Complex electrical impedance image reconstruction method based on space-wavelet dual-domain driving

Abstract

The invention belongs to the field of complex electrical impedance tomography, and particularly relates to a complex electrical impedance image reconstruction method based on space-wavelet dual-domain driving. A boundary voltage signal on a sensor is mapped into an initial complex value admittance image by using a complex number Newton-Raphson method, the initial complex value admittance image is used as an input feature of an SWU-Net model to carry out spatial feature coding and wavelet frequency domain feature construction, the SWU-Net model comprises a plurality of residual four-azimuth full convolution encoders, a plurality of rswFormer modules and a plurality of decoders, and the SWU-Net model comprises a plurality of residual four-azimuth full convolution encoders, a plurality of rswFormer modules and a plurality of decoders. Wherein the encoder and the decoder construct and fuse spatial domain features and frequency domain features respectively. Meanwhile, a jump connection module for fusing double-domain features of a space domain and a frequency domain is constructed, and the jump connection module is used for fusing the space low-frequency features and the frequency high-frequency features. The method provided by the invention has better reconstruction performance in the aspects of quantitative indexes and visual visualization effects.

Description

Technical Field

[0001] The invention belongs to the field of complex electrical impedance tomography, in particular to a space-wavelet dual-domain driven complex electrical impedance image reconstruction method. Background Art

[0002] Complex-value EIT (Cv-EIT) aims to obtain the conductivity and dielectric constant distribution images of the area through electrical measurements on the surface electrodes of the observation area. As a new non-invasive, non-ionizing and portable imaging technology, this technology is widely used in non-destructive medical monitoring, industrial detection and geophysics.

[0003] The mathematical model of the Cv-EIT problem is expressed as the famous Calderón problem. Mathematically, the electric potential in a two-dimensional region is The admittance equation, i.e. the generalized Laplace equation, is used. In practice, in order to consider the shunting effect caused by the distribution of discrete boundary electrodes and the electrochemical effect between the electrode and the object being measured, the complete electrode model (CEM) is generally used as a boundary condition constraint problem. In addition, Kirchhoff's law and the ground terminal must be applied to ensure the existence and uniqueness of the results. The measurement accuracy of CEM is very close to the experimental measurement accuracy. The uniqueness and existence of the solution based on this model have been proved.

[0004] The inverse problem of Cv-EIT is to reconstruct the internal conductivity and dielectric constant using the measured voltage on the boundary sensor. Since the number of known measured voltage signals is much smaller than the number of pixels in the area to be reconstructed, the problem is severely ill-conditioned and nonlinear. For Cv-EIT with nonlinearity, the first-order linear approximation strategy is generally used to simplify the problem.

[0005] In differential imaging, an image reconstruction algorithm is used to invert the change in conductivity based on the difference between the measured data before and after the change in conductivity distribution. Traditionally, the reconstruction of the conductivity distribution change uses an optimization solution method, that is, approximating the nonlinear observation model by linearizing the model and taking the difference between the data before and after the change. The solution method based on numerical optimization usually includes iterative regularization algorithms and direct reconstruction methods: 1) Iterative regularization methods generally constrain the stability of the solution space by introducing the idea of ​​structural features as prior information in problem (2), such as total variation regularization, p-norm / mixed regularization, group sparsity regularization, Gauss-Newton iterative method, Land-weber iterative method, etc. 2) Direct reconstruction methods obtain internal parameter distribution images by using measured data for image reconstruction or directly solving the generalized Laplace equation, such as the back projection method, Calderón / D-bar and its improved method, and shape reconstruction method. Among these methods, only the D-bar related method realizes the reconstruction of complex admittance parameters. However, the iterative / regularized method using the optimization framework relies heavily on prior information (such as unknown electrode positions, boundary shapes, or contact impedances), consumes a lot of computing resources, and the regularization terms and related hyperparameters often need to be selected empirically, resulting in unsatisfactory robustness and generalization capabilities in different scenarios.

