## 3 The Design of the New Rotational Convolution Pattern
### Reconstructed Images
Additionally, within this sample set, it can be observed that the training set achieves slightly higher quality compared to the test set. The slight difference hints at the model's ability to adeptly learn the distribution mapping from sensor signals to sample representations. For a statistical analysis of the process, we employed the Mann-Whitney U test. Given the large sample size (3147 samples in the test set), the normal approximation was used for \(p\)-value computation. The mean (\(\mu_{U}\)) and standard deviation (\(\sigma_{U}\)) of the U distribution were calculated using the following equations:  
\[\mu_{U}=\frac{n_{1}\times n_{2}}{2} \tag{13}\]  
\[\sigma_{U}=\sqrt{\frac{n_{1}\times n_{2}\times(n_{1}+n_{2}+1)}{12}} \tag{14}\]  
Here, \(n_{1}\) and \(n_{2}\) represent the sizes of the two comparative sample groups. The Z-score was determined by taking the observed U value, subtracting \(\mu_{U}\), and then dividing by \(\sigma_{U}\):  
\[Z=\frac{U-\mu_{U}}{\sigma_{U}} \tag{15}\]  
This Z-score was subsequently utilized to ascertain the corresponding \(p\)-value from the standard normal distribution. A \(p\)-value less than 0.05 indicates a statistically significant difference between the two sample groups. The obtained \(p\)-values are shown in Table 2 after the calculations. These results indicate statistically significant differences among Conv-A, Conv-B, and Conv-P. The exceedingly small p-values strongly affirm the presence of distinct statistical disparities between Conv-A, Conv-B, and Conv-P. The specific reconstructed images are presented in Figure 7. It can be seen that the CNN for three-dimensional image reconstruction in EMT is feasible. The detection signals from the 16 coils in three dimensions indeed contain information about the three-dimensional distribution of the objects. The CNN network in this paper could learn this relationship and reconstruct images of reasonable quality. As observed in Figure 7, the objects in the reconstructed images are generally clustered rather than dispersed, indicating good performance. This outcome is also related to the choice of loss function employed. Moreover, it can reconstruct positional, size, and shape information for various object configurations, including a single small sphere, a single large sphere, and a combination thereof. The reconstructed images also demonstrate that, compared to the Conv-A and Conv-B patterns, the Conv-P pattern performs better-quality image reconstruction. For instance, in the reconstructed image of the second sample, the completion and filling in of the volume of two large spheres can be observed as the process progresses from Conv-A to Conv-B and then to Conv-P. In the fifth sample, there are also some peripheral artifacts in Conv-A. The reconstructed images of Conv-B and Conv-P are almost consistent with the ground truth. In the reconstructed images of the fourth and seventh samples, the two objects that are nearby appear to be fused in the Conv-A and Conv-B patterns. In contrast, the distinction between the two objects is noticeably more apparent in the Conv-P reconstruction. Therefore, the image quality of the Conv-P reconstruction has improved compared to that of the Conv-A and Conv-B patterns. This suggests that the rotational convolution pattern with projection design positively enhances the image reconstruction quality. \begin{table}
\begin{tabular}{c c c} \hline \hline \(p\) (Conv-A, Conv-B) & \(p\) (Conv-A, Conv-P) & \(p\) (Conv-B, Conv-P) \\ \hline \(2.34\times 10^{-28}\) & \(3.31\times 10^{-73}\) & \(4.88\times 10^{-13}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The \(p\)-values between Conv-A, Conv-B, and Conv-P.  
Figure 7: Three-dimensional reconstructed images.