A method for electrical impedance image reconstruction

Abstract

The present invention belongs to the field of electrical impedance tomography, and relates to an electrical impedance image reconstruction method. A dual-branch parallel EIT deep imaging model with U-Net as the backbone model and fusion of a deformable convolution module and a hyperconvolution network is established, named DHU-Net, and the DHU-Net is composed of a dual-branch feature encoder and a feature fusion decoder. The dual-branch encoder uses different convolution operators, and is respectively composed of parallel operations consisting of deformable convolution and channel layer attention mechanism, coordinate attention mechanism and implicit hyperconvolution; skip connections based on the attention mechanism are added in a symmetrical manner between the feature pyramids corresponding to the dual-branch feature encoder and the feature fusion decoder. The DHU-Net proposed by the present invention has better robustness and reconstruction consistency, and at the same time, compared with the densely connected deep model, the number of parameters is less and the reasoning speed is faster.

Description

Technical Field

[0001] The invention belongs to the field of electrical impedance tomography, in particular to an electrical impedance image reconstruction method. Background Art

[0002] Electrical Impedance Tomography (EIT) is a non-invasive, real-time, low-cost emerging imaging technology used to observe and analyze the distribution of electrical characteristics inside an object. It is based on measuring the modulation effect of the object on the current and reconstructing the impedance distribution image through a suitable inverse problem calculation method to provide information about the internal structure and function of the object.

[0003] EIT applications mainly include industrial process parameter detection and visualization (such as multiphase fluid monitoring, non-destructive structural detection), biomedical structural and functional imaging (such as lung breathing monitoring, brain stroke treatment monitoring) and other related fields. However, due to the "soft field" characteristics of the sensitive electric field area formed in the observation area, the EIT inverse problem (i.e., image reconstruction) exhibits significant nonlinearity and pathology, resulting in inaccurate conductivity parameters of the reconstructed image and obvious blurring artifacts at the boundary.

[0004] To solve the above problems, we usually introduce a suitable penalty function to regularize the inverse problem, or use an optimization iterative method to continuously reduce the error between the calculated result and the actual result to obtain the optimal solution. For example, different regularization constraints (L p norm, total variation function, wavelet basis function), relaxed Gauss-Newton iteration method, optimized Land-weber iteration, fast iterative threshold shrinkage algorithm (FISTA), etc.; in addition, direct reconstruction method based on back-projection idea and D-Bar method of nonlinear Fourier transform are adopted. These numerical reconstruction methods often show high dependence on prior models, high computational complexity, and weak migration and generalization, and are not suitable for reconstruction tasks in different scenes.

[0005] In recent years, deep learning methods have achieved great success in the field of computer vision and have been used in inverse imaging to achieve medical image reconstruction, super-resolution reconstruction, image denoising and other tasks. As a typical nonlinear inverse problem, EIT imaging is also widely used by researchers to achieve high-quality image reconstruction using deep learning models. At present, this method can be divided into two categories. One is to directly construct the manifold transformation relationship between the boundary measurement signal and the dielectric distribution image, which is called the "data-driven" imaging method. The other idea is to use numerical calculation results or initial imaging methods to obtain a "rough" distribution, and then use deep learning methods as a post-processing network to enhance the boundary features and electrical parameter information, which is called the "image-driven" imaging method. The "data-driven" imaging method often has a lower spatial pixel resolution than the "image-driven" method, mainly because it is limited by the number of computing units in the network. In addition, the current EIT deep imaging method often uses the operation mode of the regular convolution kernel to process the spatial relationship of the pixel matrix, but ignores the various shape feature information of the inclusions. From the visualization results of the reconstructed image, it is reflected that although the artifacts are significantly suppressed, the curvature and sharpness of the boundary cannot be accurately expressed. Summary of the invention

[0006] In order to solve the problems of poor shape modeling performance caused by the use of fixed convolution kernels and large number of parameters caused by complex feature connections in the current EIT imaging model based on deep learning methods, this paper proposes a dual-branch parallel EIT deep imaging model based on deformable convolution modules and hyperconvolutional networks, named DHU-Net. Visualization experimental results show that this method has good noise robustness and model generalization ability.

[0007] The technical solution adopted by the present invention to solve the technical problem is:

[0008] The present invention provides an electrical impedance image reconstruction method, and establishes a dual-branch parallel EIT deep imaging model based on a deformable convolution module and a hyperconvolution network, named DHU-Net. The DHU-Net consists of a dual-branch feature encoder and a feature fusion decoder. The dual-branch feature encoder uses different convolution operators, which are respectively composed of parallel operations consisting of deformable convolution and channel layer attention mechanism, coordinate attention mechanism and implicit hyperconvolution; skip connections are added in a symmetrical manner between the feature pyramids corresponding to the dual-branch feature encoder and the feature fusion decoder.

[0009] Furthermore, an embedding layer is used before the dual-branch feature encoder for channel expansion, and a 1×1 convolution is used to convert the initial input features Convert to high-dimensional tensor Among them, C is the number of feature map channels, H is the number of feature map heights, and W is the number of feature map widths. is a set of real numbers.

[0010] Furthermore, the deformable convolution uses a 3×3 deformable convolution kernel to learn the shape of the inclusions, that is, the convolution kernel is expressed as:

[0011]

[0012] Assume that the input and output feature tensors of each deformable convolution operator are expressed as and The learning weight of the kth position in the convolution kernel, the position of the output feature map, and the convolution kernel The corresponding sampling points and offsets are denoted as w k ,p0,p k and Δp k ,in Then the operation form of deformable convolution is

[0013]

[0014] Among them, the compensation amount Δp k is a fraction, deformable convolution operation is performed via bilinear interpolation.

[0015] Furthermore, the algorithm of the channel layer attention mechanism includes two parts:

[0016] The first part uses global average pooling to obtain global information in the channel dimension For a C-channel feature map, the result of the c-th channel feature map after global average pooling is

[0017]

[0018] Among them, X input，c is the feature matrix of the cth channel in the feature map, i, j are the pixel units in the i-th row and j-th column of the feature matrix, and z1 is the first channel matrix of the output feature map, z c is the c-th channel feature matrix, z C is the Cth channel feature matrix;

[0019] The second part uses a multi-layer perceptron to perform nonlinear transformation on the compressed features to generate a channel attention tensor. The attention tensor is normalized by a nonlinear function and used to adjust the weight of each channel. Finally, the obtained attention tensor S is used to adjust the weight of the input feature information.

[0020]

[0021] Among them, s1 is the first channel feature matrix of the channel attention tensor, s cis the cth channel feature matrix of the channel attention tensor, s C is the Cth channel feature matrix of the channel attention tensor.

