## 6 Experimental Results and Discussion
### Comparison with State-of-the-Art Schemes
The values of PSNR, SSIM and PSNR-HVS-M for the visual results shown in Tables 9 and 10 are reported in Table 11. It can be observed that for alteration rates greater than 30%, the proposed SR-HTR method presents a better reconstruction performance in the metrics PSNR and PSNR-HVS-M. Furthermore, the process [36] provides a higher reconstruction performance for alteration rates lower than 30%. Regarding SSIM, the best results for 20% and 30% rates belong to [23] due to the SPITH transform utilized in the generation of the \begin{table}
\begin{tabular}{c c c c c} \hline \hline SR-HTR & 20\% & 30\% & 40\% & 50\% \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Visual quality comparison for the reconstruction of Kodak-15 using an alteration rate between 20% and 50%. reconstruction bits, which allows a higher quality in reconstructing the blocks. Nonetheless, the SR-HTR method maintains an acceptable performance when more than 40% of the image is modified. It is important to emphasize that the reconstructed image through SR-HTR is not significantly affected by the growth in the alteration rate. The results displayed in Tables 12-14 represent the average values of PSNR, SSIM and PSNR-HVS-M, correspondingly, for reconstructing the test images using the first alteration scheme. These results reflect the evaluation shown in Tables 9-11, where the proposed method demonstrates more balanced results between the change detection and the reconstruction process. Although a lower performance in change detection was obtained (as shown in Tables 7 and 8), the reconstructed images' quality drastically increased since the proposed method generates an authentication bit for each set of 15 reconstruction bits. The SR-HTR method aims to obtain a better performance in reconstructing large areas of modified pixels without considerably affecting the change detection process and the quality of the watermarked image, as one can see in Table 6. Subsequently, the method [36] achieves the second-best performance due to its insertion process that uses three copies of the watermarks. Methods [10; 23] are placed in the third and fourth positions because of their intolerance to high alteration rates and because of the insertion of only two copies of the reconstruction bits. Finally, methods [2; 24], which only insert a single version of the reconstruction bits, have demonstrated a lower performance due to their inability to solve the tampering coincidence problem. \begin{table}
\begin{tabular}{c c c c} SR-HTR & 60\% & 70\% & 80\% & 90\% \\ \hline \end{tabular}
\end{table} 
Table 10: Visual quality comparison for the reconstruction of Kodak-15 using an alteration rate between 60% and 90%. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & **10\%** & **20\%** & **30\%** & **40\%** & **50\%** & **60\%** & **70\%** & **80\%** & **90\%** \\ \hline SR-HTR & 0.967 & 0.935 & 0.901 & 0.868 & 0.833 & 0.793 & 0.750 & 0.696 & 0.616 \\ [PERSON] [36] & 0.972 & 0.943 & 0.906 & 0.852 & 0.780 & 0.679 & 0.561 & 0.440 & 0.336 \\ [PERSON] [23] & 0.977 & 0.959 & 0.919 & 0.875 & 0.817 & 0.676 & 0.540 & 0.347 & 0.167 \\ [PERSON] [2] & 0.934 & 0.841 & 0.743 & 0.639 & 0.537 & 0.431 & 0.326 & 0.220 & 0.111 \\ [PERSON] [24] & 0.942 & 0.854 & 0.753 & 0.648 & 0.542 & 0.429 & 0.319 & 0.210 & 0.103 \\ [PERSON] [10] & 0.974 & 0.921 & 0.834 & 0.722 & 0.603 & 0.478 & 0.359 & 0.240 & 0.122 \\ \hline \hline \end{tabular}
\end{table} 
Table 14: Comparison of average PSNR-HSV-M for the reconstruction of the test images with alteration rates between 10% and 90%.