CN114626987A - Electromagnetic backscattering imaging method of deep expansion network based on physics - Google Patents

Abstract

The invention discloses an electromagnetic backscattering imaging method based on a physical deep-developed network, which comprises the following steps: 1, constructing mixed input data, including data acquisition and preprocessing, and enriching network input information; 2, in a network structure building stage, designing a network structure of a deep expansion technology by using the deep expansion technology in combination with a traditional subspace optimization iterative algorithm; designing a loss function, and jointly optimizing a network by using the image structure similarity loss and the pixel-by-pixel loss in the objective function, particularly using the induced current loss and the scattered field loss; 4, by training the deep expansion network, the induced current, the scattering field and the contrast of the target scatterer can be quickly reconstructed with high quality. The deep-expansion network based on physics provided by the invention can effectively replace the traditional SOM iterative algorithm, enrich the physical knowledge of the network and realize rapid and high-precision electromagnetic backscatter imaging.

Description

Electromagnetic backscattering imaging method of deep expansion network based on physics

Technical Field

The invention belongs to the technical field of electromagnetic backscatter imaging, and particularly relates to electromagnetic backscatter imaging by effectively replacing a traditional SOM iteration method with a deep learning method.

Background

Electromagnetic backscattering is the determination of properties, such as position, shape and physical parameters, of unknown scatterers within a spatial region from the distribution of the scattered field within that spatial region. However, the electromagnetic backscattering problem (ISP) presents a high degree of nonlinearity and pathophysiology, the nonlinearity is due to multiple scattering effects between the measured scattering field and the scatterer, and the pathophysiology is mainly due to the fact that small perturbations of the observed data will cause large errors in the solution. The ISP can be solved by conventional objective function methods, which mainly include back propagation method (BP) of linear approximation, modified born iteration method (DBIM) of nonlinear iteration, Contrast Source Inversion (CSI), Subspace Optimization (SOM), and the like. In the traditional method, fluctuation physics is integrated into a model, but the linear method is rough in imaging, and the iterative method is high in calculation cost and long in time consumption.

In recent years, due to the strong learning mapping capability and the fast solving speed of the deep learning network, researchers successfully apply the deep learning network to solving the electromagnetic backscattering problem. For example, the Direct Inversion Scheme (DIS) proposed by Wei et al is a typical algorithm for mapping scatterers from a scattering field to a target scatterer using a neural network, but it can only reconstruct some simple scatterers within a training set. Li et al propose a 'DeepNIS' algorithm based on a rewinding product neural network by analogy of the relation between the traditional nonlinear iterative method and CNN. Some studies convert the target domain from the contrast domain to the current domain. The 'ICLM' algorithm proposed by Wei et al uses a cascaded network exclusively for learning the fuzzy part of the induced current. Huang et al simplify the backscattering problem to an image translation problem, first use the back-propagation method to obtain a coarse image, and then use the neural network to achieve high resolution reconstruction of the image. The test results in the above paper show that the current depth inverse scattering method is superior to the traditional nonlinear optimization method in both imaging quality and speed.

The above approach is limited by the quality of the input and the prior of the scatterer boundary type, and the generalization capability is limited especially when the network lacks physical knowledge guidance. The deep backscattering method needs to take into account physical model consistency and data consistency. The method makes up the gap between the traditional objective function method and the deep learning method driven by data, and effectively embeds physical knowledge into the deep neural network to realize high-quality imaging, which is a key technical problem.

Disclosure of Invention

The invention aims to solve the key technical problems and provides an electromagnetic backscattering imaging method based on a physical deep unfolding network, so that the deep unfolding technology, an SOM iteration framework and the existing physical knowledge can be effectively combined, the network learns the physical knowledge and enhances the generalization capability of a model, the rapid and high-precision electromagnetic backscattering imaging is realized, and the high-quality reconstruction of the induced current, the scattering field and the contrast of a scatterer is further realized.

