0121] In formula (26), represents the output of the discriminator D for the scene target scattering coefficient, It represents the output of the discriminator D for the fake data generated by the generator G after the decoder processes the target echo data. Here, s represents the number of samples extracted.

[0122] The encoder E and the generator G are jointly optimized through the following cost function:

[0123] (27)

[0124] In formula (27), g represents the measured value of the echo scattered by the scene target received by the probe, H represents the measurement matrix constructed from the emission field and the scattering field, represents the fake samples generated by the generator G, represents the regularization parameter, represents the prior conditional probability distribution of the latent vector z, represents the probability distribution of the latent vector z.

[0125] The imaging network is alternately trained using the generator G and the discriminator D with the min-max cost function. The specific formula is:

[0126] ℒ 2 ( E , G ) = min G max D E x ∼ P data ( x ) [ log D ( x ) ] + E z ∼ q ϕ ( z | y ) [ log( 1 − D ( G ( z ))) ] (28)

[0127] In formula (28), represents the data distribution of the training samples x, represents the prior conditional probability distribution of the latent vector z, represents the weight parameter, represents the output of the discriminator D for the training samples x, represents the discriminator D's output for the generated fake samples

[0128] Step 36: Calculate the gradient of the measurement matrix H , update the weight coefficients of the convolutional layer, update the first-order moment vector and the second-order moment vector , update the objective function parameter , until the cost function of the training converges, that is, the training cycle ends.

[0129] S4. Use the complex-target FMNIST data and the sparse-target MNIST dataset to train the PFDCI-Net imaging network to obtain the scattering coefficients of the reconstructed target scene; the trained PFDCI-Net imaging network can directly restore the original target information with high fidelity;

[0130] Specifically, in step S4, using the complex-target FMNIST data and the sparse-target MNIST dataset to train the PFDCI-Net imaging network to obtain the scattering coefficients of the reconstructed target scene, the specific process is as follows:

[0131] S41. Get training set and test set , set the maximum number of iterations T for training the PFDCI-Net imaging network, and initialize the weight parameters W of the encoder E, generator G, and discriminator D in the PFDCI-Net imaging network;

[0132] S42. In each iteration, from the training set Extract s scene target scattering coefficients from ,according to Calculate the echo measurement values ​​of scene target scattering corresponding to s scene target scattering coefficients , the echo measurement value scattered by the scene target Input into the PFDCI-Net imaging network, use the MSE function and KL divergence as the cost function of the PFDCI-Net imaging network, and train the weight parameters W of the encoder E, generator G, and discriminator D in the PFDCI-Net imaging network;

[0133] S43. After T iterations, the cost function of the PFDCI-Net imaging network gradually converges, the value of the cost function tends to a minimum, and the training of the PFDCI-Net imaging network is completed;

[0134] S44, the test set Input the trained near-field PFDCI-Net imaging network to obtain the scattering coefficient of the reconstructed target scene , achieving high-fidelity restoration of the original target information.

[0135] A PFDCI-Net imaging network for computational imaging methods;

[0136] The PFDCI-Net imaging network consists of an encoder E, a generator G, and a discriminator D; the encoder E consists of three fully connected layers in series plus two parallel five-layer fully connected layers, each fully connected layer contains N neurons; the generator G consists of five serial fully connected layers; the discriminator D consists of a convolutional layer, a Flatten layer, and a fully connected layer.

[0137] The effect of the phase-free frequency diversity computational imaging method based on VAE-GAN described in the present invention can be verified by the following simulation experiments:

[0138] 1. Embodiment 1

[0139] In order to verify the superiority of the present invention in the phase-free frequency diversity computational imaging of the near-field metasurface antenna, a set of simulation experiments is conducted to compare the present invention with the traditional method. The simulation test hardware platform parameters are shown in Table 1, and the software platform parameters are shown in Table 2:

[0140] Table 1 Hardware Platform Parameters

[0141]

[0142] Table 2 Software Platform Parameters

[0143]