[0022] Furthermore, the coordinate attention mechanism includes two steps: coordinate feature embedding and coordinate feature calculation:

[0023] S1 uses precise location information to encode long-range dependencies when modeling features. Coordinate feature embedding uses a pair of orthogonal 1D pooling to separately Perform feature aggregation along the horizontal and vertical directions respectively to obtain a pair of directional feature tensors and] x represents the cth feature map of the input tensor feature map, h and v represent the horizontal and vertical directions of the feature map, and the calculation process is:

[0024]

[0025] in, and represents the horizontal attention feature tensor and the vertical attention feature tensor, and They represent the 1st, cth, and Cth channel feature maps of the spatial attention horizontal feature tensor respectively. and They represent the 1st, cth, and Cth channel feature maps of the vertical feature tensor of spatial attention respectively;

[0026] The S2 coordinate feature calculation is used to construct the spatial attention tensor and act on the input feature tensor to amplify and splice the orthogonal feature map in formula (10), use 1×1 convolution for channel adjustment, and obtain the mixed feature map after nonlinear projection. Where r is the channel attenuation coefficient, the hybrid feature map combines the spatial encoding information in the horizontal and vertical directions, and then Separate, use 1×1 convolution and nonlinear projection to encode the x-direction and y-direction features again to obtain the directional attention features and And acts on the input feature tensor,

[0027]

[0028] in, Represents the fused feature map tensor after horizontal attention feature extraction and vertical attention feature extraction. and Represents the feature maps The 1st, cth and Cth channels of represents the input feature vector of the fusion module, express The c-th channel feature map of and They represent the horizontal attention feature extraction tensor and the vertical attention feature extraction fused feature map tensor, respectively. h and g v express and Sub-feature map of , the superscript index c represents the c-th channel (c = 1, 2, ..., C):

[0029] When the coordinate attention feature map is obtained Finally, the global information is represented from the abstract spatial feature map.

[0030] Furthermore, the implicit superconvolution is: input two coordinate parameters with the same size as the 5×5 convolution kernel in the x direction and the y direction

[0031]

[0032] Among them, i, j represents the pixel cell in the i-th row and j-th column of the feature map;

[0033] Use implicit representation to fit the coordinate information (i, j) and the corresponding convolution kernel weight parameters The mapping relationship between

[0034]

[0035] Among them, Φ θ Indicates the construction of an implicitly fitted neural network structure. In DHU-Net, a fixed-node full convolution network with 4 layers and a convolution kernel size of 1×1 is used to map the weight relationship between the spatial coordinates of the feature map and the corresponding convolution kernel. The number of nodes in the last layer is recorded as N L is a hyperparameter representing the capacity of the implicit hyperconvolutional model.

[0036] Furthermore, the skip connection is connected in the following way: And coordinate attention-superconvolution features After linear projection, they are recorded as value vectors And the key vector K, and the other input of the corresponding decoder is the upsampled feature map Recorded as feature query vector Perform attention operations,

[0037]

[0038] Among them, dk is the dimension of the vector. After the feature fusion of SA, the decoding module uses two 3×3 convolution operations to aggregate the channel features and restore the decoding features, and the output is used as the input feature of the next decoding module.

[0039] Furthermore, the loss function of DHU-Net is defined as:

[0040]

[0041] in, is the target conductivity image to be reconstructed, y is the input initialization conductivity distribution, is a given training sample, θ is the hyperparameter of DHU-Net to be trained, Used to ensure that the output of the model is as close to the label distribution as possible. is the regularization term of the loss function, and the corresponding λ is the regularization term parameter.

[0042] The advantages and positive effects of the present invention are:

[0043] 1. The DHU-Net of the present invention uses a large number of simulation samples for training and parameter fine-tuning, and is verified on an experimental water tank. The numerical quantification results show that the RMSE result is 2.0637, the SSIM result is 0.9522, and the RSNR result is 46.4597. Compared with the SOTA model, it has better reconstruction visualization effect, and the quantitative indicators are more consistent with the reconstruction results.

[0044] 2. Experimental results show that the DHU-Net proposed in this paper has better robustness and reconstruction consistency, indicating that deformable convolution and implicit neural networks have better expressive ability in shape modeling. At the same time, compared with densely connected deep models, it has fewer parameters and faster inference speed, which can promote the real-time application of EIT in structure and function detection.

[0045] 3. The present invention constructs a new "end-to-end" deep imaging inverse problem solving model, and is used in solving the "soft field" electrical impedance tomography (EIT) problem with pathological and nonlinear characteristics. The deep imaging model designs a symmetrical network structure consisting of a new dual-branch parallel processing encoder and a new attention feature jump connection method. This method divides the traditional EIT image reconstruction problem into a parallel medium shape reconstruction task and an inclusion conductivity parameter reconstruction task, and has a better model operation mechanism compared to a single image reconstruction task.

[0046] 4. In the dual-branch parallel U-Net structure, the traditional convolution layer with a fixed-shape convolution kernel is optimized using a deformable convolution with better geometric shape modeling feature capability. The deformable convolution used in the present invention uses a new parameter compensation operation to model complex geometric shapes, making its modeling capability for graphics more flexible than that of traditional fixed-size convolution kernels, and is particularly suitable for complex shape reconstruction in EIT. This method solves the problem of EIT graphics reconstruction.

[0047] 5. In the dual-branch parallel U-Net structure, the traditional deformable convolution is optimized, and the SE channel attention mechanism is used to learn and characterize the global features. This method aims to solve the problem of ignoring pixel distribution due to focusing on shape features in traditional deformable convolution. At the same time, considering the correspondence of conductivity parameters in pixel distribution in EIT imaging problems, the SE channel attention method is used to model global parameters, and different attention scores are assigned to obtain the corresponding weights of different channels.

[0048] 6. In the dual-branch parallel U-Net structure, the coordinate attention mechanism is used to model the global features in combination with the characteristics of the global conductivity parameter distribution. This module uses a pair of orthogonal convolution kernels to construct global spatial features. The orthogonal convolution kernel is a pair of convolution kernels in the x-direction and y-direction, which respectively construct the conductivity parameter distribution features in two orthogonal directions, and use the attention score method to assign weights to the global parameter distribution, so that different conductivity parameters have different weights.

[0049] 7. Considering the impact of the model parameters on the imaging speed, the present invention uses an implicit convolution structure (i.e., superconvolution) to reduce the number of parameters in conventional convolution operations. The advantage of superconvolution is that it generates weights for another network responsible for the main task, which can improve parameter efficiency and provide flexibility without significantly sacrificing expressiveness. The present invention uses implicit kernel functions for superconvolution calculations, avoiding the problem of large amounts of parameter storage and computation required in traditional convolutions. Implicit kernels can be dynamically generated when needed without explicitly storing all kernel weights, which improves computational efficiency while improving the robustness of the model.

