## 3 The Design of the New Rotational Convolution Pattern
### Comparison of Convolution Patterns  
When applying a CNN to EMT, the targets of convolution are the detection signals collected by the sensors, namely, the different projections. These signals are arranged according to the order of acquisition, without a special secondary design for convolution. For clarity, we chose to set the total number of coils to 5 in Figures 4-6, aiming to make the convolution pattern descriptions more intuitive. Nonetheless, the entire process is consistent with the 16-coil EMT model in this article.  
Figure 4: Convolution pattern: Conv-A.  
Figure 5: Convolution pattern: Conv-B.  
Typically, the process involves two conventional patterns: a two-dimensional convolution pattern and a one-dimensional convolution pattern. Figure 4 illustrates the conventional two-dimensional convolution pattern termed 'Conv-A', which involves sequential convolution over a \(2\times 2\) matrix region, moving from left to right and top to bottom, executing a total of \((n-1)^{2}\) convolution operations, where \(n\) represents the number of coils.  
Figure 5 shows the normal one-dimensional convolution pattern, termed 'Conv-B' in this paper, which consists of executing convolution sequentially over a \(1\times 2\) region of a vector. In practice, the normal one-dimensional convolution operation is performed on a one-dimensional vector, with a total of \(\frac{n\times(n-1)}{2}-1\) convolution operations conducted.  
It is observed that part of the convolution process in Conv-A and Conv-B is chaotic. In Conv-A, many adjacent projection combinations do not participate in convolution. In Conv-B, after the convolution of \(p_{1-4}\) and \(p_{1-5}\) is completed, \(p_{1-5}\) must be followed by \(p_{2-3}\), and the two projections \(p_{1-5}\) and \(p_{2-3}\) are not adjacent. Therefore, we refer to the development of CNN, how it works in image recognition, and the reconstruction mode of tomography (this part has been described in Section 1.3). Building on these insights, we introduce a rotational convolution pattern with projection design termed 'Conv-P'.  
In Figure 6, the convolution process, according to the logical working principle of EMT, is depicted in five steps. Starting with Step 1, convolution begins with the projection from \(p_{1-2}\) to \(p_{1-5}\), using coil 1 for excitation. Since the previous step concluded with the projection direction \(p_{1-5}\), Step 2 begins at this point, ensuring continuity by concatenating the convolution related to coil 1 with that of coil 5. Consequently, the excitation shifts from coil 1 to coil 5. The convolution proceeds from \(p_{1-5}\) to \(p_{4-5}\) and concludes at \(p_{4-5}\), indicating that the sequential convolution involving coil 5 is completed. This process is repeated through three additional steps, with each convolution movement between steps being rotational in the spatial projection. Notably, in Step 5, the final projection is \(p_{2-1}\), which coincides with the initial projection from Step 1, thus creating a closed loop. Therefore, from Step 1 to Step 5, a total of \(n\times(n-2)+1\) convolution operations are executed.