[0144] 2. Simulation Results and Analysis

[0145] A two-dimensional parallel-plate waveguide metasurface antenna with a waveguide slot feeding mechanism was designed and constructed. The specific parameters are as follows: An open-ended waveguide (OEWG) probe was used as the receiving antenna, and the antenna panel size was 250 , with a dielectric constant of 3.66 and a loss tangent of 0.003. The upper conductor of the waveguide used cELC metamaterial resonators, and the Q value of each resonator was between 50 and 60. The substrate thickness between the copper ground plane and the conductive copper metamaterial aperture was 0.5 . The imaging experiment was based on the simulated radiation pattern data of the metasurface antenna and the imaging scenario. The operating bandwidth of this antenna was 33 - 37 GHz, the frequency sampling interval was 10 MHz, and the radiation pattern at each frequency point was sampled along the two-dimensional spherical coordinate system of elevation angle and azimuth angle. The size of the elevation angle of the field of view (FOV) was , and the azimuth sampling line of sight was , with a sampling interval of 10 MHz. The radiation pattern at each frequency point was sampled along the two-dimensional spherical coordinate system of elevation angle and azimuth angle. The size of the elevation angle of the field of view (FOV) was , and the azimuth sampling line of sight was , with a sampling interval of , and the size of the original radiation pattern T was .

[0146] During the simulation process, the initial image sizes of the complex target FMNIST data and the sparse target MNIST dataset were modified to , the random scene target scattering coefficient values range from 0 to 1. 20,000 target images are selected from each of the above two datasets, and the PFDCI-MNIST and PFDCI-FMNIST datasets are generated through computational imaging methods, and they are divided into a 70% training set and a 30% test set. The Adam optimization technique is adopted, with a learning rate of 0.0001, a batch size of 256, the dimension of the latent vector z is set to 40, and the imaging model is configured to be trained for 1000 epochs. It should be emphasized that the imaging simulation considers a noiseless scene throughout the process, and for a fixed measurement mode and scene compression ratio. In order to conduct numerical experiments and performance evaluations more reasonably, three targets are selected from the above datasets respectively for imaging comparison. The measurement mode of the measurement matrix is selected as 400, which is equivalent to the scene information sampling rate M / N = 0.1. The network reconstruction results are as Figure 4 shown.

[0147] To further evaluate the performance of the computational imaging method proposed in the present invention, the experimental conditions with different scene information compression ratios are set to 0.025, 0.05, and 0.1, and the scene target scattering coefficient ranges from 0 to 1. The computational imaging method proposed in the present invention can still provide reconstructed targets with clear target contours and good resolutions, demonstrating the strong flexibility and efficiency of the computational imaging method proposed in the present invention. The experimental results are as Figure 5 shown.

[0148] Then, in order to further illustrate the performance of the computational imaging method proposed in the present invention, the experimental conditions under different scene compression ratios are set to 0.025, 0.05, and 0.1, and the scene target scattering coefficients of all point scatterings vary from 0 to 1. At the same time, a comparative experiment is conducted between the traditional sparse Bayesian learning algorithm (SBL) and the computational imaging method proposed in the present invention under the same experimental conditions. The experimental results are as Figure 6 shown.

[0149] As Figure 7 shown, the peak signal-to-noise ratio (PSNR) and the structural similarity index measure (SSIM) are used to qualitatively evaluate the accuracy of imaging reconstruction and the quality of imaging results. As the scene information compression ratio M / N increases, the PSNR and SSIM of both computational imaging methods increase. At the same scene sampling rate, the images reconstructed by the computational imaging method proposed in the present invention have a significant improvement in PSNR.

[0150] In addition, the time spent on reconstructing the scene target for the two computational imaging methods was also recorded. Considering that the neural network-based method can be easily parallelized and the end-to-end network can directly convert the amplitude values of the echo signals into the target after compression, the classical computational imaging method requires multiple iterations to predict a feasible solution. Therefore, the reconstruction time of the PFDCI network algorithm was recorded using the CPU and GPU. Table 3 shows the average running time of 10 experimental tests of the two computational imaging methods on different targets. The computational imaging method proposed in the present invention takes less time than the SBL computational imaging method. Therefore, this method has superiority in terms of imaging efficiency.

