Space-wavelet dual-domain driven complex resistive impedance image reconstruction method

Abstract

The present application belongs to the field of complex impedance tomography, and particularly relates to a complex impedance image reconstruction method driven by space-wavelet dual domains. The boundary voltage signals on the sensor are mapped into an initial complex-valued admittance image by using a complex Newton-Raphson method, and the initial complex-valued admittance image is taken as an input feature of a SWU-Net model to perform space feature coding and wavelet frequency domain feature construction. The SWU-Net model comprises multiple residual four-orientation full convolution encoders, multiple rswFormer modules and multiple decoders, wherein the encoders and the decoders construct and fuse the space domain features and the frequency domain features, respectively. Meanwhile, a skip connection module for fusing the space domain features and the frequency domain features is constructed to fuse the space low-frequency features and the frequency high-frequency features. The method has better reconstruction performance in terms of quantitative indexes and visual visual effects.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of complex impedance tomography, and particularly relates to a complex impedance image reconstruction method driven by space-wavelet dual domains. BACKGROUND

[0002] Complex-value EIT (Cv-EIT) aims to obtain the conductivity and permittivity distribution images inside a region by electrical measurements on the surface electrodes of the observation region. As a new non-invasive, non-ionizing and portable imaging technology, the technology is widely applied 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. From the mathematical point of view, the electric potential The admittivity equation, i.e. the generalized Laplace equation, is used in practice. In order to consider the shunt effect caused by the distribution of discrete boundary electrodes and the electrochemical effect between the electrodes and the measured object, the complete electrode model (CEM) is generally used as the boundary condition constraint problem. In addition, the Kirchhoff law and the ground terminal must be applied to ensure the existence and uniqueness of the results. The measurement accuracy of the CEM is very close to the experimental measurement accuracy, and the uniqueness and existence of the solution based on the model have been proved.

[0004] The Cv-EIT inverse problem is to reconstruct the internal conductivity and permittivity by using the measured voltage on the boundary sensor. Since the number of known measured voltage signals is much smaller than the number of pixels of the region to be reconstructed, the problem has serious ill-posedness and nonlinearity. For the Cv-EIT with nonlinearity, a first-order linear approximation strategy is generally used to simplify the problem.

[0005] In differential imaging, the conductivity changes are inverted using image reconstruction algorithms from the difference between the forward and the backward measurements caused by the conductivity distribution changes. Traditionally, the reconstruction of the conductivity distribution changes employs optimization-based solution methods, i.e., approximating the nonlinear observation model by linearization and taking the difference between the forward and the backward measurements. The optimization-based solution methods generally include iterative regularization algorithms and direct reconstruction methods: 1) Iterative regularization methods generally constrain the stability of the solution space by introducing structural characteristics as prior information in problem (2), such as total variation regularization, p-norm / mixed regularization, group sparsity regularization, Gauss-Newton iterative method, Landweber iterative method, etc. 2) Direct reconstruction methods obtain the internal parameter distribution image by using the measurement data for image reconstruction or directly solving the generalized Laplace equation, such as the back-projection method, Calderón / D-bar and its improved methods, and shape reconstruction methods. Among these methods, only the D-bar related methods realize the reconstruction of complex admittance parameters, but the iterative / regularization methods using the optimization framework rely heavily on prior information (such as unknown electrode positions, boundary shapes, or contact impedances), consume a large amount of computing resources, and the regularization terms and related hyperparameters often need to be selected empirically, which has an undesirable robustness and generalization ability in different scenarios.

[0006] Learning-based methods have received a lot of attention in imaging inverse problem tasks, and the same method has also been used to solve the EIT inverse problem. Solving the EIT inverse problem based on supervised learning methods can generally be divided into: the first type is an end-to-end method based on image post-processing to obtain high-quality reconstructed images, the second type is to use a model-driven deep unfolding network to integrate prior knowledge to construct an interpretable deep imaging model, and the third type is to use measurement data and labeled electrical parameter distribution to directly construct a neural network to learn the nonlinear mapping relationship. In addition, semi-supervised / unsupervised methods have also been 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 represent the spatial features of the inclusions distribution; (2) the scheme using the deep unfolding strategy needs to introduce the Jacobian matrix after linearization, however, multiple iterations will cause the amplification of approximation errors; (3) the strategy of directly constructing a nonlinear mapping will project low-dimensional manifold data to high-dimensional space, which will cause the instability of the inverse problem solution and increase the ill-posedness; (4) the unsupervised strategy, although it does not rely on data samples, but it needs to solve the forward problem in the iteration process, which significantly increases the imaging time. At the same time, it is worth noting that most of the current research focuses on the reconstruction method of the conductivity parameter, ignoring the contribution of the permittivity to the measurement signal. SUMMARY