[0050] 8. The present invention uses a skip connection method based on the attention mechanism, which optimizes the direct skip connection method in the traditional encoding and decoding structure. This structure uses the shape feature map and conductivity parameter distribution feature map obtained in the dual-branch encoder as the value vector and key vector of the attention mechanism, and the feature map obtained by upsampling in the decoder as the query vector, and performs self-attention score matching together to obtain the most weighted. Compared with the traditional direct skip connection or additive skip connection, the method used in the present invention can obtain more optimized parameters and improve the problem of long-distance feature information loss. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 Flowchart of the overall structure of DHU-Net;

[0052] FIG2(a) is a flowchart of the deformable convolution (DeformableConvolution) and channel allocation attention mechanism (SE channel-wise Attention) structure used by the feature extraction module operation unit for shape feature learning, and FIG2(b) is a flowchart of the coordinate attention mechanism (CoordinateAttention) and implicit representation hyperconvolution (HyperConvolution) structure used by the feature extraction module operation unit for global parameter learning;

[0053] Figure 3 This is a flowchart of the Skip-Attention Connection.

[0054] Figure 4 Schematic diagram of the reconstruction results of different methods in the simulation test sample;

[0055] FIG5(a) is a diagram showing the RMSE and SSIM quantitative index analysis of different methods in simulation test samples, and FIG5(b) is a diagram showing the PSNR quantitative index analysis of different methods in simulation test samples;

[0056] Figure 6 Schematic diagram of the reconstruction results of different methods in the water tank test sample;

[0057] Figure 7(a) is a quantitative index analysis diagram of RMSE of different methods in water tank test samples, Figure 7(b) is a quantitative index analysis diagram of SSIM of different methods in water tank test samples, and Figure 7(c) is a quantitative index analysis diagram of PSNR of different methods in water tank test samples;

[0058] Figure 8 Schematic diagram of imaging results at different SNR levels, where the 1st and 2nd columns are one inclusion model, the 3rd and 4th columns are two inclusion models, the 5th and 6th columns are three inclusion models, and the 7th and 8th columns are four inclusion models. The size and position of the medium in each model are randomly placed;

[0059] FIG9(a) is a diagram showing the RMSE and SSIM quantitative index analysis of imaging results at different SNR levels, and FIG9(b) is a diagram showing the PSNR quantitative index analysis of imaging results at different SNR levels;

[0060] Fig.10 Schematic diagram of imaging results with different conductivity contrasts. DETAILED DESCRIPTION

[0061] The present invention is further described in detail below through specific examples. The following examples are only illustrative and not restrictive, and the protection scope of the present invention cannot be limited thereto.

[0062] The overall inventive concept of the present invention is:

[0063] 1. Using the "image-driven" approach, a dual-branch deep imaging model with a dual-branch encoding feature extraction module and a deep feature fusion decoding feature recovery module was designed. Different convolution kernel sizes and structures were used for the electrical parameter reconstruction task and shape reconstruction task in EIT imaging respectively.

[0064] 2. Use the deformable convolution operator to extract shape features, and introduce the SE-channel attention mechanism to improve the degree of attention to different shapes in DCN, which can better focus on ROI shape features and avoid the influence of background parameters;

[0065] 3. In order to reduce the traditional electrical parameter feature representation using large convolution kernels for global feature learning, an implicitly expressed hyperconvolution network (HyperConvNets) is used to optimize the model parameters. At the same time, the coordinate attention mechanism (Coordinate) is used to extract the directional feature map before inputting the feature, thereby realizing implicit convolution kernel weight learning.

[0066] The present invention takes a two-dimensional observation area as an example, the observation area is denoted as Ω, and the corresponding boundary is At the border Evenly add L electrodes, denoted as Use an alternating current of a certain frequency I l The induced potential u(x) is injected into the observation area Ω (internal conductivity distribution is σ(x), x is the spatial position) from L contact electrodes and the response voltage of the remaining sensing electrodes is measured (for an EIT sensing system containing L electrodes, a total of L×(L-3) effective voltages are measured to reconstruct one frame of the conductivity image).

[0067] The EIT forward problem is modeled using the complete electrode model (CEM), which includes the conductivity Laplace equation

[0068]

[0069] And the boundary conditions

[0070]

[0071] Among them, n is the boundary The outward normal vector, z lis the contact impedance of the lth electrode, I l , U l is the injection current and boundary measurement voltage of the lth electrode, e l represents the lth sensing electrode. In addition, in order to ensure the uniqueness and existence of the solution, the current conservation and voltage conservation equations are added to the CEM, that is,

[0072]

[0073] The above mathematical models (1)-(3) are solved using the finite element method (FEM), and considering the additive measurement Gaussian noise ε, the observation model is expressed as

[0074]

[0075] in, is the standard measurement voltage vector, is the discrete conductivity vector in the field, is the forward operator.

[0076] The mathematical model of the inverse problem of EIT imaging based on deep learning can be expressed as:

[0077]

[0078] In formula (5), is the training sample, To train the network model, is the loss function, and R(θ) is the regularization term of the model parameters. In the present invention, a differential mode imaging method is used, that is, the conductivity change image is reconstructed using the measured voltage at different times and the potential difference under the reference state.

[0079] The overall structure of DHU-Net is as follows Figure 1As shown in the figure, it is mainly composed of a dual-branch feature encoder and a feature fusion decoder. Specifically, the dual-branch encoder of DHU-Net uses different convolution operators, which are composed of parallel operations consisting of deformable convolution and channel layer attention mechanism, coordinate attention mechanism and implicit super convolution. The decoder has a symmetrical structure, which is used to decode and expand the latent space features learned by the encoder step by step to achieve image restoration and detail reconstruction. DHU-Net adds skip connections in a symmetrical manner between the feature pyramids corresponding to the encoder and decoder, which helps to restore fine-grained details in the prediction. Unlike ordinary skip connections, DHU-Net bridges the gap between the encoder and decoder by designing a new non-local structure (Non-local Networks) based on the attention mechanism.

[0080] An embedding layer is used before the encoder to perform channel amplification, such as Figure 1 As shown, the initial input features are transformed using 1×1 convolution Convert to high-dimensional tensor Among them, C is the number of feature map channels, H is the number of feature map heights, and W is the number of feature map widths. is a set of real numbers.