[0006] Methods based on learning strategies have received a lot of attention in the task of inverse imaging problems, and this method is also used to solve the EIT inverse problem. The supervised learning method for solving the EIT inverse problem can generally be divided into: the first category is an end-to-end method based on image post-processing to obtain high-quality reconstructed images, the second category is to use a model-driven deep unfolding network to integrate prior knowledge to build an interpretable deep imaging model, and the third category is to use measured data and labeled electrical parameter distributions to directly build a neural network to learn nonlinear mapping relationships. In addition, semi-supervised / unsupervised methods are also used to solve the EIT imaging inverse problem. The limitations of the learning strategy framework for solving the nonlinear Calderón inverse problem are: (1) The "end-to-end" framework usually requires a large number of training samples. However, the training samples obtained by simulation cannot fully characterize the spatial characteristics of the inclusion distribution; (2) The scheme using the deep expansion strategy requires the introduction of the linearized Jacobian matrix, but multiple iterations will cause the amplification of the approximation error; (3) The strategy of directly constructing a nonlinear mapping projects the low-dimensional manifold data into a high-dimensional space, which will cause the instability of the solution to the inverse problem and increase the ill-posedness; (4) Although the unsupervised strategy does not rely on data samples, it needs to solve the direct problem during the iteration process, resulting in a significant increase in imaging time. It is also worth noting that most of the current research focuses on the reconstruction method of the conductivity parameters, ignoring the contribution of the dielectric constant to the measurement signal. Summary of the invention

[0007] The purpose of the present invention is to overcome the shortcomings of the prior art and provide a space-wavelet dual-domain driven complex impedance image reconstruction method to solve the problem that the image reconstruction of Cv-EIT is pathological and nonlinear, resulting in obvious boundary blur and inaccurate parameter information.

[0008] The technical solution adopted by the present invention to solve the technical problem is:

[0009] The present invention proposes an image reconstruction method based on an end-to-end strategy, which uses a low-quality complex conductivity parameter distribution to obtain a high-quality complex conductivity parameter image. Specifically, an improved U-shaped network structure is proposed, in which the encoder and decoder construct and fuse spatial domain features and frequency domain features respectively. At the same time, a jump connection module that fuses the dual-domain features of the spatial domain and the frequency domain is constructed to fuse the spatial low-frequency features and the frequency high-frequency features. Experimental results show that compared with the currently popular Cv-EIT reconstruction method, this method has better reconstruction performance in terms of quantitative indicators and visual visualization effects. At the same time, the method proposed in the present invention has better noise robustness, and the ablation study confirms the effectiveness of the multi-scale spatial-frequency feature fusion scheme.

[0010] The specific steps of the spatial-wavelet dual-domain driven complex electrical impedance image reconstruction method of the present invention are as follows: first, the boundary voltage signal on the sensor is converted into Mapping to the initial complex-valued admittance image The initial complex-valued admittance image As the input features of the SWU-Net model, spatial feature encoding and wavelet frequency domain feature construction are performed. The SWU-Net model includes multiple residual four-way full convolution encoders, multiple rswFormer modules, and multiple decoders. In the feature map of the residual four-way full convolution encoder after discrete wavelet transform, the LL low-frequency sub-band features are used to construct spatial features, and the high-frequency sub-band features in the horizontal, vertical and diagonal directions are input into the rswFormer module for jump connection after inverse discrete wavelet transform operation. At the same time, the spatial input of the decoder is also input into the rswFormer module as a low-frequency feature to perform spatial-wavelet dual-domain feature fusion. Symmetrically, the decoder first uses upsampling operation to interpolate and restore the spatial features, and then uses the high-frequency features in the rswFormer module and the upsampled low-frequency features as the input of Cross-Attention to perform high-frequency-low-frequency feature cross-fusion to finally obtain the imaging result.

[0011] Furthermore, the residual four-way fully convolutional encoder includes two branches: a residual branch based on spatial domain features and a wavelet domain feature branch. The residual branch based on spatial domain features is composed of downsampling based on 2×2 pooling kernel and downsampling based on 3×3×2C k The convolution kernel is composed of spatial convolution, the wavelet domain feature branch is composed of two operators, and the input feature of the kth encoder is The output features are First, use Haar wavelet to perform wavelet operation to obtain the LL low-frequency subband features and high-frequency sub-band features, wherein the high-frequency sub-band features include high-frequency components in horizontal, vertical and diagonal directions Then, the LL low-frequency subband features As the input of the four-way full convolution operator ODConv, multi-scale spatial features are constructed;

[0012] The model constructed by the residual four-way full convolution encoder feature is:

[0013]

[0014] in, is the spatial domain residual branch feature of the k-th encoder, is the wavelet domain feature of the kth encoder, is the wavelet low-frequency subband feature of the k-th encoder.