[0007] The present application aims to overcome the deficiencies of the prior art, and provides a complex impedance image reconstruction method driven by space-wavelet dual domains, which solves the problems of ill-conditioned and non-linear image reconstruction of Cv-EIT, resulting in significant boundary blur and inaccurate parameter information.

[0008] The technical scheme adopted by the present application to solve the technical problems is:

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

[0010] The specific steps of the complex impedance image reconstruction method driven by space-wavelet dual domains of the present application are as follows: first, the boundary voltage signals on the sensor are mapped into the initial complex-valued admittance image using the complex Newton-Raphson method The initial complex-valued admittance image is used as the input feature of the SWU-Net model to perform spatial feature coding and wavelet frequency domain feature construction, the SWU-Net model includes multiple residual four-direction full convolution encoders, multiple rswFormer modules, and multiple decoders, wherein the residual four-direction full convolution encoder performs spatial feature construction on the LL low-frequency subband feature in the feature map subjected to discrete wavelet transform, the high-frequency subband features in the horizontal direction, the vertical direction and the diagonal direction are input to the rswFormer module after inverse discrete wavelet transform operation, and the spatial input of the decoder is also input to the rswFormer module as low-frequency feature, for spatial-wavelet dual domain feature fusion, symmetrically, the spatial feature is first interpolated and restored using up-sampling operation in the decoder, then the high-frequency feature in the rswFormer module and the up-sampled low-frequency feature are input as Cross-Attention to perform high-frequency-low-frequency feature cross fusion, and finally the imaging result is obtained

[0011] ​Further, the residual quad-orientation full convolutional encoder comprises two branches: a residual branch based on spatial domain features and a wavelet domain feature branch, respectively, the residual branch based on spatial domain features is composed of down-sampling based on 2x2 pooling kernel and 3x3x2C k convolution kernel, and the wavelet domain feature branch is composed of two operators, the input feature of the kth encoder is The output feature is First, wavelet operation is performed using Haar wavelet to obtain LL low-frequency sub-band features and high-frequency sub-band features, the high-frequency sub-band features include high-frequency components in horizontal, vertical and diagonal directions Then, the LL low-frequency sub-band features are used to construct multi-scale spatial features as the input of the quad-orientation full convolutional operator ODConv.

[0012] The model of the residual quad-orientation full convolutional encoder feature construction is:

[0013]

[0014] Wherein, is the spatial domain residual branch feature of the kth encoder, is the wavelet domain feature of the kth encoder, is the wavelet low-frequency sub-band feature of the kth encoder.

[0015] Further, the kth rswFormer module uses inverse discrete wavelet transform to reconstruct the high-frequency sub-band features into query vectors, and obtains the real part and the imaginary part of the query vector through depth separable convolution The low-frequency feature output of the k+1th decoder is used as the key vector and the value vector respectively, and the real part and the imaginary part of the key vector are obtained through depth separable convolution and the real part and the imaginary part of the value vector respectively, and the multi-head self-attention calculation is realized in the real part conductivity and the imaginary part dielectric constant feature space, and the process is written as:

[0016]

[0017] Wherein is the transpose of the real part of the key vector, is the transpose of the imaginary part 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 kth layer attention vector, is the imaginary part of the k-th layer attention vector;

[0019] wherein is the imaginary unit, in the rswFormer module, a feedforward network is implemented using complex convolution operation, and the output of the rswFormer module is

[0020] Further, a residual connection branch is added to the rswFormer module to strengthen the high-frequency boundary features Meanwhile, a 2x2 upsampling operation is used to make the output features of the skip connection have the same spatial dimension as the corresponding encoder / decoder, and the output result of the SWU-Net skip connection is

[0021]