[0081] The encoding module of DHU-Net is the core part of feature extraction and latent space representation. A new dual-branch feature learning structure is designed, which uses 3×3 local deformable convolution kernels and channel layer attention mechanism to realize shape modeling, and uses coordinate attention mechanism and 5×5 implicit hyperconvolution to realize global parameter learning, which can effectively reduce the number of model parameters while improving the flexibility of the network structure.

[0082] Among them, Deformable Convolution is a method that introduces deformable sampling into traditional convolution operations. It allows the convolution kernel to perform local sampling on the input feature map, so that the model can more accurately capture the details, shape and spatial relationship of the target and improve the modeling ability; secondly, deformable convolution expands the receptive field by offsetting the sampling points, improving the model's perception of the global structure. In addition, compared with standard convolution, deformable convolution does not require additional parameters, and deformable modeling is achieved by adjusting the sampling points, which can improve the model's expression ability while maintaining a relatively small amount of parameters and calculations. DHU-Net uses a 3×3 deformable convolution kernel to learn the shape of the inclusions, that is, the deformable convolution uses a 3×3 deformable convolution kernel to learn the shape of the inclusions, that is, the convolution kernel is expressed as:

[0083]

[0084] Assume that the input and output feature tensors of each deformable convolution operator are expressed as and The learning weight of the kth position in the convolution kernel, the position of the output feature map, and the convolution kernel The corresponding sampling points and offsets are denoted as w k ,p0,p k and Δp k ,in Then the operational form of deformable convolution is:

[0085]

[0086] Among them, the compensation amount Δp k It is usually a fraction, and the calculation process of formula (7) is realized by bilinear interpolation. k It is usually a fraction, and the operation process of formula (7) can be realized by bilinear interpolation, as shown in (a) of Figure 2. In actual operation, firstly, a common convolution layer is used to obtain a tensor that is consistent with the input feature tensor. The same feature map, and the output offset field is the same as the input feature map and output features They have the same spatial resolution (C×H×W), and the number of channels of the offset field is 2N, corresponding to N learning compensation hyperparameters in the x direction and N learning compensation hyperparameters in the y direction.

[0087] After deformable convolution models the features of the contents, the output feature map often focuses more on the expression of spatial structure information and ignores global parameter information. DHU-Net adaptively learns the importance weights between channels by introducing the Squeeze-and-Excitation Attention method (SE-Attention). As shown in (a) in Figure 2, the SE module is divided into two main parts: the first part uses global average pooling (GAP) to obtain global information in the channel dimension. (As shown in the figure F sq (·)). For a feature map of C channels, the result of global average pooling of the feature map of the cth channel is

[0088]

[0089] Among them, X input，c is the feature matrix of the cth channel in the feature map, i, j are the pixel units in the i-th row and j-th column of the feature matrix, and z1 is the first channel matrix of the output feature map, zc is the c-th channel feature matrix, z C is the Cth channel feature matrix;

[0090] The second part is to use a multi-layer perceptron (MLP) to perform nonlinear transformation on the compressed features to generate a channel attention tensor. The attention tensor is normalized by a nonlinear function to adjust the weight of each channel (as shown in the figure F ex (·, W), where F ex (·, W) represents a compression module with weight W). Finally, the obtained attention tensor S is used to adjust the weight of the input feature information (as shown in F scale (·), where F scale (·) represents the scale factor learning module), that is,

[0091]

[0092] Among them, s1 is the first channel feature matrix of the channel attention tensor, s c is the cth channel feature matrix of the channel attention tensor, s C is the Cth channel feature matrix of the channel attention tensor.

[0093] Through the feature encoding of the modules (7)-(9), shape feature modeling can be realized while giving different degrees of attention to different parameter information, so that the network can better focus on key features and understand the model's attention to input features and weight distribution, thereby improving the discriminability of features.

[0094] The coordinate attention mechanism applies the self-attention mechanism to the spatial coordinates, and uses the coordinate information to model the position relationship, so that the network can better perceive the correlation between different positions, and thus better understand the image content. Its structure is shown in (b) in Figure 2. CA includes two main steps: coordinate feature embedding and coordinate feature calculation: S1 encodes the long-range dependency with precise position information when modeling the feature. Coordinate feature embedding uses a pair of orthogonal 1D pooling to respectively process the input tensor Perform feature aggregation along the horizontal direction (x-axis) and the vertical direction (y-axis) to obtain a pair of direction feature tensors (direction-aware feature maps) and x crepresents the cth feature map of the input tensor feature map, h and v represent the horizontal and vertical directions of the feature map, and the calculation process is as follows:

[0095]

[0096] in, and represents the horizontal attention feature tensor and the vertical attention feature tensor, and They represent the 1st, cth, and Cth channel feature maps of the spatial attention horizontal feature tensor respectively. and They represent the 1st, cth, and Cth channel feature maps of the vertical feature tensor of spatial attention respectively;

[0097] This spatial information feature aggregation captures long-range dependencies along the spatial direction and retains more accurate structural features in the space orthogonal to this direction. After obtaining the above orthogonal feature map, S2 coordinate feature computation is used to construct the spatial attention tensor and act on the input feature tensor. The orthogonal feature map in formula (10) is amplified and spliced, and the channel is adjusted using 1×1 convolution, and the mixed feature map is obtained through nonlinear projection. Where r is the channel attenuation coefficient, the hybrid feature map combines the spatial encoding information in the horizontal and vertical directions, and then Separate, use 1×1 convolution and nonlinear projection to encode the x-direction and y-direction features again to obtain the directional attention features and And acts on the input feature tensor,

[0098]

[0099] in, Represents the fused feature map tensor after horizontal attention feature extraction and vertical attention feature extraction. and Represents the feature maps The 1st, cth and Cth channels of represents the input feature vector of the fusion module, express The c-th channel feature map of and They represent the horizontal attention feature extraction tensor and the vertical attention feature extraction fused feature map tensor, respectively. h and g v express and Sub-feature map of , the superscript index c represents the c-th channel (c = 1, 2, ..., C):

[0100] When the coordinate attention feature map χ is obtained CA Finally, the global information is represented from the abstract spatial feature map. However, large-scale convolution kernels (such as 5×5, 7×7, etc.) will result in a large amount of computing resource consumption and poor robustness of the model. DHU-Net uses a hyper-convolution operation (Hyper-Convolution) with implicit feature construction to achieve the global parameter information representation of the 5×5 convolution operation. The core idea of ​​Hyper-Convolution is an implicit representation of the convolution kernel. The coordinate information of the same size as the convolution kernel is input and all weights are generated in the convolution kernel using a neural network, and the implicit coupling is expressed through the function of the hyper-network. Unlike the standard convolution operation, the size of the convolution kernel is a design choice, which does not affect the number of learnable parameters. Its structure is shown in (b) in Figure 2. Specifically, two coordinate parameters with the same size as the 5×5 convolution kernel in the x-direction and y-direction are input.

