# Electromagnetic Imaging of Uniaxial Objects by Two-Step Neural Network
## 4 Numerical Results  
In our investigation, we operate under the assumption that anisotropic objects are situated within free space, surrounded by emitters and receivers distributed uniformly around the scattering object. Both TM and TE waves are emitted in diverse directions to  
Figure 4: Convolution neural network architecture.  
Figure 3: Deep convolutional neural network architecture. \(M\) denotes the receivers, \(N_{i}\) denotes the transmitter point, and N denotes the number of split units.  
illuminate the anisotropic objects, while we gather scattered field data from these unknown scatterers. Leveraging this received scattered field data, we employ a DCNN to estimate the initial permittivity. Subsequently, this estimate is fed into a CNN to reconstruct a precise electromagnetic image.  
In our simulated environment, we partition the edge constant size of the scatterer into \(\frac{0.2\lambda_{0}}{\sqrt{\varepsilon_{r}}}\), where \(\varepsilon_{r}\) stands for the relative permittivity of the anisotropic object, and \(\lambda_{0}\) represents the wavelength in free space. We vary the dielectric coefficient of the scatterer from 1 to 2.5, while maintaining the frequency of the incident wave at 3 GHz. We deploy 32 transmitter and receiver antennas evenly. To mimic real-world conditions, we introduce Gaussian noise of 5% and 20% into the simulated environment for analysis. We gauge the dielectric constant distribution using scatter field information through the DCNN in the first stage, i.e., to input the real and imaginary parts, respectively, into the DCNN. In the second stage, we use the preliminary image from the DCNN to reconstruct a more accurate dielectric constant distribution through a convolutional neural network architecture. In the artificial intelligence segment, we allocate 80% of the scattered field for the training set and the rest for the test set. We utilize ADAM uniformly to train the two-step module, setting the training parameters with a learning rate ranging from \(10^{-3}\) to \(10^{-4}\), and a maximum epoch of 40. For every optimization epoch, we ensure that the training data are shuffled.  
We use the root mean square error and image similarity to verify the results of the numerical simulation as well as conduct comparison and analysis. The equations are as follows:  
\[-\left(E_{z}^{i}\right)=([G_{1}][\tau_{z}]-[I])(E_{z}) \tag{15}\]  
\[(E_{z}^{s})=[G_{2}][\tau_{z}](E_{z}) \tag{16}\]  
\(\overset{=}{\varepsilon_{r}}\) and \(\overset{=r}{\varepsilon_{r}}\) are the ground truth and reconstructed relative permittivity profiles, respectively, \(\mathrm{M_{t}}\) represents the number of tests conducted, and \(\mathrm{F}\) denotes the Frobenius norm.  
In this context, \(\overset{-}{y}\) and \(\mathrm{y}\) represent the reconstructed and true relative permittivity profiles, respectively. \(\mathrm{\mu_{y}}\) denotes the mean of \(\mathrm{y}\), \(\overset{2}{\sigma_{y}^{2}}\) signifies the variance of \(\mathrm{y}\), and \(\sigma_{\overset{-}{y}}\) represents the covariance of \(\overset{-}{y}\) and \(\mathrm{y}\). To prevent division by zero, two small constraints \(\mathrm{C_{1}}=\left(\mathrm{K_{1}D}\right)^{2}\) and \(\mathrm{C_{2}}=\left(\mathrm{K_{2}D}\right)^{2}\) are added, where \(\mathrm{K_{1}}=0