[0151] Table 3 Imaging running time

[0152]

[0153] To further evaluate the flexibility and noise resistance of the computational imaging method proposed in the present invention, additive noise was incorporated into the generation process of the dataset. The scene information sampling rate of the dataset was set to 0.1, and the signal-to-noise ratio SNR was set to 0 dB, 5 dB, and 10 dB. After 1000 rounds of testing, the reconstruction results are as Figure 8 shown, demonstrating the effectiveness of the PFDCI network algorithm in reconstructing complex scenes. At the same time, the changes in the PSNR and SSIM curves of the complex target FMNIST data and the sparse target MNIST dataset were quantitatively analyzed at different signal-to-noise ratios and a fixed scene information sampling rate of 0.1. The experimental results are as Figure 9 shown.

[0154] In summary, the beneficial effects that the present invention can bring are as follows:

[0155] 1. The scene is observed using the spatial radiation field generated by the metasurface antenna, and frequency-diversity scene imaging without phase is achieved by combining deep neural network and compressive sensing technologies, thus completely avoiding the errors caused by phase recovery and reducing the computational complexity of the frequency-diversity CI reconstruction problem.

[0156] 2. Utilizing the superior prior inference ability of the Variational Auto-Encoders (VAE) and the powerful generation ability of the Generative Adversarial Networks (GAN), an inference model and a conditional prior model are added to the generative model to extract the prior knowledge of the target from the amplitude values of the echo measurements scattered by the provided scene target, improving the performance of target image generation.

[0157] 3. Use the PFDCI-Net training algorithm to optimize the imaging network model by combining the use of MSE and KL divergence as cost functions, update the cost function using the Adam method, and perform iterations using the gradient descent method. After training, the cost function can quickly tend to converge, achieving fast and accurate reconstruction of the original target, and improving the imaging accuracy and efficiency.

[0158] As described above, only the specific preferred embodiments of the present invention are provided, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention, according to the technical solution and inventive concept of the present invention, makes equivalent substitutions or changes, and should be covered within the protection scope of the present invention.