[0015] Furthermore, the kth rswFormer module uses inverse discrete wavelet transform to transform the high-frequency subband features Reconstruct into query vector, and obtain the real and imaginary parts of the query vector through depth-wise separable convolution The low-frequency feature outputs of the k+1th decoder are used as the key vector and value vector respectively, and the real and imaginary parts of the key vector are obtained through depthwise separable convolution. and the real and imaginary parts of the value vector The multi-head self-attention calculation is implemented on the real conductivity and imaginary dielectric constant feature spaces respectively, and the process is written as:

[0016]

[0017] in is the real part transpose of the key vector, is the imaginary transpose of the key vector, d k is the dimension of the key vector;

[0018] The obtained attention vector is is the real part of the k-th layer attention vector, is the imaginary part of the k-th layer attention vector;

[0019] in is an imaginary unit. In the rswFormer module, complex convolution operation is used to implement the feedforward network. The output of the rswFormer module is

[0020] Furthermore, a residual connection branch is added to the rswFormer module to enhance the high-frequency boundary features. At the same time, a 2×2 upsampling operation is used to make the output features of the jump connection have the same spatial dimension features as the corresponding encoder / decoder. The output result of the SWU-Net jump connection is

[0021]

[0022] Furthermore, the decoder is composed of upsampling operation and CrossHL, and the input feature of the kth decoder is The output features are By 3×3×2C k After the implemented transposed convolution upsampling operation, we get As the input of CrossHL, the input of the CrossHL module in the kth decoder consists of the low-frequency spatial features LF obtained by the upsampling operation and the high-frequency spatial features HF output by the skip connection. and high frequency features Decomposed into two channel features, real part and imaginary part, respectively. The real and imaginary parts of The real and imaginary parts of CrossHL uses a cross fusion strategy for feature fusion, and its calculation method is:

[0023]

[0024] is the real feature output by the CrossHL module, It is the imaginary feature output by the CrossHL module;

[0025] The output of CrossHL is Realize the fusion of spatial low-frequency features and wavelet domain high-frequency features.

[0026] Furthermore, the loss function of the SWU-Net model is composed of wavelet domain loss and reconstruction image domain loss composition,

[0027]

[0028] in:

[0029]

[0030] k represents the number of encoders / decoders of SWU-Net, n represents the number of training samples, is the low-frequency wavelet feature output by the decoder, is the high-frequency wavelet feature output by the decoder, λ is the weight of the wavelet domain loss, HQ coefL Represents the low-frequency component of label distribution, HQ coefH Represents the high-frequency component of the label distribution. The high-frequency component consists of high-frequency components in the horizontal, vertical and diagonal directions. and Represents the reconstructed image and label distribution. Both variables are complex values. The feature maps output by different decoders are decomposed into two channels: real and imaginary parts. and is the Charbonnier error function, ε is the root mean square error function, is the total variation regularization penalty function, and its discrete form is is the pixel value of the image at position (i, j), i is the horizontal pixel index of the image, j is the vertical pixel index of the image, p is the training sample index, and c is the category of the high-frequency subband, such as HL, LH, HH.

[0031] The advantages and positive effects of the present invention are:

[0032] 1) This paper proposes a new residual four-way full convolution coding module (Res-OmniConvolution, abbreviated as roConv): an innovative dual-branch structure of a spatial domain residual branch and a wavelet domain dynamic convolution branch is designed. The global information is retained by the residual branch, and the local features obtained by constructing the dynamic convolution operator using low-frequency wavelet coefficients are realized, realizing the effective extraction of multi-scale spatial structure information corresponding to the complex admittance parameters.

[0033] 2) The present invention proposes a space-frequency dual-domain fusion Transformer module, Residual Spatial-Wavelet Transformer (rswFormer for short): high-frequency sub-band features and spatial features are dual-domain fused, and conductivity and dielectric constant features are enhanced through deep separable convolution and multi-head self-attention mechanism. This module can better couple real and imaginary features while making full use of the global complex admittance represented by spatial low-frequency information and the inclusion boundary features represented by local high-frequency information.

[0034] 3) The present invention proposes a module based on low-frequency-high-frequency cross-fusion transposed attention mechanism (CrossHL): the low-frequency spatial features obtained by upsampling and the high-frequency spatial features obtained by rswFormer are fused at multi-scale by cross-transposed attention to obtain an output result with the same dimension as the input feature. This multi-scale spatial-frequency complementary module can fully retain and restore complex electrical parameter information and shape features.

