# Efficient Reversible Data Hiding Scheme for AMBTC-Compressed Images
## 4 Experimental Results  
In this section, tests of the performance of the proposed scheme on six public 512 \(\times\) 512 images shown in Figure 8 are described. MATLAB R2010a was used to program the proposed scheme and five previous schemes in the experiments, including AMBTC, [PERSON] [14], [PERSON] et al. [15], and [PERSON] et al. [16; 20]. As for the remaining existing schemes, we cite the experimental results from their published articles. The objective measures, peak signal-to-noise ratio (PSNR), embedding capacity (EC), efficiency rate, and bit rate, were performed to estimate performance in this paper. For the \(P\times Q\) grayscale image, the PSNR is calculated by Equation (7), where MSE is the mean square error and is defined as shown in Equation (8). It is noted that the proposed scheme has the reversibility feature, and the reconstructed image will be the same as the AMBTC-reconstructed image after hidden secret data have been successfully extracted. To prove our proposed scheme is reversible data hiding for AMBTC-compressed images, the definitions of the original image and reconstructed image are the same as those defined by AMBTC. The bit rate and efficiency rate are calculated by Equations (9) and (10), respectively. \[PSNR=10\log_{10}\left(\frac{255^{2}}{MSE}\right) \tag{7}\]  
\[MSE=\frac{1}{P\times Q}\sum_{i=1}^{P}\sum_{j=1}^{Q}\left(X_{ij}-X_{ij}^{ \prime}\right)^{2} \tag{8}\]  
\[bit\ rate=\frac{|CS|}{P\times Q} \tag{9}\]  
\[efficiency=\frac{EC}{|CS|} \tag{10}\]  
where \(X_{ij}\) and \(X_{ij}^{\prime}\) are the pixel values of the original image and the AMBTC-reconstructed image, respectively. \(EC\) is the embedding capacity, and \(|CS|\) denotes the size of the code stream \(CS\). \(EC\) is calculated as \(EC=3\times N-62\) bits, where \(N\) is the number of \(|D_{i}|<2^{m}\). In the proposed scheme, \(m\) is the parameter that can affect the performance of the proposed scheme; therefore, in Table 1, difference values of \(m\) were used to test the results of the proposed scheme. As can be observed in Table 1, the PSNRs of the image were not changed with the difference values of \(m\). Basically, the value of \(m\) is only ranged from 3 to 5. This is because when \(m=3\), it only takes eight bits at most to encode each difference value for either the high mean table or low mean table. In other words, the size of the final code stream of our proposed scheme will be the same as that of conventional AMBTC. Based on the experimental results, we can observe that when the value of \(m\) is increased from 3 to 5, the embedding capacity is gained while the value of the bit rate is also increased. Therefore, it is suggested that the value of \(m\) should be set to 4 in the proposed scheme to achieve both a high embedding capacity and an acceptable bit rate at the same time. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Images** & **Performance** & _m = 3_ & _m = 4_ & _m = 5_ \\ \hline \multirow{3}{*}{Lena} & PSNR (dB) & 33.97 & 33.97 & 33.97 \\ \cline{2-5}  & EC (bits) & 60,010 & 75,128 & 87,199 \\ \cline{2-5}  & bit rate (bpp) & 2.05 & 2.13 & 2.24 \\ \hline \multirow{3}{*}{Baboon} & PSNR (dB) & 26 & 26 & 26 \\ \cline{2-5}  & EC (bits) & 40,048 & 64,882 & 86,902 \\ \cline{2-5}  & bit rate (bpp) & 2.07 & 2.13 & 2.24 \\ \hline \multirow{3}{*}{Peppers} & PSNR (dB) & 33.4 & 33.4 & 33.4 \\ \cline{2-5}  & EC (bits) & 63,010 & 78,799 & 88,771 \\ \cline{2-5}  & bit rate (bpp) & 2.04 & 2.13 & 2.24 \\ \hline \multirow{3}{*}{F16} & PSNR (dB) & 31.95 & 31.95 & 31.95 \\ \cline{2-5}  & EC (bits) & 71,233 & 81,097 & 88,648 \\ \cline{2-5}  & bit rate (bpp) & 2.03 & 2.13 & 2.24 \\ \hline \multirow{3}{*}{GoldHill} & PSNR (dB) & 33.16 & 33.16 & 33.16 \\ \cline{2-5}  & EC (bits) & 56,710 & 76,603 & 89,569 \\ \cline{2-5}  & bit rate (bpp) & 2.05 & 2.13 & 2.24 \\ \hline \multirow{3}{*}{Boat} & PSNR (dB) & 31.15 & 31.15 & 31.15 \\ \cline{2-5}  & EC (bits) & 65,620 & 78,178 & 88,321 \\ \cline{1-1} \cline{2-5}  & bit rate (bpp) & 2.04 & 2.13 & 2.24 \\ \hline \end{tabular}
\end{table}