The invention adopts the following technical scheme for solving the technical problems:

the invention discloses an electromagnetic backscattering imaging method based on a physical deep unfolding network, which is characterized by comprising the following steps of:

step one, constructing mixed input data, including data acquisition and preprocessing;

step 1.1, the electromagnetic scattering system adopts T transmitting antennas and R receiving antennas, and a target scatterer is placed in a square region of interest D

The transmitting antennas sequentially transmit plane wave signals to the region of interest D, and the R receiving antennas simultaneously measure a scattered field;

step 1.2, during forward performance, calculating the target scatterer by adopting a moment method

Analog induced current of

And simulating the scattered field

Step 1.3, during inversion, dispersing the region of interest D into a grid with the size of M multiplied by M, and forming M by the same²A sub-grid;

step 1.4, the simulated scattered field is decomposed by using singular values

Processing to obtain dimension [ M²,T]Deterministic partial current

Wherein, T represents T transmitting antenna channels;

step 1.5, changing deterministic partial Current

And obtaining the dimension of [ T, M]Three-dimensional current image matrix of

Step 1.6, three-dimensional current image matrix

Adding a dimension for storing the three-dimensional current image matrix

Real and imaginary parts of (a), thereby obtaining a dimension of [ T, N ]₁,M,M]Deterministic current matrix

Wherein, N₁Representing said deterministic current

The number of real and imaginary channels of (1);

step 1.7, utilizing a back propagation method to simulate the scattered field

Processing to generate dimension [ M, M]Low resolution scatterer image χ_BP；

Step 1.8, correcting the low-resolution scatterer image chi_BPAdding a dimension for storing the low resolution scatterer image χ_BPTo obtain an imaginary part of dimension [ N ]₂,M,M]Three-dimensional image matrix of

Step 1.9, the three-dimensional image matrix is processed

Adding one dimension for storing T three-dimensional image matrixes

To obtain a dimension of [ T, N₂,M,M]Low resolution contrast image of

Wherein N is₂Representing the low resolution contrast image

The number of imaginary channels of (a);

step 1.10, the deterministic current is applied

And the low resolution contrastDegree image

Splicing in the second dimension to obtain the dimension [ T, N, M]Mixed input data x of (2); wherein N is N₁+N₂Representing mixed input data x₁The number of real and imaginary channels of (a);

step two, building a deep expansion network P_θAnd mixing the input data x₁As a deep developed network P_θBy said deep-developed network P_θOutputting the target scatterer

Approximately true full induced current of

Step 2.1, cascading K subnetworks { P }_θ,k|k∈[1,K]Form a deep-developed network P_θ(ii) a Wherein, P_θ,kRepresents the kth cascaded subnetwork; and the kth cascaded subnetwork P_θ,kAdopting a U-net structure comprising a contraction path and an expansion path;

the contraction path is formed by adding a maximum pooling layer after two convolution blocks in sequence, wherein each convolution block is formed by a convolution layer with convolution kernel size of a multiplied by a, a BN layer and a ReLU activation function;

the expansion path is formed by adding two convolution blocks after one deconvolution operation in sequence, the deconvolution operation is formed by a deconvolution layer with a convolution kernel of b multiplied by b, and the structure of the convolution blocks is the same as that of the contraction path;

step 2.2, when k is 1, the mixed input data x₁Inputting the deep developed network P_θAnd passes through the kth sub-network P_θ,kThe feature map f with the dimension of c x c is obtained by the contraction path processing of (1)_kThen the k-th sub-network P is output after the processing of the expanded path_θ,kPredicted induced current

According to the induced current

Obtaining the target scatterer by using a state equation, a data equation and a contrast updating formula of the SOM

K predicted total field of

Predicted scatter field k

And the k-th predicted contrast image

When K is 2,3, K, the K-1 st sub-network P_θ,k-1Output induced current matrix

And the k-1 st scattered field image matrix

Splicing in the second dimension to obtain the kth mixed input data x_kAnd passes through the kth sub-network P_θ,kOutput the k-th predicted induced current matrix

Thereby consisting of the Kth sub-network P_θ,KOutputting the Kth predicted induced current matrix

And as a deep deployment network P_θApproximate real complete induction current of output

Then according to the complete induction current which is approximate to the real

Further obtaining the target scatterer by using a state equation, a data equation and a contrast updating formula of the SOM

Including predicting the total field

Predicting the scattered field

And predicting the contrast image

Step three, designing a loss function and establishing a deep expansion network P_θThe optimization objective of (2);

step 3.1, constructing a deep expansion network P by using the formula (1)_θTarget loss function L of_P：

L_P＝L_J+L_E+λ₁L_SSIM+λ₂L_MSE (1)