Claims

1. A computational imaging method for non-phase frequency diversity based on VAE-GAN, characterized in that, The method includes the following steps: S1. Construct a mathematical model for near-field imaging of the metasurface antenna; In step S1, the process of constructing the mathematical model for near-field imaging of the metasurface antenna is as follows: S11. The probe of the metasurface antenna receives the echo measurement value g scattered by the target in the scene to be detected; among them, the echo measurement value g scattered by the scene target includes all the backscattering components of the scene target, and the echo measurement value g scattered by the scene target comes from the incident field scattered by the objects in the scene; S12. Construct a scene measurement matrix H; among them, the scene measurement matrix H is a set of radiation electric fields from the transmitting antenna and the receiving probe at each position in the scene; S13. By constructing the mapping relationship between the echo measurement value g scattered by the scene target, the scene measurement matrix H, and the scene target scattering coefficient σ, obtain the mathematical model for near-field imaging of the metasurface antenna; S2. Based on the mathematical model for near-field imaging of the metasurface antenna, and by combining deep neural network and compressive sensing technology, construct the PFDCI-Net imaging network; In step S2, based on the mathematical model for near-field imaging of the metasurface antenna, and by combining deep neural network and compressive sensing technology, construct the PFDCI-Net imaging network, the specific process is as follows: S21. Input the echo measurement value scattered by the scene target into the encoder E of the PFDCI-Net imaging network, infer a latent vector z, and learn the relationship between the training samples and the latent vector z; S22. Input the latent vector z into the generator G of the PFDCI-Net imaging network to generate fake samples for training; S23. By training the discriminator D of the PFDCI-Net imaging network, use the discriminator D to monitor and discriminate the fake samples generated by the generator G and the real samples from the real data; S3. Design a network training algorithm for the PFDCI-Net imaging network, and optimize the PFDCI-Net imaging network to minimize the loss of the PFDCI-Net imaging network; In step S3, design a network training algorithm for the PFDCI-Net imaging network, and optimize the PFDCI-Net imaging network to minimize the loss of the PFDCI-Net imaging network, specifically: S31. Obtain a training dataset \(\{(σ_1,g_1),(σ_2,g_2),(σ_3,g_3),\cdots,(σ_n,g_n)\}\) containing \(n\) training samples \(x\). Based on the mathematical model of metasurface antenna imaging \(|g|\) n ,g n )\}, design a network training algorithm for the PFDCI-Net imaging network according to \(|g|\) i | 2 =|Hσ i +n| 2 . Among them, σ i is the scattering coefficient of the i-th scene target in the training dataset; g i is the echo measurement value scattered by the i-th scene target in the training dataset; S32. In the PFDCI-Net imaging network, input the measurement matrix H, the number of iterations T, the echo measurement value g scattered by the scene target, the scene target scattering coefficient σ, and initialize the encoder E, the generator G, and the discriminator D; S33. Use the mean square error function MSE to calculate the loss MSE between the fake sample and the real sample as: In formula (4), σ i represents the i-th original scene target scattering coefficient in σ = [σ1, σ2, σ3, …, σ n , and σ^ i represents the fake sample generated by the generator G; S34. Use the KL divergence D KL Calculate the gap between the probability distribution of the training sample x and the probability fitting distribution. The specific formula is as follows: In formula (5), p(x) represents the probability distribution of sample x, and q(x) represents the probability fitting distribution of sample x; Optimize the objective function L(θ), and the specific formula is: In formula (6), q φ (z|x) represents the output distribution function of the decoder, p θ (x,z) represents the joint probability distribution of the training sample x and the latent vector z, p(z) represents the prior distribution function of the latent vector z, z ∼ q means that the latent vector z follows the probability distribution of the output distribution function, p θ (x|z) represents the conditional distribution function; S35. Use the Adam algorithm to update the cost functions of the discriminator D and the generator G: In formula (7), D(σ) represents the output of the discriminator D for the scene target scattering coefficient, D(G(E(g))) represents the output of the discriminator D for the fake data G(E(g)) generated by the generator G after the target echo data passes through the decoder, and s represents the number of samples extracted; The encoder E and the generator G are jointly optimized by the following cost function: In formula (8), g represents the measured echo value of the scene target scattered received by the probe, H represents the measurement matrix constructed by the emission field and the scattering field, G(E(g)) represents the fake sample generated by the generator G, λ represents the regularization parameter, and q φ (z|y) represents the prior conditional probability distribution of the latent vector z, p θ (z) represents the probability distribution of the latent vector z; The imaging network is alternately trained using the generator G and the discriminator D with the min-max cost function, and the specific formula is: In formula (11), x ~ P data (x) represents the data distribution of the training sample x, z ~ q φ (z|y) represents the prior conditional probability distribution of the latent vector z, φ represents the weight parameter, D(x) represents the output of the discriminator D for the training sample x, and D(G(z)) represents the output of the discriminator D for the generated fake sample G(z); Step 36, calculate the gradient of the measurement matrix H Update the weight coefficients of the convolutional layer, and update the first-order moment vector and the second-order moment vector Update the objective function parameters Until the cost function of the training converges, that is, the training cycle ends; S4. Use the target FMNIST data and the target MNIST dataset to train the PFDCI-Net imaging network to obtain the scattering coefficients of the reconstructed target scene In step S4, use the target FMNIST data and the target MNIST dataset to train the PFDCI-Net imaging network to obtain the scattering coefficients of the reconstructed target scene. The specific process is as follows: S41. Obtain the training set (σ tr , g tr ) and the test set g t , set the maximum number of iterations T for training the PFDCI-Net imaging network, and initialize the weight parameters W of the encoder E, generator G, and discriminator D in the PFDCI-Net imaging network; S42. In each iteration, s scene target scattering coefficients {σ1, σ2, σ3, …, σ tr , g tr} are extracted from the training set (σ s , g i ). According to |g 2 | i = |Hσ 2 + n| s , the echo measurement values {g1, g2, g3, …, g s} corresponding to the s scene target scattering coefficients are calculated for the scene target scattering. The echo measurement values {g1, g2, g3, …, g s} of the scene target scattering are input into the PFDCI-Net imaging network. The mean squared error (MSE) function and the Kullback-Leibler (KL) divergence are used as the cost functions of the PFDCI-Net imaging network to train the weight parameters W of the encoder E, generator G, and discriminator D in the PFDCI-Net imaging network; S43. After T iterations, the cost function of the PFDCI-Net imaging network gradually converges, and the value of the cost function tends to a minimum value, and the training of the PFDCI-Net imaging network is completed; S44. Input the test set g t into the trained near-field PFDCI-Net imaging network to obtain the scattering coefficient σ of the reconstructed target scene t .