[0035] 4) Experimental results show that the SWU-Net method proposed in this paper achieves better results in multiphase inclusion reconstruction. It can simultaneously reconstruct the conductivity distribution and dielectric constant distribution images, providing richer inclusion material resolution information. Visualization results and quantitative numerical indicators show that compared with the existing improved complex depth imaging framework, the spatial-frequency dual-domain fusion method has better feature expression capabilities. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 Reconstruct the overall network structure diagram for the SWU-Net dual domain;

[0037] Figure 2 is the k-th encoder module diagram;

[0038] Figure 3 is the k-th skip connection,decoder module diagram;

[0039] Figure 4 The reconstruction results of the water tank experiment (wherein, the model setting scene distribution map and the corresponding conductivity / dielectric constant true value distribution map are given, as well as the reconstruction results of the comparison algorithm and the method proposed in the present invention. The first line is the conductivity distribution map, and the second line is the dielectric constant distribution map. The yellow arrow indicates the medium distribution position mark under low contrast conditions.) DETAILED DESCRIPTION

[0040] 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.

[0041] The present invention proposes a spatial-wavelet dual-domain U-Net framework based on convolutional neural network and discrete wavelet transform enhancement to solve the Cv-EIT inverse problem and reconstruct the complex admittance parameter distribution image, named SWU-Net. This method is based on the "end-to-end" idea and uses a numerical iterative algorithm to map the measured complex voltage signal into an initial complex admittance distribution image and convert it into a complex pixel distribution. The initial imaging result is used as the input feature of SWU-Net, and multi-scale features are constructed through spatial domain feature processing, wavelet domain feature processing, and spatial-wavelet dual-domain fusion module to reconstruct a high-resolution complex admittance parameter image.

[0042] The overall structure of the SWU-Net model proposed in this invention is as follows: Figure 1 As shown in Figure 1, it includes two reconstruction steps: First, the boundary voltage signal on the sensor is converted to Mapping to the initial complex-valued admittance image Since the Cv-NR algorithm uses the first-order approximate Jacobian matrix iterative framework, the initial complex-valued admittance image There are obvious boundary artifacts and inaccurate parameter expressions. Next, As the input features of SWU-Net, spatial feature encoding and wavelet frequency domain feature construction are performed. In the residual four-way fully convolution encoder part, in the feature map after the DWT action, the LL subband is used as the low-frequency feature component to construct the spatial feature, and the horizontal subband, vertical subband and diagonal subband (HL, LH and HH) are used as high-frequency feature components after the Inverse Discrete Wavelet Transform (IDWT) operation and input into the rswFormer jump connection. At the same time, the spatial input of the decoder is also input into the rswFormer module as a low-frequency feature for spatial-wavelet dual-domain feature fusion. Symmetrically, the decoder first uses upsampling operations to interpolate and restore the spatial features, and then uses the high-frequency features in the rswFormer and the upsampled low-frequency features as the input of Cross-Attention to perform high-frequency-low-frequency feature cross-fusion, and finally obtains the imaging result. In SWU-Net, the input feature of the kth residual four-way fully convolutional encoder is The output features are Symmetrically, the input features of the kth decoder are The output features are In order to obtain a reconstructed image with clear boundaries, we designed a wavelet loss and reconstruction losses The combined loss function performs multi-level supervision in reconstructed images at different resolutions.

[0043] The residual four-way fully convolutional encoder roConv of SWU-Net consists of two branches: a residual branch based on spatial domain features and a dynamic convolutional spatial feature construction branch based on wavelet domain low-frequency features, such as Figure 2 Specifically, the residual branch of the spatial domain feature consists of a downsampling (DS) based on a 2×2 pooling kernel and a 3×3×2 pooling kernel. k The spatial convolution composition of the convolution kernel (Conv 3×3 ). The wavelet domain feature branch consists of two operators, First, use Haar wavelet to perform wavelet operation to obtain low-frequency subband features (LL) And high-frequency sub-band features, corresponding to the high-frequency components in the horizontal, vertical and diagonal directions (HL, LH, HH) Then, the LL feature As the input of the four-way full convolution operator (ODConv), multi-scale spatial features are constructed. The model of encoder feature construction is:

[0044]