[0022] Further, the decoder is composed of an upsampling operation and a CrossHL, and the input feature of the k-th decoder is The output feature is After a transpose convolution upsampling operation implemented by 3x3x2C k , the output is As the input of the CrossHL, the input of the CrossHL module in the k-th decoder includes the low-frequency spatial feature LF obtained by the upsampling operation and the high-frequency spatial feature HF output by the skip connection, and the low-frequency feature and the high-frequency feature are respectively decomposed into two channel features of real part and imaginary part, The real part and the imaginary part of The real part and the imaginary part of CrossHL adopts a cross-fusion strategy for feature fusion, and its calculation method is

[0023]

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

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

[0026] Further, the loss function of the SWU-Net model is composed of a wavelet domain loss and a reconstructed image domain loss ,

[0027]

[0028] wherein:

[0029]

[0030] k denotes the number of encoders / decoders of the SWU-Net, n denotes 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, and λ is the weight of the wavelet domain loss, coefL represents the low-frequency component of the label distribution, and coefH represents the high-frequency component of the label distribution, which is composed of high-frequency components in the horizontal direction, the vertical direction, and the diagonal direction, and represent the reconstructed image and the label distribution, both of which are complex values, and the feature maps output by different decoders are decomposed into real and imaginary parts, respectively, and is the Charbonnier error function, and 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, and HH.

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

[0032] 1) The present application proposes a new residual four-orientation full convolutional encoding module (Res-OmniConvolution, referred to as roConv): a dual-branch structure of spatial domain residual branch and wavelet domain dynamic convolution branch is innovatively designed. Through the residual branch, global information is preserved, and at the same time, local features obtained by constructing dynamic convolution operators using low-frequency wavelet coefficients are utilized, realizing effective extraction of multi-scale spatial structure information corresponding to complex admittance parameters.

[0033] 2) The present application proposes a spatial-frequency dual-domain fusion Transformer module, residual spatial-wavelet Transformer (referred to as rswFormer): the high-frequency subband features and spatial features are fused in dual domains, the conductivity and permittivity features are enhanced through depth separable convolution and multi-head self-attention mechanism, and this module can better couple the real and imaginary parts while fully utilizing the global complex admittance represented by spatial low-frequency information and the boundary feature represented by local high-frequency information.

[0034] 3) The application proposes a CrossHL module based on low-frequency-high-frequency cross fusion transpose attention mechanism: the low-frequency spatial features obtained by upsampling and the high-frequency spatial features obtained by rswFormer are fused in a cross transpose attention manner 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) The experimental results show that the SWU-Net method proposed in the application obtains better results in multi-phase inclusion reconstruction, which can simultaneously reconstruct conductivity distribution and permittivity distribution images, and provide more rich inclusion material resolution information. The visualization results and quantitative numerical indicators show that compared with the existing improved complex deep imaging framework, the spatial-frequency dual-domain fusion method has better feature expression capability. BRIEF DESCRIPTION OF DRAWINGS

[0036] Figure 1 Fig. 1 is a diagram of the overall structure of the SWU-Net dual-domain reconstruction network;

[0037] Figure 2 Fig. 2 is a diagram of the kth encoder module;

[0038] Figure 3 Fig. 3 is a diagram of the kth skip connection and decoder module;

[0039] Figure 4 Fig. 4 is a reconstruction result of a sink experiment (wherein the model setting scene distribution diagram and the corresponding conductivity / permittivity true value distribution diagram are given, and the reconstruction results of the comparative algorithm and the method proposed in the application are compared. The first line is the conductivity distribution diagram, and the second line is the permittivity distribution diagram. The yellow arrow indicates the medium distribution position label under low contrast conditions.) DETAILED DESCRIPTION

[0040] The application will be further described in detail below through specific embodiments. The following embodiments are only descriptive and not limiting, and cannot limit the protection scope of the application.

[0041] The application 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, reconstruct the complex admittance parameter distribution image, and is named as SWU-Net. The method is based on the idea of "end-to-end", uses a numerical iterative algorithm to map the measured complex voltage signal to 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 the SWU-Net, and the spatial domain feature processing, wavelet domain feature processing and spatial-wavelet dual-domain fusion module are used to construct multi-scale features to reconstruct a high-resolution complex admittance parameter image.