In the formula (1), L_JRepresents an induced current loss and is obtained by the formula (2); l is_ERepresents the scattered field loss and is obtained by the formula (3); l is_SSIMRepresents a loss of contrast image quality and is obtained by equation (3); l is_MSERepresents the pixel-by-pixel loss and is obtained by the formula (4); lambda₁，λ₂Is a hyper-parameter used to balance the effects of image quality loss and pixel-by-pixel loss;

in the formula (2), the reaction mixture is,

target scatterer corresponding to j-th transmitting antenna

Approximately real induced current matrix of

Target scatterer corresponding to j-th transmitting antenna

The simulated induced current of (a);

in the formula (3), the reaction mixture is,

representing the scattered field predicted by the depth expanded network corresponding to the ith receiving antenna,

target scatterer corresponding to the first receiving antenna

The true fringe field of (a);

in the formula (4), SSIM represents loss of image structural similarity;

in the formula (5), N represents the number of pixels of one contrast image;

representing a predicted contrast image

The corresponding contrast value of the qth pixel point of (1);

representing a target scatterer

The corresponding contrast value of the qth pixel point of (1);

fourthly, reconstructing induced current, scattering field and contrast of the scatterer by training a deep unfolding network;

based on the mixed input data x₁For the deep developed network P_θLearning is performed and the loss function L is calculated_PIn the process, the network parameter theta is continuously optimized, so that the induced current, the scattering field and the contrast ratio image output by network reconstruction are gradually fitted to the physical quantity corresponding to the real scatterer, and an optimal network model is obtained and is used for realizing the reconstruction of the induced current, the scattering field and the contrast ratio image with high quality.

Compared with the prior art, the invention has the beneficial effects that:

1. the invention provides an electromagnetic backscattering imaging method of a deep expansion network based on physics, which uses two characteristic information of induction current and contrast to carry out mixed input network, enriches the input characteristic information, reduces the nonlinear difficulty of network learning, and improves the network reconstruction quality and the network reconstruction efficiency.

2. The method utilizes the deep expansion technology to combine the traditional SOM iteration method and the existing physical knowledge to establish physical network mapping, uses the characteristic information such as induced current, scattered field and contrast to carry out comprehensive constraint, effectively replaces the traditional SOM iteration method, contains rich physical knowledge, and improves the network prediction accuracy and generalization capability.

3. In addition to a contrast loss function, a current loss function and a scattered field loss function are particularly introduced into the target function, so that the consistency of a physical model and the consistency of data are ensured, and the generalization capability of a physical network is better enhanced.

Drawings

FIG. 1 is a flow chart of the method of the present invention;

FIG. 2 is a diagram of a deep expanded subnetwork structure of the present invention;

FIG. 3 is a diagram showing a result of reconstructing a MNIST handwritten digital data set according to the present invention;

FIG. 4 is a graph showing the reconstruction results of Test #1 induced current and scattered field with 10% noise added according to the present invention;

FIG. 5 is a diagram showing the reconstruction result of "Austria" data set with different proportions of noise added according to the present invention;

FIG. 6 is a graph showing the reconstruction results of induced current and scattered field of "Austria" with 25% noise added in accordance with the present invention;

FIG. 7 is a diagram showing the result of experimental data reconstruction with a frequency of 3GHz according to the present invention;

FIG. 8 is a graph showing the reconstruction results of induced current and scattered field of the experimental data with the frequency of 3GHz according to the present invention.

Detailed Description

In this embodiment, an electromagnetic backscatter imaging method based on a physical deep expansion network is to mix input data x₁As a deep developed network P_θOf the approximate real induced current matrix of the scatterer

As a deep developed network P_θAn output of (d); the traditional SOM method is effectively replaced by using a deep expansion technology in combination with the traditional SOM iterative process, and one-time iterative process of the SOM is mapped into a deep expansion network P_θEach module updates the induced current and the contrast simultaneously, and the deep spreading network P_θRealize complete inductionBesides the high-quality reconstruction of the current, the scattering field and the contrast can be further obtained through calculation of a state equation, a data equation and a contrast updating formula of the SOM. Specifically, as shown in fig. 1, the method comprises the following steps:

step one, constructing mixed input data, including data acquisition and preprocessing;

step 1.1, the electromagnetic scattering system adopts 16 transmitting antennas T and 32 receiving antennas R, and places target scatterers in a square region of interest D

The transmitting antenna sequentially transmits plane wave signals to the interested region D, and the scattering fields are measured simultaneously by 32 receiving antennas; assuming an operating frequency of 400MHZ, the region of interest D is 2.0 meters by 2.0 meters.