[0045] The designed SWU-Net jump connection consists of rswFormer module and residual feature transfer, which is used to fuse low-frequency features with high-frequency features, and use the complex convolution operator to complement the conductivity (real part feature) and dielectric constant (imaginary part feature) of the complex admittance parameter. Taking the kth rswFormer module as an example, Figure 3 As shown, the high frequency subband is transformed into Reconstruct into query vector, and obtain the real and imaginary parts of the query vector through depth-wise separable convolution The low-frequency feature outputs of the k+1th decoder are used as the key vector and value vector respectively, and the real and imaginary parts of the key vector are obtained through depthwise separable convolution. and the real and imaginary parts of the value vector The multi-head self-attention calculation is implemented on the real conductivity and imaginary dielectric constant feature spaces respectively, and the process can be written as:

[0046]

[0047] in is the real part transpose of the key vector, is the imaginary part transpose of the key vector, and the resulting attention vector is (in In the rswFormer module, complex-value convolution (CvConv) is used to implement the feedforward network. The output of the rswFormer module is In addition, the residual connection branch is added to rswFormer to strengthen the high-frequency boundary features. At the same time, 2×2 upsampling is used. 2×2 ) makes the output features of the jump connection have the same spatial dimension features as the corresponding encoder / decoder. The output result of the SWU-Net jump connection is:

[0048]

[0049] The decoder mainly consists of upsampling operations and CrossHL. By 3×3×2C k After the implemented transposed convolution upsampling operation, we get As the input of CrossHL. The input of the CrossHL module in the kth decoder consists of the low-frequency spatial features (LF) obtained by upsampling and the high-frequency spatial features (HF) output by the skip connection. Similar to the transposed attention mechanism, the low-frequency features and high frequency features Decomposed into two channel features, real part and imaginary part, respectively. The real and imaginary parts of The real and imaginary parts of CrossHL uses a cross fusion strategy for feature fusion, and its calculation method is:

[0050]

[0051] The output of CrossHL is The fusion of spatial low-frequency features and wavelet domain high-frequency features is achieved.

[0052] In order to ensure that the reconstructed complex admittance image has consistent parameter distribution and clear boundary features with the real complex admittance image, we propose a loss-based and reconstruction image domain loss The mixed loss function is

[0053]

[0054] in:

[0055]

[0056] k represents the number of encoders / decoders of SWU-Net, n represents the number of training samples, HQ coefL and HQ coefH LL and HL, LH, HH representing label distribution, and Represents the reconstructed image and label distribution. Both variables are complex values. In order to facilitate the calculation of the loss function, we decompose the feature maps output by different decoders into two channels: real and imaginary parts, which are and is the Charbonnier error function, ε is the root mean square error function, is the total variation regularization penalty function, and its discrete form is Basically, the goal of the method of the present invention is to predict the subband coefficients of a high-quality image (the image to be reconstructed) from the subband coefficients of a low-quality image (the initial imaging result). These predicted subband coefficients are combined with the inverse wavelet transform module to generate the final high-quality image.

[0057] SWU-Net uses simulation data for training and parameter fine-tuning, and uses a water tank device to measure boundary voltage to verify the robustness and generalization of the method. The simulation training data is implemented using the COMSOL multi-physics field and Matlab joint simulation platform: consistent with the water tank experiment, a circular area with a diameter of 19 cm is set as the measurement sensitive field, 16 electrode sensors are evenly set outside the measurement area, and the "adjacent excitation-adjacent measurement" method is used to modulate the current signal of the observation area. The injected current is 4.5mA and the frequency is 50kHz, and the voltage response signal on the electrode is collected. NaCl solution is set as the background in the uniform field, and circular inclusions with different radii and different numbers are used as the medium. The number of inclusions is set to 1-4, the radius of the inclusions is set to 2cm-4cm, and the inclusions do not overlap with each other. The conductivity of the uniform field is set to 0.06S / m, the dielectric constant is set to 80, the internal medium is set to different conductivity parameters, and the conductivity and dielectric constant are set to be between 10 -6 —10 6 S / m, any value in the range of 3-10000. A total of 42,430 circular inclusion simulation samples were generated, and the training samples, validation samples and test samples were set to account for 80%, 10% and 10% of the entire database respectively. The EIT positive problem was numerically solved using the finite element method. The observation domain was discretized into a dense triangular grid using the finite element method (FEM) and the complex admittance equation (1) was numerically solved. For the 16-electrode EIT measurement model, all electrodes were excited and measured once to obtain a total of 208 effective voltages. The positive problem used a square grid division method with a resolution of 256×256 to represent the distribution characteristics of the conductivity and dielectric constant in the region.