[0042] The overall structure of the SWU-Net model is shown in Figure 1 , which includes two reconstruction steps: first, the boundary voltage signals on the sensor are mapped into the initial complex-valued admittance image using the complex Newton-Raphson (Cv-NR) method . Since the Cv-NR algorithm uses a first-order approximation Jacobian matrix iterative framework, the initial complex-valued admittance image contains obvious boundary artifacts and inaccurate parameter representation problems. Next, , the input features of the SWU-Net are used for spatial feature encoding and wavelet frequency domain feature construction. In the residual quad full convolutional encoder part, the LL subband is used as the low-frequency feature component for spatial feature construction, and the horizontal subband, vertical subband, and diagonal subband (HL, LH, and HH) are used as high-frequency feature components after inverse discrete wavelet transform (IDWT) operation and input to the rswFormer jump connection. At the same time, the spatial input of the decoder is also input to the rswFormer module as a low-frequency feature for spatial-wavelet dual-domain feature fusion. Symmetrically, the spatial feature is first interpolated and restored using the up-sampling operation in the decoder, and then the high-frequency features in the rswFormer and the up-sampled low-frequency features are used as the input of the Cross-Attention for high-low feature cross-fusion to finally obtain the imaging result In the SWU-Net, the input feature of the kth residual quad full convolutional encoder is , and the output feature is . Symmetrically, the input feature of the kth decoder is , and the output feature is To obtain a reconstructed image with clear boundaries, we designed a loss function based on the combination of wavelet loss and reconstruction loss for multi-level supervision in reconstructed images at different resolutions.

[0043] The residual quad full convolutional encoder roConv of the SWU-Net includes two branches: a residual branch based on spatial domain features and a dynamic convolution spatial feature construction branch based on low-frequency features in the wavelet domain, as shown in Figure 2 . Specifically, the residual branch of the spatial domain features is composed of downsampling (DS) based on a 2x2 pooling kernel and spatial convolution based on a 3x3x2C k convolution kernel (Conv 3×3 ). The wavelet domain feature branch is composed of two operators, First, Haar wavelet operations are used to obtain the low-frequency subband features (LL). And high-frequency sub-band characteristics, corresponding to the high-frequency components (HL, LH, HH) in the horizontal, vertical, and diagonal directions, respectively. Then, LL features The input to the four-directional fully convolutional operator (ODConv) is used to construct multi-scale spatial features. The model for constructing encoder features is as follows:

[0044]

[0045] The designed SWU-Net skip connections consist of rswFormer modules and residual feature transfer, which fuse low-frequency and high-frequency features and use complex convolution operators to spatially complement the conductivity (real part feature) and dielectric constant (imaginary part feature) of the complex admittance parameters. Taking the k-th rswFormer module as an example, ... Figure 3 As shown, IDWT is used to divide the high-frequency subband The query vector is reconstructed and then subjected to a depthwise separable convolution to obtain the real and imaginary parts of the query vector. The low-frequency feature outputs of the (k+1)th decoder are used as the key vector and value vector, respectively, and then subjected to depthwise separable convolution to obtain the real and imaginary parts of the key vector. and the real and imaginary parts of the value vector. Multi-head self-attention calculations are performed on the characteristic spaces of real conductivity and imaginary permittivity, respectively. The process can be written as follows:

[0046]

[0047] in This is the transpose of the real part of the key vector. The attention vector is obtained by transposing the imaginary part of the key vector. (in (where the unit is imaginary). In the rswFormer module, a feedforward network is implemented using complex-value convolution (CvConv). Therefore, the output of the rswFormer module is... In addition, residual connection branches are added to rswFormer to enhance high-frequency boundary features. Simultaneously use 2×2 upsampling operation 2×2 This ensures that the output features of the skip connections have the same spatial dimension as the corresponding encoder / decoder. The output of the SWU-Net skip connections is:

[0048]

[0049] The decoder mainly consists of up-sampling operation and CrossHL. After the transposed convolution up-sampling operation is implemented, the low frequency spatial features (LF) and high frequency spatial features (HF) are obtained. k After the transposed convolution up-sampling operation is implemented, the low frequency spatial features (LF) and high frequency spatial features (HF) are obtained. As the input of CrossHL. The input of CrossHL module in the kth decoder consists of low frequency spatial features (LF) obtained by up-sampling operation and high frequency spatial features (HF) output by skip connection. Similar to the transposed attention mechanism, the low frequency features and high frequency features are decomposed into two channel features of real part and imaginary part respectively, The real part and imaginary part of The real part and imaginary part of CrossHL adopts cross fusion strategy for feature fusion, and its calculation method is:

