# A Novel CDMA-Based Secret Message Multiplexing Scheme by Image Data Hiding +
## 4 Experimental Results and Discussion
### Robustness against Noise Attacks
For the salt-and-pepper noise attack, three different density values are chosen, which are 0.1, 0.15, and 0.2, respectively. Figure 9 displays the tainted Lena images with number of users \(N\) equal to 16. For each corrupted image, evidently, the image quality is worse than the noise-free marked image. The PSNR values for the marked Lena image contaminated with the salt-and-pepper noise are listed in Table 6 and plotted in Figure 10a. Compared with the noise-free marked image, the PSNR drop is significant. However, for each density value, as \(N\) increases from 2 to 32, little has changed in the PSNR. The BER values of the extracted secret from the Lena image with different values of \(N\) under the salt-and-pepper noise are listed in Table 7 and plotted in Figure 10b. In contrast to Gaussian noise, for each density value, BER increases gradually with the increase in number of users. Similarly, for each \(N\) value, BER increases with the increase in noise density. The maximum BER is about 0.36 with noise density equal to 0.2 and \(N\) equal to 32. Owing to the impulse nature of the salt-and-pepper noise, when the noise occurs, it is very likely that all the \(N\) secret bits embedded in the \(N\)-digit CDMA codeword group will be destroyed. Thus, when the number of users \(N\) increases, BER is expected to increase accordingly. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Noise \(\sigma\)** & \(N=2\) & \(N=4\) & \(N=8\) & \(N=16\) & \(N=32\) \\ \hline
2.55 & 0.4982 & 0.4404 & 0.2386 & 0.0660 & 0.0150 \\
8.06 & 0.4980 & 0.4994 & 0.4985 & 0.4093 & 0.2521 \\
18.03 & 0.4993 & 0.4987 & 0.4988 & 0.4979 & 0.4448 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: BER of the extracted secret from the Lena image versus number of users \(N\) under Gaussian noise. Figure 8: BER of the extracted secret from the Lena image versus number of users \(N\) under Gaussian noise. (**a**) \(\sigma=2.55\); (**b**) \(\sigma=8.06\); (**c**) \(\sigma=18.03\). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Noise \(\sigma\)** & \(N=2\) & \(N=4\) & \(N=8\) & \(N=16\) & \(N=32\) \\ \hline
2.55 & 0.4982 & 0.4404 & 0.2386 & 0.0660 & 0.0150 \\
8.06 & 0.4980 & 0.4994 & 0.4985 & 0.4093 & 0.2521 \\
18.03 & 0.4993 & 0.4987 & 0.4988 & 0.4979 & 0.4448 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Expected BER of the extracted secret versus number of users \(N\) under Gaussian noise. Based on the previous analysis, we know that data loss may occur under the two kinds of noise attacks. Next, we will take logotype binary images as the secret data, which can tolerate some amounts of bit errors. Several logotype binary images, each for a distinct participant, are embedded into the Lena image. The secret extraction results of two logotype secret images sized \(90\times 90\) corrupted by Gaussian noise and the salt-and-pepper noise are listed in Tables 8 and 9, respectively. For Gaussian noise, the visual quality of both images improves with the increase in \(N\). When \(N\) reaches 16, even the four Chinese characters in the second image become recognizable. As for the salt-and-pepper noise, the visual quality of the images is higher than the average of the two images. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Noise Density** & \(N=2\) & \(N=4\) & \(N=8\) & \(N=16\) & \(N=32\) \\ \hline
0 & 45.13 & 39.91 & 34.38 & 28.65 & 22.66 \\
0.10 & 15.42 & 15.43 & 15.37 & 15.30 & 14.76 \\
0.15 & 13.67 & 13.64 & 13.62 & 13.56 & 13.24 \\
0.20 & 12.42 & 12.42 & 12.38 & 12.38 & 12.13 \\ \hline \end{tabular}
\end{table} 
Table 6: PSNR values (dB) versus number of users \(N\) for the Lena image under salt-and-pepper noise. Figure 10: (a) PSNR values versus number of users \(N\) for the Lena image under salt-and-pepper noise. (b) BER of the extracted secret from the Lena image versus \(N\) under salt-and-pepper noise.