# Dual Partial Reversible Data Hiding Using Enhanced Hamming Code
## 4 Experimental Results and Discussions
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Method** & **Measure** & **[PERSON]** & **[PERSON]** & **[PERSON]** & **[PERSON]** \\ \hline \multirow{3}{*}{[PERSON] et al. (2007) [13]} & bpp & 1.00 & 1.00 & 1.00 & 1.00 \\  & PSNR\#1 & 45.12 & 45.14 & 45.13 & 45.13 \\  & PSNR\#2 & 45.13 & 45.15 & 45.11 & 45.14 \\  & bpp & 1.53 & 1.53 & 1.53 & 1.53 \\ [PERSON] et al. (2013) [14] & PSNR\#1 & 39.89 & 39.94 & 39.89 & 39.9 \\  & PSNR\#2 & 39.89 & 39.94 & 39.89 & 39.9 \\  & bpp & 1.07 & 1.07 & 1.07 & 1.07 \\ [PERSON] \& [PERSON] (2013) [15] & PSNR\#1 & 49.76 & 49.75 & 49.75 & 49.77 \\  & PSNR\#2 & 50.42 & 50.34 & 50.44 & 50.54 \\  & bpp & 1.00 & 1.00 & 1.00 & 1.00 \\ [PERSON] et al. (2015) [16] & PSNR\#1 & 52.11 & 51.25 & 52.12 & 52.12 \\  & PSNR\#2 & 41.58 & 41.52 & 41.58 & 41.58 \\  & bpp & 1.00 & 1.00 & 1.00 & 1.00 \\ [PERSON] et al. (2015) [17] & PSNR\#1 & 51.13 & 51.15 & 49.22 & 49.23 \\  & PSNR\#2 & 51.15 & 51.14 & 49.2 & 49.18 \\  & bpp & 0.21 & 0.21 & 0.21 & 0.21 \\ [PERSON] et al. (2018) [21] & PSNR\#1 & 52.71 & 52.67 & 52.7 & 52.73 \\  & PSNR\#2 & 52.81 & 52.72 & 52.76 & 52.78 \\  & bpp & 1.50 & 1.50 & 1.50 & 1.50 \\ Proposed scheme & PSNR\#1 & 48.19 & 48.2 & 48.22 & 48.2 \\  & PSNR\#2 & 49.01 & 49.02 & 48.96 & 49.06 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of maximum bpp and PSNR of existing methods and our proposed method. In Figure 5b, the relationship between PSNR and bpp for stego image #2 is illustrated. At an embedding rate of 0.2 bpp, the proposed method achieves a PSNR of 56.83 dB, marking the highest recorded value among all evaluated approaches. Furthermore, the proposed method consistently maintains the highest PSNR across the entire embedding range up to 1.5 bpp, ensuring superior image quality preservation. On the other hand, the method of [PERSON] et al. (2021) [23] achieves the second-highest PSNR performance among the evaluated techniques, further demonstrating its effectiveness in maintaining image quality. Overall, our proposed method effectively balances high embedding capacity and PSNR, making it a competitive solution for reversible data hiding. The ability to sustain high PSNR values across a broad embedding range highlights its robustness in preserving image quality while embedding a substantial amount of data. The RS analysis results in Figure 6 illustrate the resistance of the proposed method against regular-singular (RS) analysis attacks. RS analysis is a commonly used statistical attack technique that helps detect the presence of hidden information in an image by  
Figure 5: Comparative average PSNR of #1 (**a**) and #2 (**b**) with different ERs for all test images in different schemes, based on the methods in [15; 22; 23]. analyzing local pixel patterns. In this method, each shadow image is divided into three distinct categories:  
* **Regular Group (RM or R-M)--**Represents smooth pixel regions that follow predictable patterns. * **Singular Group (SM or S-M)--**Represents highly textured or noisy pixel regions. * **Unchanged Group (U)--**Represents pixels that remain stable and are not affected by the embedding process. The RM and SM (or R-M and S-M) values indicate the proportion of regular and singular pixels, respectively, under different masks (M or -M). In our experiments, four consecutive pixels were grouped together, with the applied mask M is defined as [0,1,1,0]. The statistical relationship between the regular and singular groups must satisfy the following conditions:  
\[RM+SM\leq 1,\quad R-M+S-M\leq 1, \tag{10}\]  
\[RM\approx R-M,\quad SM\approx S-M. \tag{11}\]  
From Figure 6, it can be observed that both shadow images (number 1 and number 2) conform to the constraints defined in Equations (10) and (11), ensuring that the statistical integrity of the stego images is preserved. This indicates that the proposed method effectively maintains a balanced distribution of regular and singular groups, making it resilient against RS analysis attacks. Figure 6: RS analysis for each shadow of Boat.