[0050]

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

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

[0053]

[0054] Where:

[0055]

[0056] k represents the number of encoder / decoder of SWU-Net, n represents the number of training samples, HQ coefL and HQ coefH represent the LL and HL, LH, HH of label distribution, and represent the reconstructed image and label distribution, both variables are complex values. In order to facilitate the calculation of loss function, we decompose the feature map output by different decoders into two channels of real part and imaginary part, which are and is Charbonnier error function, ε is root mean square error function, is the total variation regularization penalty function, and its discrete form is Fundamentally, the goal of the inventive method 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 an inverse wavelet transform module to generate the final high quality image.

[0057] SWU-Net is trained and fine-tuned using simulation data, and the boundary voltage is measured using a water tank device to verify the robustness and generalization of the method. The simulation training data is realized using the COMSOL multi-physics 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 uniformly set outside the measurement area, the "adjacent excitation-adjacent measurement" method is used to modulate the current signal of the observation area, the injected current is 4.5 mA, the frequency is 50 kHz, and the voltage response signal on the electrode is collected. NaCl solution is set as the background in the uniform field, and different radii and numbers of circular inclusions are used as media. The number of inclusions is set to 1-4, and the radius of the inclusions is set to 2 cm-4 cm, and the inclusions do not overlap each other. The conductivity of the uniform field is set to 0.06 S / m, and the dielectric constant is set to 80, and the internal medium is set to different conductivity parameters. The conductivity and dielectric constant are set to any value in the range of 10 -6 -10 6 S / m, 3-10000. A total of 42,430 circular inclusion simulation samples are generated, and the training samples, validation samples and test samples are set to 80%, 10% and 10% of the total database respectively. The EIT forward problem is numerically solved using the finite element method (FEM), and the observation domain is discretized into a dense triangular grid for numerical solution of the complex admittance equation (1). For the 16-electrode EIT measurement model, a total of 208 effective voltages are obtained for each excitation-measurement. The forward problem uses a square grid division method with a resolution of 256x256 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-orientation full convolutional encoder modules and decoder modules of SWU-Net is set to 5, the number of rswFormer modules is set to 5, and the channel number of the input features of the residual four-orientation full convolutional encoder / decoder is set to C in =[8, 16, 32, 64, 128]. In the residual four-orientation full convolutional encoder, in the 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 a s , input channel dimension direction a c , output channel dimension direction ao , the convolution kernel dimension direction a w ) parameter settings are k x k (k = 3), c in x 1, c out x 1, a x 1 (a = 1). In the rswFormer module, the image block size is set to 4, 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, the CrossHL first performs feature construction on the input features through 1 x 1 x 2C k and 3 x 3 x 2C k , and uses tensor shape adjustment to reshape the feature map to and In the cross-transposed 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, and 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, with RAM of 32GB, and the acceleration training process is implemented on an NVIDIA GeForce RTX 2080Ti (GPU, with a display memory of 11GB) platform. The SWU-Net uses the small batch adaptive moment estimation optimizer (Adamax, β1 = 0.9, β2 = 0.999, and the relative tolerance range is set to ε = 10 -5 ) to train the network model, wherein the size of the mini-batch is 64, the number of training times is set to 1200, and 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 application uses five comparison methods to compare the performance of SWU-Net, and the current research on deep learning methods based on complex EIT is less, so we choose a deep learning network based on complex MRI, and use the same data set in the same experimental environment to make a fair comparison, and the comparison methods include Cv-NR iterative method [P.M.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. NMR in Biomedicine, 33(7), p.e4312.], Cv ISTA-Net method [Wang, S., Cheng, H., Ying, L., Xiao, T., Ke, Z., Zheng, H. and Liang, D., 2020. Deep complex MRI: Exploiting deep residual network for fast parallel MR imaging with complex convolution. Magnetic resonance 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 deep CNN. Pattern Recognition, 111, p.107639.] and CvDenseUNet method [Dedmari, M.A., Conjeti, S.Estrada, S., Ehses, P.,. T. and Reuter, M., 2018, September. Complex fully convolutional neural networks for MR image reconstruction. In International Workshop on Machine Learning for Medical Image Reconstruction (pp. 30-38). Cham: Springer International Publishing.]. The quantitative evaluation indicators root mean square error (RMSE), peak 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), the calculation complexity (FLOPs) and the imaging time (Time) of the comparison method and the method proposed in the present application.

