## 3 The Design of the New Rotational Convolution Pattern
### Reconstructed Images  
The simulation environment is the multiphysics software from COMSOL 5.4. The network is constructed and implemented in PyCharm based on the TensorFlow environment. Upon establishing the network, we implement the image reconstruction process in two  
Figure 6: Rotational convolution pattern: Conv-P.  
steps. First, we train the network with a pre-determined training set and then use the test set to test the results on the trained network. The evaluation parameters for reconstructed images are the Image Correlation Coefficient (CC), the Relative Image Error (IE), the Peak Signal-to-Noise Ratio (PSNR), and the Structural Similarity Index Measure (SSIM). \[CC =\frac{\sum_{i=1}^{N}(\hat{g}_{i}-\tilde{\hat{g}})(g_{i}-\tilde{ \hat{g}})}{\sqrt{\sum_{i=1}^{N}(\hat{g}_{i}-\tilde{\hat{g}})^{2}\sum_{i=1}^{N}( g_{i}-\tilde{\hat{g}})^{2}}} \tag{8}\] \[IE =\frac{\|\hat{g}-\hat{g}\|}{\|\hat{g}\|}\] (9) \[\text{MSE} =\frac{1}{N}\sum_{i=1}^{N}[g_{i}-\hat{g}_{i}]^{2}\] (10) \[\text{PSNR} =10\cdot\log_{10}\left(\frac{\text{MAX}_{g}^{2}}{\text{MSE}}\right)\] (11) \[\text{SSIM} =\frac{(2\mu_{g}\mu_{g}+c_{1})(2\sigma_{g\hat{g}}+c_{2})}{(\mu_{ g}^{2}+\mu_{\hat{g}}^{2}+c_{1})(\sigma_{g}^{2}+\sigma_{\hat{g}}^{2}+c_{2})} \tag{12}\]  
Here, \(g\) denotes the vector of the actual distribution (the ground truth), while \(\hat{g}\) represents the vector of the predicted distribution (reconstructed image). Both \(g\) and \(\hat{g}\) have dimensions of \(1\times 3240\). \(MAX_{g}\) is the maximum possible pixel value of the image (in this paper, it is 1). \(\mu_{g}\) is the average value of the actual distribution. \(\mu_{\hat{g}}\) is the average value of the predicted distribution. \(\sigma_{g}^{2}\) is the variance of the actual distribution. \(\sigma_{\hat{g}}^{2}\) is the variance of the predicted distribution. \(\sigma_{g\hat{g}}\) is the covariance between the actual distribution and the predicted distribution. \(c_{1},c_{2}\) are small constants added to avoid division by zero. Reconstructed images with higher imaging quality generally tend to have higher CCs, lower IEs, higher PSNRs, and higher SSIMs. Table 1 presents the average values of the CC, IE, PSNR, and SSIM across all training and testing sets. In terms of imaging quality metrics, the efficacy of the convolution patterns is ranked as follows: Conv-P > Conv-B > Conv-A. The superiority of Conv-P over Conv-B suggests that the rotational convolution pattern with projection design is more adept at utilizing the spatial projection information inherent in the EMT sensing modality. This approach can provide the CNN with more spatial structural information from the sensors. The fact that Conv-B outperforms Conv-A indicates that the current one-dimensional convolution pattern is more effective in imaging than the two-dimensional approach, possibly because the latter does not adequately exploit the spatial projection information of EMT. In Conv-A, signals with low correlations may be convoluted together, contributing to effective feature extraction. However, it is noteworthy that the differences among Conv-P, Conv-B, and Conv-A are not substantial. If a 3D industrial application requires faster computing speed, and if Conv-B's imaging accuracy meets on-site demands, then Conv-B could also be a viable \begin{table}
\begin{tabular}{c c c c c} \hline \hline Train Set & CC & IE & PSNR (dB) & SSIM \\ \hline Conv-A & 0.7840 & 0.7685 & 18.0234 & 0.8397 \\ Conv-B & 0.8006 & 0.6927 & 18.4263 & 0.8624 \\ Conv-P & 0.8438 & 0.5721 & 18.7501 & 0.8702 \\ \hline Test Set & CC & IE & PSNR (dB) & SSIM \\ \hline Conv-A & 0.7689 & 0.7974 & 18.0841 & 0.8422 \\ Conv-B & 0.7735 & 0.7363 & 18.2479 & 0.8631 \\ Conv-P & 0.8052 & 0.6398 & 18.3705 & 0.8695 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The evaluation parameters of reconstructed images. option. This is especially relevant considering that Conv-P has nearly twice the number of parameters compared to Conv-B.