[0058] Experimental parameter configuration:

[0059] (1) Model parameter setting: The number of residual four-way fully convolutional encoder modules and decoder modules of SWU-Net is set to 5, the number of rswFormer modules is set to 5, and the number of channels of residual four-way fully convolutional encoder / decoder input features is set to C. in =[8, 16, 32, 64, 128]. In the residual four-dimensional fully convolutional encoder, in Omni-Convolution, the feature compression rate of the fully connected layer (FC) is set to r = 1 / 8, and the four dynamic convolution branches (spatial dimension direction α s , input channel dimension direction α c , output channel dimension direction αo , convolution kernel dimension direction α w ) parameter settings are k×k (k=3), c in ×1, c out ×1, a×1 (a=1). In the rswFormer module, the image block size is set to 4 and the number of attention heads is set to d N = [8, 16, 16, 16, 32], and the number of attention blocks is 1. In the decoder, CrossHL first transforms the input features through a 1×1×2C k and 3×3×2C k Perform feature construction and use tensor shape adjustment to reshape the feature map into and In the cross-transpose attention module, the image block size is set to 4 and the number of attention heads is set to d N =[8, 8, 8, 8, 8], and the number of attention blocks is 1.

[0060] (2) The SWU-Net model is implemented on a Windows 10 platform based on Python 3.9. The training environment is the open source framework Pytorch 1.12.1 and CUDA and CUDNN. The hardware composition of the training platform is Intel (R) Core (TM) i7-9700K CPU @ 3.60GHz, RAM is 32GB, and the accelerated training process is implemented on the NVIDIA GeForce RTX2080Ti (GPU, video memory is 11GB) platform. SWU-Net uses a small batch adaptive moment estimation optimizer (Adamax, β1 = 0.9, β2 = 0.999, the relative tolerance range is set to ε = 10 -5 ) trains the network model, where the mini-batch size is 64, the number of training times is set to 1200, the initial value of the learning rate is 0.0001, and the learning rate is reduced to half of the original value every 300 times.

[0061] The present invention uses five comparison methods to compare and illustrate the performance of SWU-Net. Currently, there are few studies on deep learning methods based on complex EIT. We chose a deep learning network based on complex MRI and used the same data set for fair comparison in a consistent experimental environment. The comparison methods include the Cv-NR iterative method [PM Edic, D. Isaacson, G. J. Saulnier, H. Jain and J. C. Newell, "An iterative Newton-Raphson method to solve the inverse admittivity problem," in IEEE Transactions on Biomedical Engineering, vol. 45, no. 7, pp. 899-908, July 1998, doi:10.1109 / 10.686798.], CvU-Net method [El-Rewaidy, H., Neisius, U., Mancio, J., Kucukseymen, S., Rodriguez, J., Paskavitz, A., Menze, B. and Nezafat, R., 2020. Deep complex convolutional network for fast reconstruction of 3D late gadolinium enhancement cardiac MRI.NMRinBiomedicine, 33(7), p.e4312.], Cv ISTA-Net method [Wang, S., Cheng, H., Ying, L., Xiao, T., Ke, Z., Zheng, H. and Liang, D., 2020. DeepcomplexMRI: Exploiting deep residual network for fast parallel MR imaging with complex convolution.Magneticresonance imaging, 68, pp.136-147.], Cv ResUNet method [Quan, Y., Chen, Y., Shao, Y., Teng, H., Xu, Y. and Ji, H., 2021. Image denoising using complex-valued deepCNN.Pattern Recognition, 111, p.107639.] and the CvDenseUNet method [Dedmari, MA, Conjeti, S.,Estrada,S.,Ehses,P.,. T.andReuter,M.,2018,September.Complex fully convolutional neural networks for MR image reconstruction.In InternationalWorkshop on Machine Learning for Medical Image Reconstruction(pp.30-38).Cham:Springer International Publishing.]. The quantitative evaluation indicators root mean square error (RMSE), signal-to-noise ratio (PSNR) and structural similarity index (SSIM) are used to measure the difference and similarity between the reconstructed image and the real image. In addition, we give the parameter quantity (Params), computational complexity (FLOPs) and imaging time (Time) of the comparison method and the method proposed in the present invention.

