# Suppression of Multiple Reflection Interference Signals in GPR Images Caused by Rebar Using VAE-GAN
## 3 Validation on Synthetic GPR Data
### Comparative Experiments  
To validate the effectiveness of the proposed model in suppress rebar clutter, three widely used unsupervised learning models were chosen as baselines (UNIT, CycleGAN [31], DualGAN [32]). UNIT combines the concepts of VAE and GAN to achieve unsupervised image-to-image translation across different styles and content by shared latent representations. CycleGAN and DualGAN achieve unsupervised image-to-image translation between two different domains through adversarial training and cycle consistency loss. We conducted comparative experiments between these three models and the our proposed model. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Media** & **Relative Permittivity** & **Conductivity (S/m)** \\ \hline Rebar & 300 & \(1.0\times 10^{8}\) \\ Concrete & 8\(\sim\)10 & \(1.0\times 10^{-4}\) \\ Water & 81 & \(1.0\times 10^{-3}\) \\ Air & 1 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The relative permittivity and conductivity of various media. Figure 4: The simulation models and The GPR images. (**a**) The simulation model contains rebars and void defect. (**b**) The GPR image contains rebars and void defect. (**c**) The simulation model contains only void defect. (**d**) The GPR image contains only void defect. In the experiments, we selected GPR images of void defects with rebar clutter interference from the test dataset as input for the trained models. We compared the suppression effects of different models, with the outcomes displayed in Figure 5.  
As shown in the figure, it is evident that our model performs best in suppressing rebar clutter as the rebar clutter in the original images is effectively suppressed while more features of void defects are preserved. UNIT and CycleGAN also effectively suppress rebar clutter signals, but they reconstruct void defects incompletely with less clarity and accuracy in details. CycleGAN even incorrectly reconstructs some non-void clutter. In contrast, DualGAN shows slightly poorer performance in clutter suppression as rebar clutter is not completely suppressed and more clutter remains at the overlap of void signals, leading to distortion of void defect signals. Overall, our model significantly outperforms other models by effectively suppressing rebar clutter and preserving clear and intact void defect signals. The void defect signals that were previously masked or interfered with by rebar clutter can now be more easily identified. This validates the superior performance of our model. To quantitatively compare the effectiveness of various models in suppress rebar clutter, this study uses Root Mean Square Error (RMSE), Peak Signal-to-Noise Ratio (PSNR), and Structural Similarity Index Measure (SSIM) to evaluate the images before and after rebar suppression [33; 34]. RMSE measures the root mean square error between the original and denoised image. The formula is shown as Equation (8):  
\[\text{RMSE}=\sqrt{\frac{1}{mn}\sum_{i=1}^{m}\sum_{j=1}^{n}[I(i,j)-K(i,j)]^{2}} \tag{8}\]  
where \(I(i,j)\) and \(K(i,j)\) denote the pixel values of the original and denoised images, respectively, while \(m\) and \(n\) denote the width and height, respectively. PSNR measures the peak signal-to-noise ratio between the original and denoised image. The formula is shown in Equation (9):  
\[\text{PSNR}=10\log_{10}\left(\frac{MAX^{2}}{MSE}\right) \tag{9}\]  
Figure 5: Comparison of rebar suppression results of different models. (**a**) Original GPR image with rebar clutter interference. (**b**) GPR image of void defects corresponding to the original image. (**c**) Our model. (**d**) UNIT. (**e**) CycleGAN. (**f**) DualGAN. where \(MAX\) is the maximum possible pixel value, \(MSE\) is the mean squared error. SSIM measures the similarity between the original and denoised images.