Rotational Convolution Design in Convolutional Neural Networks for Direct 3D Electromagnetic Tomography

The three-dimensional (3D) reconstruction of Electromagnetic Tomography (EMT) is an important task for many applications, such as the non-destructive testing of inner defects in rail systems. Additionally, image reconstruction algorithms utilizing deep learning methods have been verified to be useful in recent years. Therefore, the interpretability of deep learning is a question that is relevant to its application in other areas. This paper proposes an innovative rotational convolution pattern, Conv-P, for convolutional neural network (CNN) image reconstruction in a 3D EMT system. This pattern is based on the projection relationships inherent in tomographic imaging, where each convolution is performed on adjacent projections along the excitation rotation direction. The advantage of this pattern is that it can generate the convolution process by utilizing the 3D structural information from real sensors. To verify the effectiveness of this convolution pattern, we constructed a 3D dual-layer 16-coil EMT model and tested its image reconstruction performance. The results demonstrate that, compared with two common convolution patterns, Conv-P achieves a 4.7% and 4.1% increase in the Image Correlation Coefficient (CC), a 19.8% and 13.1% reduction in the Relative Image Error (IE), a 0.67% and 1.59% increase in the Peak Signal-to-Noise Ratio (PSNR), and a 3.24% and 0.74% increase in the Structural Similarity Index Measure (SSIM).