# Reversible Data Hiding in Encrypted Image Based on Multi-MSB Embedding Strategy
## 4 Experimental Results and Analysis
### Comparisons with Related Methods and Analysis  
In order to demonstrate superiority of the proposed method, we compare the proposed method with different framework methods [31; 35; 36; 38; 39] in terms of maximum pure embedding rate and reconstructed image quality with only encryption key. It is noted that the method by [PERSON] et al. [31] is based on the VRBE framework, while the other methods [35; 36; 38; 39] are based on the BBRE framework. In particular, two MSB prediction methods proposed by [PERSON] et al. [38] and [PERSON] et al. [39] are overwhelmingly related with the proposed method. Overall, the five compared methods are all about the RDH algorithm in the encryption domain. The proposed method and another two methods proposed in [38] and [39] are all based on an MSB embedding strategy. Thus, we compared with these two methods in terms of maximum embedding rate. We use the eight well-known images of Lena, Airplane, Man, Crowd, Baboon, Hill, Peppers, and Lake for comparison. The comparison results are as shown in Table 4. For the approach of [PERSON] et al. CPE [38], the original image is modified in order to avoid all prediction errors. We can see that the maximum embedding rate is 1 bpp for each tested image because every pixel of the image can accommodate a bit in this approach. However, it will cause some damage to the quality of the reconstructed image. In the approach of [PERSON] et al. EPE [38], the information about the error location is recorded in the encrypted image, thus the embedding capacity is slightly smaller than the approach of [PERSON] et al. CPE [38]. However, during the decoding phase, the original image can be recovered losslessly. For the method proposed by [PERSON] et al. [39], different from the two approaches in [38], two bits can be embedded into one pixel, which can improve the embedding rate especially in smooth images. In the methods proposed in [38] and [39], one or two bits of data can be embedded into a pixel at most, which limits the embedding rate. In the proposed method, the number of data bits that a pixel can accommodate increases to 5 (at most 5). For the images with different smooth levels, we can select the most suitable value of \(m\) to embed data which is more flexible than the methods in [38] and [39]. For our method and [PERSON] et al. [39], the maximum embedding rate differences of eight tested images are relatively large, because the embedding capacity of these two methods has a great relationship with the smoothness of the image. When the image is more complex, the embedding capacity is smaller. For the image Baboon, which is more complex, the embedding rate is much smaller than that of other images. Compared with the two approaches in [38], the proposed method has a higher embedding rate in all tested images except for image Baboon, and the average embedding rate of the eight tested images increases by 0.4268 bpp and 0.4647 bpp, respectively. Compared with [PERSON] et al. [39], the proposed method has a higher pure embedding rate in all eight tested images, and the average embedding rate increases by 0.4437 bpp. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \(GER\) & 0.1 & 0.3 & 0.5 & 0.7 & 0.9 & 1.1 & 1.3 & 1.5 & 1.7 \\ \hline parameters & (7,1) & (7,2) & (7,5) & (7,19) & (6,4) & (6,6) & (6,12) & (5,5) & (5,7) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Optimal parameters (\(m^{\star}\), \(T^{\star}\)) under different \(GER\) (bpp) of image Lena. In order to further demonstrate the superiority of the proposed method in maximum embedding rate, we compare our method with the methods of [38] and [39] on 10,000 tested images from the BOWS-2 database [41]. As shown in Table 5, our average embedding rate of 10,000 images is 1.7215 bpp, which is higher than 1 bpp and 0.9681 bpp of two approaches in [PERSON] et al. [38] and 1.3512 bpp in [PERSON] et al. [39]. Especially for those extremely smooth images, the proposed method can achieve a very high embedding rate.