Step 1.2, placing a target scatterer in the region of interest D during forward operation

To avoid the occurrence of the "inverse crime" phenomenon in the inverse problem, for each incidence, the target scatterers were calculated on a 100 × 100 grid using the moment method

Analog induced current of

And simulating the scattered field

Step 1.3, in inversion, dispersing the region of interest D into a grid with a size of M × M-64 × 64, and forming M together²4096 sub-grids;

step 1.4, simulating a scattering field by using singular value decomposition

Processing to obtain dimension [ M²,T]＝[4096,16]IndeedQualitative partial current

Step 1.5, changing deterministic partial Current

And obtaining the dimension of [ T, M]＝[16,64,64]Three-dimensional current image matrix of

Step 1.6, three-dimensional current image matrix

Adding a dimension for storing a three-dimensional current image matrix

To obtain the real and imaginary components of dimension [16,2, 64%]Deterministic current matrix

Step 1.7, simulating the scattered field by using a back propagation method

Processing to generate dimension [ M, M]Low resolution scatterer image χ_BP；

Step 1.8, aiming at low-resolution scatterer image chi_BPAdding one dimension for storing low-resolution scatterer images x_BPTo obtain an imaginary part of dimension N₂,M,M]＝[1,64,64]Three-dimensional image matrix of

Step 1.9, three-dimensional image matrix

Adding one dimension for storing T-16 three-dimensional image matrixes

To obtain a dimension of [ T, N₂,M,M]＝[16,1,64,64]Low resolution contrast image of

Step 1.10, deterministic Current

And low resolution contrast images

Splicing in the second dimension to obtain the dimension [16,3,64]Mixed input data x of₁；

The invention adopts MNIST handwritten figures added with random circles as a training set, each scatterer is assumed to be uniform and has no loss, the relative dielectric constant is randomly distributed between 1.5 and 2.5, and the background is a free space; wherein the training set scattered field does not contain noise, and the test set scattered field is added with 10% of Gaussian noise. 5000 pieces of MNIST training sets added with a random circle are randomly selected as training sets, 2500 pieces of MNIST training sets are selected as verification sets, and 1500 pieces of MNIST testing sets added with a random circle are randomly selected as tests. In order to verify the effectiveness of the model under different shapes and different noise levels and the generalization capability of the model to real data, four pieces of experimental data with different shapes, different proportions of noise added, dielectric constant of 2 and configuration frequency of 3GHz are generated respectively;

step two, building a deep expansion network P_θAnd mixing the input data x₁As a deep developed network P_θBy a deep-developed network P_θOutput target scatterer

Approximately true full induced current of

Step 2.1, cascading K sub-networks { P }_θ,k|k∈[1,K]Form a deep-expanded network P_θ(ii) a Wherein, P_θ,kRepresents the kth cascaded subnetwork; in the present embodiment, K ═ 4; and the kth cascaded subnetwork P_θ,kAdopting a U-net structure comprising a contraction path and an expansion path; the network structure of the sub-network is shown in fig. 2; in this embodiment, the number of input channels and the number of output channels of the deep-scaling network are 3 and 2, respectively.

The contraction path is formed by adding a maximum pooling layer after two convolution blocks in sequence, wherein each convolution block is formed by a convolution layer with convolution kernel size of 3 multiplied by 3, a BN layer and a ReLU activation function; the maximum pooling layer performs down-sampling on the output feature map of the convolution block, the size of the feature map is reduced by half and the number of channels is multiplied by 2 after each down-sampling;

the expansion path is formed by adding two convolution blocks after one deconvolution operation in sequence, the deconvolution operation is formed by a deconvolution layer with a convolution kernel size of 2 multiplied by 2, and the convolution blocks have the same structure as the contraction path; after each deconvolution, the size of the feature graph is doubled and the number of channels is halved, and meanwhile, after each deconvolution operation, feature information of different depths is fused by using jump connection and feature graphs with the same size from corresponding contraction paths. At the last layer of the network, a 1 × 1 convolutional layer is provided, and this operation can convert the 64-channel features into the required number of feature channels;

step 2.2, when k is 1, mixing the input data x₁Input deep unfolding network P_θAnd passes through the kth sub-network P_θ,kThe feature map f having a dimension of c × c 16 × 16 is obtained by the narrowing-down path processing of (1)_kThen the k-th sub-network P is output after the processing of the expanded path_θ,kPredicted induced current