[0101]

[0102] Among them, i, j represents the pixel cell in the i-th row and j-th column of the feature map;

[0103] Use implicit representation to fit the coordinate information (i, j) and the corresponding convolution kernel weight parameters The mapping relationship between

[0104]

[0105] Among them, Φ θ Indicates the construction of an implicitly fitted neural network structure. In DHU-Net, a fixed-node full convolution network with 4 layers and a convolution kernel size of 1×1 is used to map the weight relationship between the spatial coordinates of the feature map and the corresponding convolution kernel. The number of nodes in the last layer is recorded as N L The hyperparameter represents the capacity of the implicit hyperconvolution model. There are two main advantages of using Hyper-Convolution:

[0106] First, this method uses implicit kernel functions for superconvolution calculations, avoiding the problem of large amounts of parameter storage and computation required in traditional convolution. Implicit kernels can be generated dynamically when needed without explicitly storing all kernel weights, which improves computational efficiency. Specifically, for a Φ with L layers, θ , when the number of channels of the input and output feature maps are C input and C output When , the parameter quantity of the operation unit is

[0107]

[0108] Where N l Indicates the number of nodes in the lth layer, N L is the number of nodes in the last layer. It can be seen from formula (14) that the calculation parameters of Hyper-Convolution do not depend on the size of the convolution kernel, but mainly depend on the number of input and output channels and the number of nodes in each layer. It is worth noting that in the CNNs structure, the number of input and output feature map channels is usually greater than 8. θ The number of hidden layer channels in is set to be less than 8 (i.e. N l <8), then the main parameter of Hyper-Convolution can be expressed as (N L +1)×C input ×C output ,Thus, for a fixed number of parameters, the proposed method can achieve dense kernels with arbitrarily large receptive fields, capturing high-resolution contextual information in the features.,Hyperconvolutions can therefore provide an extended receptive field with high capacity, limiting the risk of overfitting, without increasing the number of trainable parameters.

[0109] 2. Hyper-Convolution robustness: According to the theory that implicit networks tend to learn "low-frequency functions of spectral deviations", there is a correlation between kernel weight values ​​during initialization and gradient-based updates in Hyper-Convolution, which regularizes the convolution kernel weights and makes them smoother in space. It is assumed that the smooth kernel will suppress the high-frequency components of the input features. This is an advantage in the presence of noise, such as pixel additive noise or adversarial perturbations, so Hyper-Convolution can play an important role in the robustness of deep models.

[0110] The feature reconstruction module of the decoder presents symmetric characteristics with each branch of the encoder. Compared with the downsampling block, the present invention uses deconvolution to upsample the low-resolution feature map to the high-resolution feature map, and then merges it through a skip attention connection method to capture semantic and fine-grained information. Combined with the dual-branch feature abstraction structure of the encoder, the present invention designs a skip connection method based on the attention mechanism to replace the feature aggregation method of series connection or addition in the general U-shaped structure module. Its structure is as follows: Figure 3 As shown. The specific connection method is: after the deformable convolution-SE attention feature And coordinate attention-superconvolution features After linear projection, they are recorded as value vectors And the key vector K, and the other input of the corresponding decoder is the upsampled feature map Recorded as feature query vector Performing attention calculation

[0111]

[0112] Among them, d k is the dimension of the vector. After the feature fusion of SA, the decoding module uses two 3×3 convolution operations to aggregate the channel features and restore the decoding features, and the output is used as the input feature of the next decoding module.

[0113] The loss function of DHU-Net is defined as:

[0114]

[0115] in, is the target conductivity image to be reconstructed, y is the input initialization conductivity distribution, is a given training sample, θ is the hyperparameter of DHU-Net to be trained, Used to ensure that the output of the model is as close to the label distribution as possible. is the regularization term of the loss function, and the corresponding λ is the regularization term parameter.

[0116] In the present invention, it is set to 0.01. The training process of the model is to monitor the change of the loss function so that the final model parameter θ * This allows the network to reconstruct the result x that is most consistent with the target * .

[0117] The data used for DHU-Net training and validation are simulation samples based on numerical calculations. A circular area is used to establish an electrically sensitive field, and 16 electrodes are placed at equal intervals as excitation-measurement sensors. The data acquisition mode of "adjacent excitation-adjacent measurement" is adopted. All electrodes are excited and measured once to obtain a total of 208 effective voltages, and the control equations of equations (1)-(3) and the corresponding boundary conditions are used to calculate the EIT positive problem. Among them, the diameter of the observation field is 0.19m, the magnitude of the injected current is 4.5mA, the frequency is 100kHz, water is used as the background inside, and the conductivity is set to 0.06S / m. The internal medium is simulated using different conductivity parameters, and the conductivity is set to 10 -6 -10 -12 Any value within the range of S / m. In addition, the radius of the inclusions is set to 0.02-0.08m, including 42,430 circular samples, 400 samples of other shapes, and a total of 42,830 simulation training samples, of which the training samples, verification samples, and test samples are set to account for 80%, 10%, and 10% of the entire database respectively.

[0118] Based on the simulation training samples of numerical calculation, each set of samples includes a pair of independent feature information vectors, namely, the boundary voltage vector after differential processing. and a discrete numerical matrix describing the conductivity distribution in the region In addition, the sensitivity matrix As prior information, it is used for manifold transformation to convert the measured voltage signal into image pixel features. The voltage features are used as the input of the model for forward propagation to obtain the predicted pixel matrix, and the label information and predicted medium distribution are used as independent variables of the loss function to supervise and constrain the training process of the deep learning model.

[0119] Methods based on deep learning often benefit from a good initialization feature (warm-starting), that is, initialization near the local minimum of the loss function to obtain pre-reconstruction results. For the EIT reconstruction task, the present invention uses a regularization method based on the 2-norm

[0120] x initial =(J T J+αL T L) -1 J T b (17)

[0121] Convert voltage features into image features, where b is the differential voltage vector, x initial is the initial reconstruction result, J is the sensitivity matrix, L is the regularization matrix. For simple calculation, L is set as a diagonal matrix, and α = 0.01 is the regularization coefficient. After calculation by formula (17), the measured boundary voltage vector can be converted into the corresponding conductivity distribution feature matrix as the input of DHU-Net.

[0122] DHU-Net uses a small batch adaptive moment estimation optimizer (Adamax) to train the network model. The total number of training (and parameter update iterations) is 400 times for every 128 training samples. The initial learning rate is set to 0.1, and the learning rate is adjusted according to the update method of formula (18) every time the parameters are updated.

