## Appendix A  
_Appendela.1. Optimization of Hyperparameters_  
In this section, the optimization of three parameters is described.  
\begin{tabular}{l l} \(\bullet\) & Number of neurons in the output layer. This indicates the number of pixels in the reconstructed image. The output image size or number of output neurons varied (10,000, 8100, 4900, 3600, and 2500) (see Figure 11) \\ \(\bullet\) & Number of hidden layers. \\ \(\bullet\) & Number of neurons in the hidden layer. \\ \end{tabular}  
Figure 11: (a) SSIM of 243 test cases with different output sizes. The green dashed line is the mean of the distribution; the red line is the median. (b) Evolution of SSIM for different numbers of hidden neurons.  
The Structural Similarity Index Measure (SSIM) was used during the optimization process is as a cost function to measure the quality of the reconstruction and the mean square error was used with increasing epochs to measure the convergence of the NN. To perform the variation study and to see how it affects the quality of the reconstruction, some parameters were left unchanged:  
* The learning rate was set to an initial value of 0.9 for all the cases and the adaptation equation was \(\alpha_{new}=\alpha_{old}\cdot 0.9\), where \(\alpha_{new}\) is the updated learning rate and \(\alpha_{old}\) is the previous one. This rule additionally incorporates a patience parameter.
* The batch size was set to 10.
* The number of epochs was set to 2000.
* Random seed. Although this is not a parameter of neural networks per se, it allows for a consistent comparison across variations  
Number of neurons in the output layer  
We can observe in Figure 11 that as the number of pixels decreased (number of outputs in the output layer), the average SSIM increased. Notably, larger output image sizes required greater numbers of output neurons, leading to higher computational costs and heavier training. The reduction in SSIM can be attributed to the small size of the internal objects: although the morphological reconstruction improved, errors in the pixel intensity values became more pronounced. Consequently, when errors occurred, they affected a larger number of pixels, thereby worsening the reconstruction quality.  
Since the best results were obtained with a 50 \(\times\) 50 resolution and the number of objects did not produce a significantly higher resolution or finer distinction, we selected this size for the output. Additionally, its lower computational cost makes it a suitable choice.  
To further improve the reconstruction quality, we analyzed the variations in the number of neurons in the hidden layer. The parameter variation was non-uniform, while the neural network output remained fixed at 50 \(\times\) 50 pixels. As the number of hidden layer neurons increased (Figure 11b), the SSIM distribution shifted toward higher values, indicating improved reconstruction quality. However, this improvement stabilized at around 10,000 neurons, suggesting that this number represents a threshold for optimal SSIM. Consequently, an effective configuration involved setting the number of hidden neurons equal to the number of output neurons.  
Number of hidden layers  
In this case, the analysis involved adding more intermediate layers and examining their effect on the same evaluation distribution (Figure 12). As shown in Figure 12, increasing the number of intermediate layers did not necessarily improve the SSIM, as the average value (dashed green line) remained approximately constant at 0.84. Therefore, for a 50 \(\times\) 50 output, the optimal configuration only includes one intermediate layer, as it provides a good balance between computational efficiency during training and reconstruction quality.  
Figure 14: Best tomographic reconstructions of actual measurements using conventional algorithms based on SSIM metric: (**A**) FBP, (**B**) CART, (**C**) FBP, and (**D**) FBP.