According to the induced current

Obtaining the target scatterer by using a state equation, a data equation and a contrast updating formula of the SOM

K predicted total field of

K predicted scatter field

And the k-th predicted contrast image

When K is 2,3,.., K, the K-1 st sub-network P_θ,k-1Output induced current matrix

And a k-1 st fringe field image matrix

Splicing in the second dimension to obtain the kth mixed input data x_kAnd passes through the kth sub-network P_θ,kOutput the k-th predicted induced current matrix

Thereby consisting of the Kth sub-network P_θ,KOutputting the Kth predicted induced current matrix

And as a deep deployment network P_θApproximate real complete induction current of output

Then according to the complete induction current which is approximate to the real

Further obtaining the target scatterer by using a state equation, a data equation and a contrast updating formula of the SOM

Including predicting the total field

Predicting the scattered field

And predicting the contrast image

Step three, designing a loss function and establishing a deep expansion network P_θThe optimization objective of (2);

deep-developed network P_θAnd continuously obtaining an optimized physical parameter theta in the back propagation process of the loss function, and guiding the network to better learn induced current, scattering field and contrast ratio reconstruction of the target scatterer.

Step 3.1, constructing a deep expansion network P by using the formula (1)_θTarget loss function L of_P：

L_P＝L_J+L_E+λ₁L_SSIM+λ₂L_MSE (1)

In the formula (1), L_JRepresents an induced current loss and is obtained by the formula (2); l is_ERepresents the scattered field loss and is obtained by the formula (3); l is a radical of an alcohol_SSIMRepresents a loss of contrast image quality and is obtained by equation (3); l is_MSERepresents the pixel-by-pixel loss and is obtained by equation (4); lambda [ alpha ]₁，λ₂Is a hyper-parameter to balance the effects of image quality loss and pixel-by-pixel loss;

in the formula (2), the reaction mixture is,

target scatterer corresponding to j-th transmitting antenna

Approximately real induced current matrix of

Target scatterer corresponding to j-th transmitting antenna

The simulated induced current of (a);

in the formula (3), the reaction mixture is,

representing the scattered field predicted by the depth expanded network corresponding to the ith receiving antenna,

target scatterer corresponding to the first receiving antenna

The true fringe field of (a);

in the formula (4), SSIM represents loss of image structural similarity;

in the formula (5), in this embodiment, the number N of pixels in one contrast image is 4096;

representing a predicted contrast image

The corresponding contrast value of the qth pixel point of (1);

representing a target scatterer

The corresponding contrast value of the qth pixel point of (1);

fourthly, reconstructing induced current, scattering field and contrast of the scatterer by training a deep unfolding network;

based on mixed input data x₁For deep developed network P_θLearning is carried out, the nonlinear difficulty of network learning is reduced, the predicted induced current, scattering field and contrast output by a deep expansion network and the physical quantity of a real scatterer are used as constraints, and a loss function L is calculated_PAnd optimizing a network parameter theta, and selecting an optimal network model for realizing high-quality induced current, scattered field and contrast image reconstruction, thereby ensuring the consistency of the physical model and the data consistency.

The deep-unfolding network uses an Adam optimizer, setting beta₁＝0.9，β₂At 0.999, the batch size is set to 1, the training epoch is set to 40, the first 20 epochs maintain an initial learning rate of 0.0002, the learning rate decays linearly from the 21 st epoch until the last epoch learning rate drops to 0. Continuously adjusting network parameters according to the error of the verification set after the mth training, and simultaneously adjusting the hyper-parameter lambda in the experimental process₁And λ₂Balancing the weights between losses until the losses of the network converge, and selecting an optimal model to achieve high-quality reconstruction of unknown scatterers。

The present invention uses Structural Similarity (SSIM) and Root Mean Square Error (RMSE) as evaluation indicators for both intra-and cross-dataset testing. The method provided by the invention is compared with a method for reconstructing the relative dielectric constant by using a U-net network, wherein the target loss function used by the U-net network is L_U＝L_SSIMFor the sake of comparison, the method of reconstructing an image using a U-net network is referred to as U-net in the description of the result.