[0123]

[0124] Among them, η t , η t-1 represents the learning rate of the t-th and t-1-th times, and t and T represent the t-th and T-th learning processes.

[0125] Before model training, the weight parameters were randomly set to a Gaussian distribution with a mean of 0 and a standard deviation of 0.01.TM The model was trained in Python 3.8, TensorFlow 1.14.0 and Keras software package environment on i7-9700K@3.6GHz CPU RAM 32GB+NVIDIA 2080TiGPU. The model training took about 38 hours for a total of 400 steps.

[0126] DHU-Net uses the classic U-Net as the backbone model, and the dual-branch encoder is used to extract local features and global features. The spatial dimensions of the feature map are 128, 64, 32, 16, and 8 (height and width), and the corresponding channel dimensions are 8, 16, 32, 64, and 128, respectively. In addition, in the DCN-SE local feature branch, the channel reduction ratio of the fully connected layer (FC) in the SE attention mechanism is set to r SE =4, 4, 8, 8, 16. In the CA-HC global feature branch, the channel reduction ratio of the fully connected layer (FC) in the CA attention mechanism is set to r CA =4,4,8,8,16, the node parameter of super convolution is set to N L =4, the two adjacent modules of the encoder are connected using average pooling, and the pooling kernel size is set to 5×5. Symmetrically, the upsampling in the decoder uses a reverse convolution connection, and the expansion rate of the convolution kernel is 3.

[0127] In order to verify the DHU-Net reconstruction performance proposed in the present invention, the present invention uses a classic numerical solution algorithm and an EIT image reconstruction method based on a deep CNNs model.

[0128] (1) Numerical optimization method: The conjugate gradient (CG) iterative algorithm is selected as the numerical optimization method because the CG algorithm quickly approaches the optimal solution by using an adaptive step size and the conjugate property of the gradient direction, thereby reducing redundant information and iterative steps and accelerating convergence.

[0129] (2) Reconstruction method based on deep CNNs model: The present invention selects a new reconstruction model composed of a module with vanilla U-Net as the backbone model and combined with new feature connections. Such as VD-Net [F.Li, C.Tan, and F.Dong, "Electrical Resistance Tomography Image Reconstruction With Densely ConnectedConvolutional Neural Network," (in English), IEEE Trans.Instrum.Meas., Articlevol.70, p.11, 2021, Art no.4500811, doi: 10.1109 / tim.2020.3013056], VA-Net [ZCWang, vol.72, p.18, 2023, Art no.5011318, doi: 10.1109 / tim.2023.3265108], HIHU-Net[D.Wang, (IST) / IEEEInternational School on Imaging, Electr Network, Jun 21-23 2022, NEW YORK: IEEE, in IEEE International Conference on Imaging Systems and Techniques, 2022, doi: 10.1109 / ist55454.2022.9827773.[Online].Available:<Go to ISI> : / / WOS:000853020700066] and HybridDenseU-Net[Zhang, B., Wang, Z, Chen, X., Wang, Q., Xie, N. and Liu, L., 2023. HybridDenseU-Net: learning a multi-scale convolution and dense connectivity CNN for inverse imaging problems. Measurement Science and Technology, 35(3), p.035404.]. Among them, VD-Net and VA-Net are two new deep imaging frameworks with U-shaped structure as the backbone, adding dense connection and attention features, HIHU-Net is a multi-scale dense feature connection encoding-decoding model for EIT image reconstruction, and HybridDenseU-Net is a symmetrical structure image reconstruction framework with dual-branch encoder and feature fusion decoder. .

[0130] In order to quantitatively evaluate the reconstruction performance between the reconstruction results and the true distribution, the root mean square error (RMSE), peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) were selected for quantification:

[0131]

[0132]

[0133]

[0134] Where Rec represents the reconstructed image, label represents the label distribution, N is the total pixel value of the image, μ and Σ represent the mean and covariance matrix respectively, C1 and C2 are constants, which are set to 10 in this patent. -6 .

[0135] In order to demonstrate the effectiveness of the DHU-Net proposed in the present invention in nonlinear soft-field EIT imaging, the present invention conducted a series of simulation experiments and water tank experiments, and the relevant visualization results and quantitative index analysis are given in detail below.

[0136] The present invention randomly selected test samples for visualization experiments and compared the reconstruction results of the relevant numerical solution method and the method based on deep learning. The results are as follows Figure 4As shown in FIG5 , Model 1 and Model 2 are the results of inclusion reconstruction, Model 3 and Model 4 are the results of shape reconstruction, the first column is the model setting, and the second to seventh columns are the reconstruction results using different imaging methods; the corresponding quantitative index results (RMSE, SSIM and PSNR) are shown in FIG5 , and the present invention uses the full simulation test sample to calculate the quantitative index, and selects the average value as the result analysis.

[0137] like Figure 4 As shown, the new reconstruction performance of the deep learning-based method is better than the traditional iterative method (CG). From the reconstructed image, it can be seen that there is no large amount of artifact interference and the conductivity parameters and boundary shape information can be seen clearly. The comparison results of five imaging methods based on deep learning (VD-Net, VA-Net, HIHU-Net, HybridDenseU-net and DHU-Net proposed by the present invention) show that VD-Net, VA-Net and HIHU-Net use a single-scale encoder for feature extraction. Although it can improve the result interference caused by artifacts to a certain extent, the reconstruction results (especially in the shape reconstruction task) have obvious distortion and poor shape expression performance. At the same time, for example, objects with smaller geometric sizes in the model 2 sample are not reconstructed in the results of VD-Net, indicating that the simple feature splicing method has certain limitations. HybridDenseU-Net and DHU-Net use dual-branch encoders and perform feature fusion, which significantly improves the reconstruction results and also well preserves the "sharp" corner features. Further comparison of the two shows that DHU-Net can achieve more optimized results due to the use of deformable convolution and coordinate attention mechanism to construct potential features.

[0138] The quantitative indicators shown in Figure 5 have the same results as the above analysis. Figure 5 (a) analyzes the performance of RMSE and SSIM on different algorithms. It can be seen that DHU-Net has the best RMSE and SSIM results (that is, among the comparison methods used, the lowest RMSE is 2.028 and the best SSIM is 0.9631), indicating that the reconstruction results of DHU-Net are consistent with the actual distribution. In addition, the reconstruction results of all simulation test data are quantified by the PSNR indicator. As shown in Figure 5 (b), it can be seen that the reconstruction results of the deep imaging methods (VD-Net, VA-Net and HIHU-Net) using single-scale coding features are unstable and will be affected by the model distribution and shape complexity, while the multi-scale coding HybridDenseU-Net and DHU-Net methods have better PSNR results, and the results of DHU-Net have better consistency (that is, the quantization results of 25%-75% are not much different).

