## 3 Reversible Watermarking Based on intDCT
### Extracting Embedded Information and Reconstructing Original Data
This experiment compares the absolute quality of the stego signal of different methods. The comparison results are listed in Table 1. As shown, quality decreases with a shorter frame length. According to the results, the MOS-LQO scores of the proposed method are lower than the LPC-based method; however, the proposed method has better segSNR values. According the frame sizes \(N=512\), \(N=1024\), and \(N=2048\), the average MOS-LQO of the proposed method vs. LPC is 4.27 vs. 4.45, 4.34 vs. 4.48, and 4.41 vs. 4.5; however, according to ITU-T [39], the user satisfaction is at the same level when MOS-LQO is more than 4.3 for \"very satisfied\", which means that the proposed method has considerable objective listening quality scores compared to the LPC-based method. For segSNR score, the proposed method has better segSNR values in the level around 22 [dB], while the LPC-based method has segSNR values in the level around 16 [dB]. Theoretically, distortion may be caused by discontinuity at the border of two frames. Therefore, this result is consistent with the theoretical explanation because the number of frame borders is small when the frame length is long. The stego data generated by the proposed method are obviously superior in terms of segSNRs to the LPC-based method, which means that the difference between the stego data and original data is smaller in the time domain. A possible reason is that the proposed method selects intDCT coefficients with lower amplitude for expansion. Only the modified intDCT-IV used by the proposed method has the feature whereby when frequency increases, the amplitude decreases among the typical seven types of DCT methods. Particularly, in the highest frequency domain, the amplitude became extremely low. Thus, the differences are small after inverse DCT from the frequency domain to the time domain. Meanwhile, the LPC expands the residual value by multiplying them and then adds the payload for embedding directly in the time domain. The residual depends on the adjacent data, and there are seldom residuals with extremely small values, which benefits expansion to achieve small differences in the time domain. We also performed experiments using different capacities to determine the effect on audio quality. Capacities are set to be from 1000 bps to 7000 bps by adjusting \(M_{emb}=1,\ldots,7\), hiding from the highest DCT coefficients to the lower one. A comparison of the results is shown in Table 2. As shown, larger capacities result in more distortion in stego data quality. The proposed method has an MOS-LQO of 4.55, the same as the LPC-based method, when capacity \(\approx 1000\) bps, and comparable average MOS-LQO values when capacity increases. The MOS-LQO scores of the proposed method are lower than those of the LPC-based method; however, the proposed method has better segSNR values. According to the capacity from 1000 bps to 8000 bps, the average MOS-LQO of the proposed method vs. LPC is better than 4.46, and according to ITU-T [39], the user satisfaction is at the same level when MOS-LQO is in a range greater than 4.3 for \"very satisfied\". All of the MOS-LQO scores are better than 4.46 for both the proposed method and the LPC-based method, which means that the proposed method has considerable objective listening quality scores compared to the LPC-based method. On the other hand, the proposed method has significantly better \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Frame** & \multicolumn{2}{c}{**MOS-LQO**} & \multicolumn{2}{c}{**segSNR ([dB])**} \\
**Length** & **LPC [20]** & **Proposed** & **LPC [20]** & **Proposed** \\ \hline
512 & 4.45 & 4.27 & 16.04 & 22.23 \\
1024 & 4.48 & 4.34 & 16.11 & 22.99 \\
2048 & 4.50 & 4.41 & 16.22 & 23.31 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison with the conventional method of quality (average MOS-LQO and segSNR) of stego data for different frame lengths using 112 signals (capacity \(\approx\) 8000 bps). We also compared with other similar approaches for watermarking using SNR.