## 4 Results
### Simulated sinograms: Physical Parameter Estimation (Model 1)  
The objective of this model was to estimate the longitudinal velocities inside of the specimens (regression problem). It should be noted that, in the simulations, the densities and velocities of the cements followed a uniform distribution. Specifically, the velocity of the external cement (P1) ranged between 4585 m/s and 5056.24 m/s, while the internal cement (P2) ranged between 3934.76 m/s and 4335.79 m/s.  
Figure 18 presents four selected cases where the left images correspond to the original sample with its actual velocity map and the right images represent the reconstructed velocity map. In this sense, a good estimation of both the velocity values and the morphology of the internal cement structures can be observed. Since it is not feasible to display all 6000 cases, Figure 19a illustrates the SSIM values for the entire testing dataset. The SSIM metric ranged from 0 (completely different images) to 1 (identical images) and accounts for the similarities in both the numerical values and the morphology. As shown, the mean SSIM value exceeded 0.95, with low variance, indicating a high-quality reconstruction.  
As observed in Figure 18, when the longitudinal wave velocity of the outer cement (P1) and inner cement (P2) became more similar, the network encountered greater difficulties in performing the reconstructions (Figure 18a,b). Conversely, as the difference increased,  
\begin{table}
\begin{tabular}{l c c c c} \hline \hline \multirow{2}{*}{**Dataset**} & \multicolumn{4}{c}{**Number of Elements**} \\ \cline{2-5}  & **Total** & **Training** & **Validation** & **Testing** \\ \hline Simulated & 26,280 & 14,280 & 6000 & 6000 \\ \hline Real & 4 & - & - & 4 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Number of elements in each dataset.  
\begin{table}
\begin{tabular}{l l} \hline Neurons in input layer & 6300 \\ \hline Neurons in hidden layer & 2500 \\ \hline Neurons in output layer & 2500 \\ \hline Number of hidden layers & 1 \\ \hline Batch size & 10 \\ \hline Initial learning rate & 0.9 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Result of optimization parameters for neural network model.  
the outlines of the internal objects became sharper, leading to improved reconstruction accuracy (Figure 18c,d).  
Additionally, the blurring effect observed at material boundaries is an intrinsic characteristic of this model and was more pronounced due to the need to estimate continuous values. In contrast, the classification model described in the following section was designed to distinguish between different material types. As a result, the range of possible values was more constrained as it employs a sigmoid activation function, which exhibits a steeper derivative compared to the linear activation function used in the regression model. This sharper transition in the classification model reduces boundary blurring compared to the regression approach.  
Figure 19: Evaluation of 6000 test cases using the velocity as a parameter for the estimation model (the blue line is the mean of the distribution and the pink dot is the median) using simulation data: (**a**) SSIM value during velocity estimation in model 1 (mean \(\pm\) SD = 0.95 \(\pm\) 0.02); (**b**) SSIM value for P1 (0.95 \(\pm\) 0.03) and P2 (0.97 \(\pm\) 0.02) materials during classification process in model 2.  
Figure 18: Examples of reconstructions using the neural network and evaluation cases. The output pair from the neural network is represented at the given projections. The theoretical output is what we should obtain from the reconstruction: (**a**) different size objects (**b**) two same size objects (**c**) one embedded object (**d**) different size objects but in contact each other.