[0139] The experimental platform was collected using a 16-electrode EIT data acquisition system. The relevant parameter settings were consistent with the simulation environment: a water tank with a diameter of 0.19 m was used, the uniform background (reference measurement state) was simulated using an aqueous solution with a conductivity of 0.06 S / m, and the inhomogeneous phase (different medium distribution states) was simulated using an organic glass rod (considering that the organic glass rod is an insulating object, 10 -12 S / m assumes the conductivity of the inclusions). The data acquisition system has a signal-to-noise ratio of 70 dB, a bit resolution of 14 bits, an excitation current amplitude of 4.5 mA, and a frequency of 100 kHz. It consists of a sensor array, an FPGA master chip, a digital / analog converter, a voltage-controlled current source (VCCS), a programmable variable gain amplifier (PGA), and a PC.

[0140] The present invention uses glass rods of different sizes and shapes to simulate inclusions for image reconstruction. Figure 6 As shown in Figure 7, the corresponding quantitative index results (RMSE, SSIM and PSNR) are shown in Figure 7. Figure 6 As shown in Figure 7, the imaging method based on deep learning has better imaging quality than the CG method (consistent conclusions in both visualization results and quantitative index results). In addition, VD-Net, VA-Net and HIHU-Net only consider the encoding of spatial information and parameter information at one scale, so they do not obtain good results in reconstructing small-sized objects and complex-shaped media (the "sharp" parts in the reconstructed image are obviously smoothed, and some small objects are reconstructed incorrectly, etc.), and the corresponding quantitative indicators also have consistent conclusions. Although HybridDenseU-Net and DHU-Net both use different convolution kernels for feature learning, DHU-Net uses the deformable convolution kernel of shape modeling and the feature construction of implicit neural network, and obtains better results in reconstructing images and quantitative indicators.

[0141] In actual measurement scenarios, fluid disturbances, circuit system noise, and interference from impurities in the observation area will all cause certain disturbances to the measurement signal, so the anti-noise performance of the imaging method is very important. In order to test the robustness of DHU-Net to noise, the present invention conducted imaging experiments with a Gaussian white noise signal-to-noise ratio (SNR) of 90dB to 20dB in the test samples, and used RMSE, SSIM, and PSNR as three quantitative indicators to evaluate the image quality. Figure 8 The reconstruction results of randomly selected scenes with different inclusions at different SNRs levels are listed, and Figure 9 analyzes the results of quantitative indicators at different SNRs.

[0142] It can be seen that DHU-Net has good noise robustness: Figure 8 The reconstruction results show that when the SNR level is above 40dB, the medium distribution in the observation area can be reconstructed more accurately; when the SNR level is lower than 30dB, some distortions and artifacts appear in the shapes of the inclusions in some reconstruction results, and some small targets cannot be reconstructed in more complex scenes. The quantization results in FIG9 compare the noise resistance performance of the DHU-Net and VA-Net and HybridDenseU-Net proposed in the present invention. The results show that the strategy of multi-scale feature space encoding and latent space feature fusion can improve the noise robustness of the deep imaging model (that is, the RMSE, SSIM and PSNR indicators of DHU-Net and HybridDenseU-Net under different noise conditions are better than those of VA-Net). In addition, the introduction of deformable convolution can improve the shape modeling ability, and the implicit representation of super convolution can better filter out high-frequency features (that is, noise components) and thus smoothly retain the dominant features in the image. In the indicator analysis of FIG9, the RMSE of the DHU-Net method proposed in the present invention remains between 2.000 and 2.1500 during the gradual decrease of SNR, the SSIM remains above 0.9500, and the PSNR is higher than 47.6000, indicating that DHU-Net has good noise robustness.

[0143] Another advantage of EIT is that it can be used to visualize the distribution of conductivity parameters within the observation area. Therefore, it is necessary to evaluate the reconstruction of imaging methods in situations with different conductivity (especially medium distribution scenes containing low-contrast conductivity). Therefore, the present invention constructs three sets of observation models for non-uniform phase distribution scenes, and selects the CG iterative method, HybridDenseU-Net and DHU-Net methods to visualize the reconstruction results. The reconstruction results and analysis are as follows: Fig.10 .

[0144] like Fig.10From the results shown, it can be seen that: in the reconstruction results based on deep learning methods, when the inclusion medium is widely distributed and has high conductivity contrast, the imaging results have good performance, which can accurately express the electrical distribution parameters of the medium and clearly reconstruct the boundary shape information of the inclusions; when the conductivity contrast gradually decreases, the CG algorithm cannot display the low conductivity contrast inclusion information, and the HybridDenseU-Net and DHU-Net methods have a certain degree of improvement on the imaging results, and the approximate distribution scene of the inclusions can be seen (but there is some distortion at the boundary). In addition, since DHU-Net improves the robustness and expression ability of the model by introducing the shape modeling method of deformable convolution and the parameter mapping of implicit hyperconvolution, the conductivity parameters in the imaging results are more accurate and the boundary features are clearer (the HybridDenseU-Net expressed by conventional convolution kernel features still has some artifact disturbances in the multi-phase conductivity reconstruction task).

[0145] In summary, the DHU-Net proposed in this invention improves the robustness and expressiveness of the model by introducing deformable convolution and hyperconvolution operators, at the cost of a significant increase in the number of parameters that need to be trained (this data analysis is measured on a reconstructed image with a pixel resolution of 128×128). 2 D-Net, V 2 A-Net and others use different data formats of image pixels, so they require more computing resources, but they can directly reconstruct the actual conductivity value rather than the pixel processing result, so DHU-Net has greater practical application potential.

[0146] The above description is only a preferred embodiment of the present invention. It should be pointed out that a person skilled in the art can make several modifications and improvements without departing from the inventive concept, which all belong to the protection scope of the present invention.