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

[0063]

[0064] The quantitative indicator 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 application obtains the optimal results, especially the RMSE is significantly reduced, and the PSNR and SSIM are obviously improved. However, it is worth noting that: (1) the performance improvement of the SWU-Net method proposed in the present application is limited compared with the Cv ISTA-Net method, because the model-driven method based on deep unfolding introduces the physical prior information of the positive problem, which has 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 indicators of the real part and the imaginary part of the imaging results of the SWU-Net method proposed in the present application are lower than those of the method proposed in the present application; (2) it can be seen that the quantitative indicators of the real part and the imaginary part of the imaging results of the SWU-Net method proposed in the present application have performance differences, and the reason 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 feature is suppressed, causing the dielectric constant reconstruction effect to be slightly lower than the conductivity reconstruction effect. In addition, from the perspective of parameter quantity and calculation resources, the method proposed in the present application introduces a complex multi-head attention mechanism acting on the jump connection and the decoder, which increases the parameter quantity and the calculation complexity, and significantly increases the reconstruction time.

[0065] To verify the reconstruction results of the SWU-Net method in actual scenarios, a circular water tank and three kinds of round rods made of different materials are used to simulate different phase media. Similar to the simulation data setting, NaCl solution with a conductivity of 0.05 S / m is used as a homogeneous field background, and copper, carbon steel and resin are used as inclusions for reconstruction. The reconstruction results are shown in Figure 4 As shown in Figure 4 The reconstruction effect based on the deep learning method is obviously better than that of the Cv-NR method, which shows that the optimization algorithm of the first-order approximation will lose the complex shape information, causing the boundary to be blurred and the electrical parameter reconstruction to be inaccurate. 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 used as inclusions at the same time, the method proposed in the application can accurately express the position information and shape features in a low-contrast scene. In addition, from the reconstruction visualization results, it can be seen that the simultaneous reconstruction of the conductivity and the dielectric constant can better distinguish the same material, for example, in a scene where copper and steel materials are distributed at the same time, the combination of the conductivity and dielectric constant distribution images can accurately analyze the different material properties.

[0066] For the Cv-EIT reconstruction problem, the application proposes a space-wavelet dual-domain image reconstruction deep network SWU-Net, which can realize the simultaneous reconstruction of the conductivity and the dielectric constant in the observation region. By designing the Omni dynamic convolution and residual connection strategy of the spatial domain encoder, as well as the wavelet domain feature construction, the space-wavelet dual-domain feature fusion module rswFormer and the high-frequency low-frequency feature fusion CrossHL, the SWU-Net has better spatial resolution and electrical parameter resolution than the existing complex imaging method. The action of the wavelet frequency domain module and the cross-domain fusion module significantly improves the reconstruction performance of the backbone model, which shows that the dual-domain deep learning model is obviously better than the pure spatial feature extraction model in improving the image quality. In general, the method proposed in the application provides a new idea for the multi-parameter electrical tomography task.

[0067] The above only describes the preferred embodiments of the application, and it should be noted that for those skilled in the art, without departing from the inventive concept, several modifications and improvements can be made, which are all within the protection scope of the application.

