# Self-Attention GAN for Electromagnetic Imaging of Uniaxial Objects
## 4 Numerical Result  
This section outlines the simulation framework designed to investigate the inverse scattering characteristics of uniaxial dielectric objects situated in free space. The primary objective is to reconstruct the spatial distribution of the relative permittivity within anisotropic media. To accomplish this, both TM- and TE-polarized plane waves are continuously applied to illuminate the domain containing the target, thereby collecting a comprehensive set of scattered field data necessary for the reconstruction process.  
Since each U-Net operates independently, during training, GPU parallelization is highly suitable and efficient in computational tasks. The ADAM is configured with an initial learning rate of \(10^{-4}\). Epochs are set to drop at 70, with a drop learning rate of \(10^{-1}\). The mini-batch size is 16 and training runs for up to 200 epochs. The training data is shuffled at the beginning of each epoch to ensure robust learning. Specifically, the learning rate is set to 0.001, as higher values result in unstable training dynamics and poor convergence, whereas lower values lead to sluggish learning and suboptimal reconstruction performance. The batch size is fixed at 16 to balance training stability and computational efficiency. Empirically, smaller batch sizes introduce noisy gradient updates and destabilize the training process, while larger batch sizes impose higher memory demands and prolong convergence. The training parameter configuration as shown in Table 1.  
To evaluate the effectiveness of each method, we utilize the Root Mean Square Error (RMSE), defined as:  
\[RMSE=\frac{1}{M_{t}}\sum_{i=1}^{M_{t}}\left\|\overline{\epsilon}_{r}-\overline{ \epsilon}_{r}^{=r}\right\|_{F}\left/\left\|\overline{\epsilon}_{r}\right\|_{F}\right. \tag{38}\]  
where \(\overline{\epsilon}_{r}\) denotes the ground truth of the relative permittivity distribution, whereas \(\overline{\epsilon}_{r}^{=r}\) refers to the reconstructed result. The parameter \(M_{t}\) indicates the total number of test samples, and \(F\) represents the Frobenius norm. To provide a more comprehensive assessment of reconstruction quality across different methods, the Structural Similarity Index Measure (SSIM) is also utilized, and it is mathematically expressed as follows:  
\[SSIM=\frac{\left(2\mu_{\widetilde{y}}\mu_{y}+C_{1}\right)\left(2\sigma_{ \widetilde{y}y}+C_{2}\right)}{\left(\mu_{\widetilde{y}}^{2}+\mu_{y}^{2}+C_{1} \right)\left(\sigma_{\widetilde{y}}^{2}+\sigma_{\widetilde{y}}^{2}+C_{2} \right)} \tag{39}\]  
where \(\widetilde{y}\) and \(\mathrm{y}\) represent the reconstructed and ground truth permittivity distributions, respectively. The term \(\mu_{y}\) denotes the meaning value of \(\mathrm{y}\), \(\sigma_{\widetilde{y}}^{2}\) corresponds to the variance of the reconstructed profile, and \(\sigma_{\widetilde{y}y}\) indicates the covariance between \(\widetilde{y}\) and \(\mathrm{y}\). The constants \(C_{1}\) and \(C_{2}\) are added to prevent division by zero, where \(C_{1}=\left(K_{1}D\right)^{2}\) and \(C_{2}=\left(K_{2}D\right)^{2}\); \(K_{1}=0.01\), \(K_{2}=0.03\), and D is the dynamic range of pixel intensities in the target image \(\mathrm{y}\)[21].