The method of the present invention performs training and testing on handwritten digital data sets and directly performs testing on "Austria" and experimental data. In the following figures, GT represents a contrast image of a real target scatterer; SOM denotes a reconstructed image using a conventional SOM iterative algorithm; u-net represents the reconstruction of images using a U-net network; the reconstruction result in the MNIST Test set is shown in fig. 3, the first graph in fig. 4 is a current distribution diagram of Test #1 under the action of the first transmitting antenna, from left to right, sequentially including input induced current, predicted complete induced current and simulated induced current, the first row is real part current, and the second row is imaginary part current; the second graph shows the fitting results of the scattered field from each transmit antenna received by all receive antennas, the first line being the real field and the second line being the imaginary field. Meanwhile, the invention also carries out cross-dataset test, and the reconstruction results on the 'Austria' dataset and the experimental data are respectively shown in FIG. 5, FIG. 6, FIG. 7 and FIG. 8. As shown in FIG. 5, the reconstructed results of "Austria" data set with dielectric constant of 2 under different scales of noise, wherein Test #5-Test #8 are sequentially added with 10%, 20%, 25% and 30% of white Gaussian noise; as shown in fig. 6, the current distribution diagram of Test #7 under the action of the first transmitting antenna is sequentially an input induced current, a predicted complete induced current and a simulated induced current from left to right, wherein the first row is a real part current, and the second row is an imaginary part current; the second graph shows the fitting results of the scattered field from each transmit antenna received by all receive antennas, the first line being the real field and the second line being the imaginary field. The result of the experimental data reconstruction with a frequency of 3GHz is shown in fig. 7, in which the dotted line represents the position of the real image; fig. 8 shows a current distribution diagram of experimental data under the action of a first transmitting antenna, which sequentially includes, from left to right, an input induced current, a predicted complete induced current, and a simulated induced current, where a first row is a real part current and a second row is an imaginary part current; the second graph shows the fitting results of the scattered field from each transmit antenna received by all receive antennas, the first line being the real field and the second line being the imaginary field.

According to the reconstruction result, the method can rapidly and accurately reconstruct physical quantities such as scatterer induced current, scattering field, contrast ratio and the like, the deep expansion network trained by the method effectively replaces the traditional SOM iterative method, the consistency and the data consistency of the physical model are ensured, the obvious advantages are shown on 'Austria' data sets and experimental data of different noises, and the fact that the trained physical model learns physical knowledge and has better generalization capability is also proved.

Claims (1)

1. An electromagnetic backscattering imaging method based on a physical depth expansion network is characterized by comprising the following steps:

step one, constructing mixed input data, including data acquisition and preprocessing;

step 1.1, the electromagnetic scattering system adopts T transmitting antennas and R receiving antennas, and a target scatterer is placed in a square region of interest D

The transmitting antennas sequentially transmit plane wave signals to the region of interest D, and the R receiving antennas simultaneously measure a scattered field;

step 1.2, during forward performance, calculating the target scatterer by adopting a moment method

Analog induced current of

And simulating the scattered field

Step 1.3, during inversion, dispersing the region of interest D into a grid with the size of M multiplied by M, and forming M by the same²A sub-grid;

step 1.4, the simulated scattered field is decomposed by using singular values

Processing to obtain dimension [ M²,T]Deterministic partial current

Wherein, T represents T transmitting antenna channels;

step 1.5, changing deterministic partial Current

And obtaining the dimension of [ T, M]Three-dimensional current image matrix of

Step 1.6, three-dimensional current image matrix

Adding a dimension for storing the three-dimensional current image matrix

Real and imaginary parts of (a), thereby obtaining a dimension of [ T, N ]₁,M,M]Deterministic current matrix

Wherein N is₁Representing said deterministic current

The number of real and imaginary channels of (1);

step 1.7, utilizing a back propagation method to simulate the scattered field

Processing to generate dimension [ M, M]Low resolution scatterer image χ_BP；

Step 1.8, aiming at the low-resolution scatterer image x_BPAdding a dimension for storing the low resolution scatterer image χ_BPTo obtain an imaginary part of dimension [ N ]₂,M,M]Of the three-dimensional image matrix