Claims

1. A method for complex impedance image reconstruction driven by a space-wavelet dual-domain approach, characterized in that, First, the boundary voltage signal on the sensor is obtained using the complex Newton-Raphson method. Mapped to the initial complex admittance image The initial complex admittance image The input features of the SWU-Net model are used for spatial feature encoding and wavelet frequency domain feature construction. The SWU-Net model includes multiple residual four-directional fully convolutional encoders, multiple rswFormer modules, and multiple decoders. In the feature map of the encoder after discrete wavelet transform, the low-frequency sub-band features of the LL direction are used to construct spatial features. The high-frequency sub-band features in the horizontal, vertical, and diagonal directions are input to the rswFormer module after inverse discrete wavelet transform operation and skip connections. At the same time, the spatial input of the decoder, as low-frequency features, is also input to the rswFormer module for 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 and upsampled low-frequency features in the rswFormer module as inputs for cross-attention to perform high-frequency-low-frequency feature cross-fusion, finally obtaining the imaging result. ; The decoder consists of upsampling operations and CrossHL, the first... The input features of each decoder are The output features are , After being After implementing the transposed convolution upsampling operation, we get As input to CrossHL, the first The input of the CrossHL module in each decoder consists of low-frequency spatial features (LF) obtained by upsampling and high-frequency spatial features (HF) output by skip connections. The low-frequency features... and high frequency characteristics The features are decomposed into two channels: real and imaginary. The real and imaginary parts are used as query vectors respectively. , The real and imaginary parts are used as the key vector and value vector, respectively. , CrossHL employs a cross-fusion strategy for feature fusion, and its calculation method is as follows: ； ； This refers to the real part feature output by the CrossHL module. The imaginary part of the output from the CrossHL module; The output of CrossHL is This achieves the fusion of spatial low-frequency features and wavelet domain high-frequency features.

2. The complex impedance image reconstruction method driven by space-wavelet dual domains according to claim 1, characterized in that, The residual four-directional fully convolutional encoder comprises 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 a residual branch based on wavelet domain features. Downsampling based on pooling kernels and The spatial convolution of the convolution kernel consists of two operators, the wavelet domain feature branch consisting of two operators, the first... The input features of each encoder are The output features are , First, Haar wavelet operations are used to obtain the LL low-frequency subband characteristics. and high-frequency subband features, the high-frequency subband features including high-frequency components in the horizontal direction, vertical direction and diagonal direction. Then, LL low-frequency subband characteristics As a four-directional fully convolution operator ODConv The input constructs multi-scale spatial features; The model constructed from the residual four-directional fully convolutional encoder features is as follows: ； in, For the first Spatial domain residual branch features of an encoder For the first Wavelet domain features of an encoder For the first Wavelet low-frequency subband features of an encoder.

3. The complex impedance image reconstruction method driven by space-wavelet dual domains according to claim 1, characterized in that, No. The rswFormer module uses inverse discrete wavelet transform to extract high-frequency subband features. The query vector is reconstructed and then subjected to a depthwise separable convolution to obtain the real and imaginary parts of the query vector. , No. The low-frequency feature outputs of each decoder are used as key vectors and value vectors, respectively, and then subjected to depthwise separable convolution to obtain the real and imaginary parts of the key vectors. and the real and imaginary parts of the value vector. Multi-head self-attention calculations are performed in the characteristic spaces of real conductivity and imaginary permittivity, respectively, and the process is described as follows: ； ； in This is the transpose of the real part of the key vector. This is the transpose of the imaginary part of the key vector. The dimension of the key vector; The resulting attention vector is , For the first k The real part of the layer attention vector. For the first The imaginary part of the layer attention vector; in The imaginary unit is used in the rswFormer module, which uses complex convolution operations to implement a feedforward network. The output of the rswFormer module is... .

4. The complex impedance image reconstruction method driven by space-wavelet dual domains according to claim 3, characterized in that, Adding residual connection branches to the rswFormer module to enhance high-frequency boundary features. Simultaneously use Upsampling ensures that the output features of the skip connections have the same spatial dimension as the corresponding encoder / decoder. The output of the SWU-Net skip connections is as follows: 。 5. The complex impedance image reconstruction method driven by space-wavelet dual domains according to claim 1, characterized in that, The loss function of the SWU-Net model consists of wavelet domain loss. and reconstruction image domain loss composition, ； in: , ， This indicates the number of encoders / decoders in SWU-Net. Indicates the number of training samples. The low-frequency wavelet features output by the decoder. The high-frequency wavelet features output by the decoder. The weights for wavelet domain loss, This represents the low-frequency components of the label distribution. This represents the high-frequency components of the label distribution. These high-frequency components consist of high-frequency components in the horizontal, vertical, and diagonal directions. and Representing 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, respectively. and , It is the Charbonnier error function. It is the root mean square error function. It is the total variational regularization penalty function, and its discrete form is: , For the image at position pixel values, For the horizontal pixel index of the image, For vertical pixel indexing of the image, For training sample index, This refers to the category of high-frequency subbands.

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