# An Adaptive Reversible Data Hiding Scheme Using AMBTC and Quantization Level Difference
## 4 The Proposed Scheme  
The section provides some experimental results to show the hiding capacity (bits) and image quality (dB) of our proposed scheme. In Figure 8, all of the experiments were performed with six commonly used grayscale test images: Lena, F-16, Sailboat, Girl, Toys, and Barbara. All are of the same size, \(512\times 512\). The size of each block \(b_{i}\) is \(4\times 4\). The embedded secret data are composed of a random bit-stream that was produced from a random number generator. In these experiments, the visual quality of the modified images was evaluated by using peak signal-to-noise ratio (PSNR) as defined in Equation (12). \[PSNR=10\times\log_{10}\left(\frac{255^{2}}{MSE}\right), \tag{12}\]  
The definition of mean square error (MSE) is shown in Equation (13). \[MSE=\frac{1}{H\times W}\sum_{i=0}^{\frac{H}{2}\times\frac{W}{K}-1}\sum_{n=0}^{k \times k-1}\left(p^{\prime i}_{n}-p^{i}_{n}\right)^{2}, \tag{13}\]  
where \(p^{\prime i}_{n}\) and \(p^{i}_{n}\) are the stego pixels and original pixels in each modified block and original block, respectively. Figure 7: (a) The modified block \(b^{\prime}_{i}\) sized \(4\times 4\), (b) Secret data S and (c) block \(b_{i}\) sized \(4\times 4\). To demonstrate the performance results for our proposed scheme, our method was compared with previous reversible data hiding methods in two aspects. In the first group, the proposed scheme was compared with other BTC-based schemes [21; 22; 23; 24]. Figure 9a and Table 2 show the results of this comparison. Figure 9a shows, the good performance for embedding capacity that was achieved in our scheme. The proposed method can embed 56 bits in each \(4\times 4\) pixel block while the difference between two quantization levels is larger than 32. However, [PERSON] et al. 's scheme can embed 16 bits in each \(4\times 4\) pixel block. And in the schemes of [PERSON] et al. 's, [PERSON] et al. 's, and [PERSON] et al. 's, each \(4\times 4\) pixel block can only be embedded 1, 2 and 4 bits, respectively. In our scheme, the capacity for, \"Lena\", \"F-16\", \"Sailboat\", \"Girl\", \"Toys\" and \"Barbara\", were 324,548 (bits); 267,386 (bits); 432,796 (bits); 388,780 (bits); 292,250 (bits) and 449,876 (bits), respectively. In our scheme, the image obtained a higher embedding capacity even with complex images such as \"Barbara\" and \"Sailboat\", because our adaptive interpolation technique is related to the difference of two quantization levels. However, the capacity is relatively small in smooth images, such as \"Lena\", \"F-16\({}^{\prime}\) and \"Toys\". Table 2 shows a comparison of image quality. In [PERSON] et al. 's and [PERSON] et al. 's schemes, the cover image cannot be directly obtained from a stego compression code. Therefore, the two methods cannot be compared in terms of image quality of a modified image. From Table 2, the proposed \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Scheme** & **Lena** & **F-16** & **Sailboat** & **Girl** & **Toys** & **Barbara** & **Average** \\ \hline Our scheme & 32.59 & 32.22 & 30.16 & 33.30 & 32.12 & 28.82 & 31.54 \\ \hline [PERSON] et al.’s [24] & 33.05 & 31.64 & 30.32 & 33.36 & 30.99 & 28.63 & 31.33 \\ \hline [PERSON] et al.’s [22] & 32.34 & 31.93 & 30.41 & 33.44 & 31.15 & 28.82 & 31.34 \\ \hline [PERSON] et al.’s [21] & \multicolumn{5}{c}{Cannot be constructed by the modified code stream} \\ \hline [PERSON] et al.’s [23] & \multicolumn{5}{c}{Cannot be constructed by the modified code stream} \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparative performance of PSNR (dB) for six test images between our method and other methods based on BTC. Figure 8: Test images (**a**) Lena; (**b**) F-16; (**c**) Sailboat; (**d**) Girl; (**e**) Toys; (**f**) Barbara. scheme cannot achieve the best PSNR in every test image. In the \"Lena\", [PERSON] et al. 's scheme achieves the best results, and [PERSON] et al. 's scheme provides the best results in the \"Saillboat\". But our method achieves a higher average.