[0062] Table 1 Average quantitative indicators (RMSE, PSNR and SSIM) of simulation test data

[0063]

[0064] The quantitative index results of the simulation data test set are shown in Table 1. It can be seen that the SWU-Net method proposed in the present invention obtains the best results, especially the RMSE is significantly reduced, and the PSNR and SSIM are significantly improved. However, it is worth noting that: (1) The performance improvement of the SWU-Net proposed in the present invention is limited compared with the Cv ISTA-Net method. The reason is that the model-driven method based on deep expansion will introduce physical prior information of the positive problem, which has a certain improvement in the generalization performance of the model. However, this nonlinear feature will lose the high-frequency boundary component after the first-order linear processing, so the quantitative index is lower than that of the method proposed by us; (2) It can be seen that there is a performance difference in the quantitative index of the real and imaginary components of the SWU-Net imaging results proposed in the present invention. The reason for the analysis is that in the measurement signal, the voltage value caused by the dielectric constant is lower than the voltage response signal caused by the conductivity, that is, the contribution of the dielectric constant in the boundary measurement signal is lower than the contribution of the conductivity, so the provided features are suppressed, resulting in the dielectric constant reconstruction effect being slightly lower than the conductivity reconstruction effect. In addition, from the perspective of parameter quantity and computing resources, the method proposed in the present invention introduces a complex multi-head attention mechanism to act in the jump connection and decoder, which increases the parameter quantity and computational complexity, and significantly increases the reconstruction time.

[0065] In order to verify the reconstruction results of the SWU-Net method in actual scenarios, we used a circular water tank and three round rods made of different materials to simulate different phase media for verification. Similar to the simulation data settings, a NaCl solution with a conductivity of 0.05S / m was used as the uniform field background, and copper, carbon steel, and resin were used as inclusions for reconstruction. The reconstruction results are shown in Figure 2. Figure 4 As shown. Figure 4 As shown, the reconstruction effect based on the deep learning method is significantly better than that of the Cv-NR method, indicating that the first-order approximation optimization algorithm will lose complex shape information, resulting in blurred boundaries and inaccurate reconstruction of electrical parameters. Among the compared learning-based reconstruction methods, the SWU-Net method has more accurate imaging distribution performance, especially when metal (conductive material) and resin (non-conductive material) are both included. The method proposed in the present invention can more accurately express the position information and shape characteristics in low-contrast scenes. In addition, it can be seen from the reconstruction visualization results that the simultaneous reconstruction of conductivity and dielectric constant can better distinguish the same materials. For example, in a scene where copper and steel materials are distributed at the same time, the different material properties can be accurately analyzed by combining the conductivity and dielectric constant distribution images.

[0066] In response to the Cv-EIT reconstruction problem, the present invention proposes a deep image reconstruction network SWU-Net based on space-wavelet dual domains, which can realize the synchronous reconstruction of conductivity and dielectric constant in the observation area. By designing the Omni dynamic convolution and residual connection strategy of the spatial domain encoder, as well as wavelet domain feature construction, spatial-wavelet dual domain feature fusion module rswFormer and high-frequency and low-frequency feature fusion CrossHL, SWU-Net has better spatial resolution and electrical parameter resolution than the existing complex imaging methods. The role of the wavelet frequency domain module and the cross-domain fusion module significantly improves the reconstruction performance of the backbone model, indicating that the dual-domain deep learning model is significantly better than the simple spatial feature extraction model in improving image quality. In general, the method proposed in the present invention provides a new idea for multi-parameter electrical tomography tasks.

[0067] 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 spatial-wavelet dual-domain driven complex electrical impedance image reconstruction method, characterized in that: First, the boundary voltage signal on the sensor is converted to Mapping to the initial complex-valued admittance image The initial complex-valued admittance image As the input features of the SWU-Net model, spatial feature encoding and wavelet frequency domain feature construction are performed. The SWU-Net model includes multiple residual four-way full convolution encoders, multiple rswFormer modules, and multiple decoders. In the feature map of the encoder after discrete wavelet transform, the LL low-frequency sub-band features are used to construct spatial features, and the high-frequency sub-band features in the horizontal, vertical and diagonal directions are input into the rswFormer module for jump connection after inverse discrete wavelet transform operation. At the same time, the spatial input of the decoder is also input into the rswFormer module as a low-frequency feature to perform spatial-wavelet dual-domain feature fusion. Symmetrically, the decoder first uses upsampling operation to interpolate and restore the spatial features, and then uses the high-frequency features in the rswFormer module and the upsampled low-frequency features as the input of Cross-Attention to perform high-frequency-low-frequency feature cross-fusion to finally obtain the imaging result.