Claims

1. A method for reconstructing an electrical impedance image, characterized in that: A dual-branch parallel EIT deep imaging model named DHU-Net was established, which uses U-Net as the backbone model and integrates deformable convolution modules and hyperconvolution networks. The DHU-Net consists of a dual-branch feature encoder and a feature fusion decoder. The dual-branch feature encoder uses different convolution operators, which are respectively composed of parallel operations consisting of deformable convolution and channel layer attention mechanism, coordinate attention mechanism and implicit hyperconvolution. Skip connections based on the attention mechanism are added symmetrically between the feature pyramids corresponding to the dual-branch feature encoder and the feature fusion decoder. The dual-branch feature encoder includes a spatial feature encoding branch and a channel feature encoding branch; The spatial feature encoding branch includes 5 encoding units, each of which implements spatial shape modeling by a local deformable convolution kernel and a channel layer attention mechanism. The input of each spatial encoding unit uses 2 layers of 3×3 convolution and a nonlinear activation function ReLU and batch normalization BN and pooling downsampling operators to perform feature dimension aggregation and channel amplification; The channel feature encoding branch includes 5 encoding units, each of which uses a coordinate attention mechanism and a 5×5 implicit superconvolution to learn the conductivity distribution parameters. The input of the spatial channel unit uses a 2-layer 3×3 convolution and a nonlinear activation function ReLU and batch normalization BN and a pooling downsampling operator to perform feature dimension aggregation and channel amplification. The output features of the dual-branch feature encoder are concatenated and convolved through a feature map for channel adjustment, and two layers of deconvolution upsampling are used to amplify the feature map space. The obtained features are used as the input of the feature fusion decoder. There are four feature fusion decoders, each of which consists of a jump self-attention mechanism module and a deconvolution upsampling layer. The input of the jump self-attention mechanism module includes the calculation features of the spatial feature encoding branch, the calculation features of the channel feature encoding branch, and the output features of the previous deconvolution upsampling. The output features of the jump self-attention mechanism module are used as the input of the deconvolution upsampling layer to expand the spatial dimension and reduce the number of channels to achieve the final image reconstruction. The skip connection is connected in the following way: through the deformable convolution-SE attention feature And coordinate attention — features of hyperconvolution After linear projection, they are recorded as value vectors And the key vector K, and the other input of the corresponding decoder is the upsampled feature map Recorded as feature query vector Perform attention operations, Among them, d k is the dimension of the vector. After the feature fusion of SA, the decoding module uses two 3×3 convolution operations to aggregate the channel features and restore the decoding features, and the output is used as the input feature of the next decoding module.

2. The electrical impedance image reconstruction method according to claim 1, characterized in that: An embedding layer is used before the dual-branch feature encoder for channel expansion, and a 1×1 convolution is used to convert the initial input features Convert to high-dimensional tensor Among them, C is the number of feature map channels, H is the number of feature map heights, and W is the number of feature map widths. is a set of real numbers.

3. The electrical impedance image reconstruction method according to claim 2, characterized in that: The deformable convolution uses a 3×3 deformable convolution kernel to learn the shape of the inclusions. The convolution kernel is expressed as: Assume that the input and output feature tensors of each deformable convolution operator are expressed as and The learning weight of the kth position in the convolution kernel, the position of the output feature map, and the convolution kernel The corresponding sampling points and offsets are denoted as w k ,p0,p k and Δp k ,in Then the operation form of deformable convolution is Among them, the compensation amount Δp k is a fraction, deformable convolution operation is performed via bilinear interpolation.

4. The electrical impedance image reconstruction method according to claim 3, characterized in that: The algorithm of the channel layer attention mechanism consists of two parts: The first part uses global average pooling to obtain global information in the channel dimension For a C-channel feature map, the result of the c-th channel feature map after global average pooling is Among them, X input,c is the feature matrix of the cth channel in the feature map, i, j are the pixel units in the i-th row and j-th column of the feature matrix, and z1 is the first channel matrix of the output feature map, z c is the c-th channel feature matrix, z C is the Cth channel feature matrix; The second part uses a multi-layer perceptron to perform nonlinear transformation on the compressed features to generate a channel attention tensor. The attention tensor is normalized by a nonlinear function to adjust the weight of each channel. Finally, the obtained attention tensor is used To adjust the weight of the input feature information, Among them, s1 is the first channel feature matrix of the channel attention tensor, s c is the cth channel feature matrix of the channel attention tensor, s C is the Cth channel feature matrix of the channel attention tensor.

5. The electrical impedance image reconstruction method according to claim 4, characterized in that: The coordinate attention mechanism includes two steps: coordinate feature embedding and coordinate feature calculation: S1 uses precise location information to encode long-range dependencies when modeling features, and coordinate feature embedding uses a pair of orthogonal 1D pooling to separately Perform feature aggregation along the horizontal and vertical directions respectively to obtain a pair of directional feature tensors and x c represents the cth feature map of the input tensor feature map, h and v represent the horizontal and vertical directions of the feature map, and the calculation process is: in, and represents the horizontal attention feature tensor and the vertical attention feature tensor, and They represent the 1st, cth, and Cth channel feature maps of the spatial attention horizontal feature tensor respectively. and They represent the 1st, cth, and Cth channel feature maps of the vertical feature tensor of spatial attention respectively; The S2 coordinate feature calculation is used to construct the spatial attention tensor and act on the input feature tensor to amplify and splice the orthogonal feature map in the S1 formula, use 1×1 convolution for channel adjustment, and obtain the mixed feature map through nonlinear projection. Where r is the channel attenuation coefficient, the hybrid feature map combines the spatial encoding information in the horizontal and vertical directions, and then Separate, use 1×1 convolution and nonlinear projection to encode the x-direction and y-direction features again to obtain the directional attention features and And acts on the input feature tensor, in, Represents the fused feature map tensor after horizontal attention feature extraction and vertical attention feature extraction. and Represents the feature maps The 1st, cth and Cth channels of represents the input feature vector of the fusion module, express The c-th channel feature map of and They represent the horizontal attention feature extraction tensor and the vertical attention feature extraction fused feature map tensor, respectively. h and g v express and The sub-feature map of , the superscript index c represents the c-th channel, c = 1, 2, ..., C; When the coordinate attention feature map is obtained Finally, the global information is represented from the abstract spatial feature map.

6. The electrical impedance image reconstruction method according to claim 5, characterized in that: The implicit superconvolution is: input 2 coordinate parameters with the same size as the 5×5 convolution kernel in the x-direction and y-direction Among them, i, j represents the pixel cell in the i-th row and j-th column of the feature map; Use implicit representation to fit the coordinate information (i, j) and the corresponding convolution kernel weight parameters The mapping relationship between them; Among them, φ θ Indicates the construction of an implicitly fitted neural network structure. In DHU-Net, a fixed-node full convolution network with 4 layers and a convolution kernel size of 1×1 is used to map the weight relationship between the spatial coordinates of the feature map and the corresponding convolution kernel. The number of nodes in the last layer is recorded as N L is a hyperparameter representing the capacity of the implicit hyperconvolutional model.

7. The electrical impedance image reconstruction method according to claim 6, characterized in that: The loss function of DHU-Net is defined as: in, is the target conductivity image to be reconstructed, y is the input initialization conductivity distribution, is a given training sample, θ is the hyperparameter of DHU-Net to be trained, Used to ensure that the output of the model is close to the label distribution, is the regularization term of the loss function, and the corresponding λ is the regularization term parameter.

Images