Step 1.9, the three-dimensional image matrix is processed

Adding one dimension for storing T three-dimensional image matrixes

To obtain a dimension of [ T, N₂,M,M]Low resolution contrast image of

Wherein N is₂Representing the low resolution contrast image

The number of imaginary channels of (a);

step 1.10, the deterministic current is applied

And the low resolution contrast image

Splicing in the second dimension to obtain the dimension of [ T, N,M,M]Mixed input data x of (2); wherein N is N₁+N₂Representing mixed input data x₁The number of real and imaginary channels of (a);

step two, building a deep expansion network P_θAnd mixing the input data x₁As a deep developed network P_θBy said deep-developed network P_θOutputting the target scatterer

Approximately true full induced current of

Step 2.1, cascading K sub-networks { P }_θ,k|k∈[1,K]Form a deep-expanded network P_θ(ii) a Wherein, P_θ,kRepresents the kth cascaded subnetwork; and the kth cascaded subnetwork P_θ,kAdopting a U-net structure comprising a contraction path and an expansion path;

the contraction path is formed by adding a maximum pooling layer after two convolution blocks in sequence, wherein each convolution block is formed by a convolution layer with convolution kernel size of a multiplied by a, a BN layer and a ReLU activation function;

the expansion path is formed by adding two convolution blocks after one deconvolution operation in sequence, the deconvolution operation is formed by a deconvolution layer with a convolution kernel size of b x b, and the convolution blocks have the same structure as the contraction path;

step 2.2, when k is 1, the mixed input data x₁Inputting the deep developed network P_θAnd passes through the kth sub-network P_θ,kThe feature map f with the dimension of c x c is obtained by the contraction path processing of (1)_kThen the k-th sub-network P is output after the processing of the expanded path_θ,kPredicted induced current

According to the induced current

Obtaining the target scatterer by using a state equation, a data equation and a contrast updating formula of the SOM

K predicted total field of

Predicted scatter field k

And the k-th predicted contrast image

When K is 2,3,.., K, the K-1 st sub-network P_θ,k-1Output induced current matrix

And the k-1 st scattered field image matrix

Splicing in the second dimension to obtain the kth mixed input data x_kAnd passes through the kth sub-network P_θ,kOutput the k-th predicted induced current matrix

Thereby consisting of the Kth sub-network P_θ,KOutputting the Kth predicted induced current matrix

And as a deep deployment network P_θApproximate real complete induction current of output

Then according to the complete induction current which is approximate to the real

Further obtaining the target scatterer by using a state equation, a data equation and a contrast updating formula of the SOM

Including predicting the total field

Predicting the scattered field

And predicting the contrast image

Step three, designing a loss function and establishing a deep expansion network P_θThe optimization objective of (2);

step 3.1, constructing a deep expansion network P by using the formula (1)_θTarget loss function L of_P：

L_P＝L_J+L_E+λ₁L_SSIM+λ₂L_MSE (1)

In the formula (1), L_JRepresents an induced current loss and is obtained by the formula (2); l is_ERepresents the scattered field loss and is obtained by the formula (3); l is_SSIMRepresents a loss of contrast image quality and is obtained by equation (3); l is_MSERepresents the pixel-by-pixel loss and is obtained by equation (4); lambda [ alpha ]₁，λ₂Is a hyper-parameter to balance the effects of image quality loss and pixel-by-pixel loss;

in the formula (2), the reaction mixture is,

target scatterer corresponding to j-th transmitting antenna

Approximately real induced current matrix of

Target scatterer corresponding to j-th transmitting antenna

The simulated induced current of (a);

in the formula (3), the reaction mixture is,

representing the scattered field predicted by the depth expanded network corresponding to the ith receiving antenna,

target scatterer corresponding to the first receiving antenna

The true fringe field of (a);

in the formula (4), SSIM represents loss of image structural similarity;

in the formula (5), N represents the number of pixels of one contrast image;

representing a predicted contrast image

The corresponding contrast value of the qth pixel point of (1);

representing a target scatterer

The corresponding contrast value of the qth pixel point of (1);

fourthly, reconstructing induced current, scattering field and contrast of the scatterer by training a deep unfolding network;

based on the mixed input data x₁For the deep developed network P_θLearning is performed and the loss function L is calculated_PIn the process, the network parameter theta is continuously optimized, so that the induced current, the scattering field and the contrast ratio image output by network reconstruction are gradually fitted to the physical quantity corresponding to the real scatterer, and an optimal network model is obtained and is used for realizing the reconstruction of the induced current, the scattering field and the contrast ratio image with high quality.

Images