2. The spatial-wavelet dual-domain driven complex impedance image reconstruction method according to claim 1, characterized in that: The residual four-way full convolution encoder includes two branches: a residual branch based on spatial domain features and a wavelet domain feature branch. The residual branch based on spatial domain features is composed of downsampling based on 2×2 pooling kernel and downsampling based on 3×3×2C k The convolution kernel is composed of spatial convolution, the wavelet domain feature branch is composed of two operators, and the input feature of the kth encoder is The output features are First, use Haar wavelet to perform wavelet operation to obtain the LL low-frequency subband features and high-frequency sub-band features, wherein the high-frequency sub-band features include high-frequency components in horizontal, vertical and diagonal directions Then, the LL low-frequency subband features As the input of the four-way full convolution operator ODConv, multi-scale spatial features are constructed; The model constructed by the residual four-way full convolution encoder feature is: in, is the spatial domain residual branch feature of the k-th encoder, is the wavelet domain feature of the kth encoder, is the wavelet low-frequency subband feature of the k-th encoder.

3. The spatial-wavelet dual-domain driven complex impedance image reconstruction method according to claim 1, characterized in that: The kth rswFormer module uses inverse discrete wavelet transform to transform the high-frequency subband features Reconstruct into query vector, and obtain the real and imaginary parts of the query vector through depth-wise separable convolution The low-frequency feature outputs of the k+1th decoder are used as the key vector and value vector respectively, and the real and imaginary parts of the key vector are obtained through depthwise separable convolution. and the real and imaginary parts of the value vector The multi-head self-attention calculation is implemented on the real conductivity and imaginary dielectric constant feature spaces respectively, and the process is written as: in is the real part transpose of the key vector, is the imaginary transpose of the key vector, d k is the dimension of the key vector; The obtained attention vector is is the real part of the k-th layer attention vector, is the imaginary part of the k-th layer attention vector; in is an imaginary unit. In the rswFormer module, complex convolution operation is used to implement the feedforward network. The output of the rswFormer module is 4. The spatial-wavelet dual-domain driven complex impedance image reconstruction method according to claim 3, characterized in that: Add residual connection branches to the rswFormer module to strengthen high-frequency boundary features At the same time, a 2×2 upsampling operation is used to make the output features of the jump connection have the same spatial dimension features as the corresponding encoder / decoder. The output result of the SWU-Net jump connection is:

5. The spatial-wavelet dual-domain driven complex impedance image reconstruction method according to claim 1, characterized in that: The decoder described above consists of upsampling operations and CrossHL. The input feature of the kth decoder is The output features are By 3×3×2C k After the transposed convolution upsampling operation is implemented, we get As the input of CrossHL, the input of the CrossHL module in the kth decoder consists of the low-frequency spatial features LF obtained by the upsampling operation and the high-frequency spatial features HF output by the skip connection. and high frequency features Decomposed into two channel features, real part and imaginary part, respectively. The real and imaginary parts of The real and imaginary parts of CrossHL uses a cross fusion strategy for feature fusion, and its calculation method is: is the real feature output by the CrossHL module, It is the imaginary feature output by the CrossHL module; The output of CrossHL is Realize the fusion of spatial low-frequency features and wavelet domain high-frequency features.

6. The spatial-wavelet dual-domain driven complex impedance image reconstruction method according to claim 1, characterized in that: The loss function of the SWU-Net model is composed of wavelet domain loss and reconstruction image domain loss composition, in: k represents the number of encoders / decoders of SWU-Net, n represents the number of training samples, is the low-frequency wavelet feature output by the decoder, is the high-frequency wavelet feature output by the decoder, λ is the weight of the wavelet domain loss, HQ coefL Represents the low-frequency component of label distribution, HQ coefH Represents the high-frequency component of the label distribution. The high-frequency component consists of high-frequency components in the horizontal, vertical and diagonal directions. and Represents the reconstructed image and label distribution. Both variables are complex values. The feature maps output by different decoders are decomposed into two channels: real and imaginary parts. and is the Charbonnier error function, ε is the root mean square error function, is the total variation regularization penalty function, and its discrete form is is the pixel value of the image at position (i, j), i is the horizontal pixel index of the image, j is the vertical pixel index of the image, p is the training sample index, and c is the category of the high-frequency subband.

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