2. A computational imaging method for phase-free frequency diversity based on VAE-GAN according to claim 1, characterized in that, In step S13, by constructing the mapping relationship between the echo measurement value g of the scene target scattering, the scene measurement matrix H, and the scene target scattering coefficient σ, the specific process is as follows: The integral form of the echo measurement value g of the scene target scattering is: In formula (1), g(f) is the measured echo value of the scene target scattered at different frequencies; V represents the near-field space; represents the magnitude of the radiated electric field of the transmitting antenna at different frequencies in the scene at the location; represents the magnitude of the radiated electric field of the receiving probe at different frequencies in the scene at the location; represents in the scene the scene target scattering coefficient at the location; represents the vector pointing to free space; Write formula (1) in the form of a discrete matrix equation, that is, the near-field imaging mathematical model of the metasurface antenna is: g = Hσ + n(2) Write formula (2) in the form of the intensity measurement of the compressed waveform, that is: |g| 2 = |Hσ + n| 2 (3).

3. A computational imaging method for phase-free frequency diversity based on VAE-GAN according to claim 1, characterized in that, In step S21, input the echo measurement value of the scene target scattering into the encoder E of the PFDCI-Net imaging network to infer a latent vector z, and learn the relationship between the training samples and the latent vector z. The specific process is as follows: Mathematical Model for Near-Field Imaging of Metasurface Antenna |g| 2 = |Hσ + n| 2 , input the measured echo value |g| of the scene target scattered 2 into the encoder E. After passing through five fully connected layers, the mean μ and variance δ of the measured echo value of the scene target scattered are obtained, and inferred to a latent vector z; The encoder E learns the hidden relationship between the training sample x and the latent vector z. Given the training sample x, the conditional probability distribution of the latent vector z is p(x|z); Among them, the latent vector z contains the contour feature information of the target scene.

4. A computational imaging method for phase-free frequency diversity based on VAE-GAN according to claim 1, characterized in that, In step S22, input the latent vector z into the generator G of the PFDCI-Net imaging network to generate fake samples for training. The specific process is as follows: Generate fake samples through generator G, and generator G learns the distribution p of training samples x g , the prior distribution p of the input noise variable z (z), and map the mapping from the latent vector z to the original scene target as G(z; θ g ), where θ g is the weight of generator G.

5. A computational imaging method for phase-free frequency diversity based on VAE-GAN according to claim 1, characterized in that, In step S23, by training the discriminator D of the PFDCI-Net imaging network, use the discriminator D to monitor and discriminate the fake samples generated by the generator G and the real samples from the real data. The specific process is as follows: The sample features are extracted by the translation of the convolutional layer of the discriminator D from the fake samples generated by the generator G or the real samples from the real data. After passing through the Flatten layer, the multi-dimensional data is converted into a one-dimensional sequence, and the extracted sample features are integrated through the fully connected layer to maximize the probability of assigning the correct label to the fake samples generated by the generator G and the real samples from the real data.

6. A PFDCI-Net imaging network applied to the computational imaging method according to any one of claims 1-5, characterized in that, The PFDCI-Net imaging network consists of an encoder E, a generator G, and a discriminator D; The encoder E consists of three serially connected fully connected layers plus two parallel five-layer fully connected layers, and each fully connected layer contains N neurons; The generator G consists of five serially connected fully connected layers; The discriminator D consists of a convolutional layer, a Flatten layer, and a fully connected layer.

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