## 3 Reversible Watermarking Based on intDCT
### Extracting Embedded Information and Reconstructing Original Data
We examined six music clips taken from YouTube, as shown in Table 4. Before the experiment, these music signals were mixed down into a single channel. The frame size of intDCT was \(N=2048\), and the number of blocks was \(M=16\). We changed the number of embedded blocks \(M_{emb}\), and \(M_{b}\) was set as \(M_{b}=M-M_{emb}+1\). Overflow of the signal depends on the amplitude distribution of the original signal. Thus, we investigated the effect of original amplitude on the overflow. First, we normalized the amplitude of all signals so that either the maximum value was 32,767 or the minimum value was \(-32\),768. After the normalization, we multiplied a coefficient \(0.5\leq\alpha\leq 1\) by all samples to control the signal's amplitude distribution. Finally, we embedded data in one to eight blocks (\(1\leq M_{emb}\leq 8\)) and observed the number of frames where overflow occurred. Then we divided the number of overflowed frames by the number of all frames to calculate the probability of overflow of one frame. Figure 11 shows the experimental result when we changed \(\alpha\) and embedded in eight blocks (\(M_{emb}=8\)). The X-axis is \(\alpha\), and the Y-axis is the probability that a frame overflows. Note that the Y-axis is a log scale, but the bottom of the axis indicates zero. As shown in the figure, when we normalize the signal at the \(-3\) [dB] level (\(\alpha=0.5\)), we observe no overflow at all. When we increase \(\alpha\), the probability increases, and we observe overflowed frames for all signals when \(\alpha=1\). The overflow probability of classic and jazz music clips was lower than that of Pops. This result is caused by not only genre differences but also differences in music production methods. Classic and Jazz music consists of recordings of acoustic instruments, while Pops clips are computer-generated signals. Moreover, the amplitude of the music signals of Pops was almost as large as the maximum throughout of the signal, probably using a dynamic range compressor [50]. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Genre** & **Music Clip Name** & **Length (s)** \\ \hline Classic & [PERSON]—Fugue G minor BMV 578 & 194 \\ \hline Classic & [PERSON]—Moonlight Sonata & 900 \\ \hline Jazz & [PERSON]—Take Five & 329 \\ \hline Jazz & [PERSON]—Giant Steps & 289 \\ \hline Pops & Wah Wah World & 206 \\ \hline Pops & DUNE ft.Miku [PERSON] & 239 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Music clips used in the experiment. Figure 11: Overflow probability of a frame for music signals with respect to the normalization factor (\(M_{emb}=8\)). Figure 12 shows the overflow probability when we change the number of embedded blocks (\(M_{emb}\)) when \(\alpha=0.9\). We can see that no overflow occurs when \(M_{emb}=1\). If we embed all eight blocks as [12], we cannot avoid overflow, which makes the embedded signal not reversible. Because our work uses the location map, we can reduce the amount of embedded blocks when we expect overflow. ## 5 Discussion

[PERSON] et al. [13] explored a target application for tampering detection based on digital watermarking, showing that a 4000 bps capacity is enough for tampering detection. We also reserve more capacity until 8000 bps to consider cases that use more information for verification, such as the combination of hash and sequence numbers. A comparison of the average MOS-LQO and segSNR scores given capacities that range from 1000 bps to 8000 bps (\(N=2048\)) based on LPC, and the proposed method is plotted in Figures 9 and 10. According to the results, both methods have MOS-LQO scores better than 4.27, which falls between \"imperceptible\" and \"perceptible but not annoying\", where distortion is difficult to distinguish. The proposed method has comparable MOS-LQO values with LPC methods, and it is inferior when capacity increases to 7000 bps. According to the result shown in Figure 10, the proposed method had constantly higher segSNR than that of LPC, with the best average of 39.74 [dB] and the worst average of 22.23 [dB], which promises clear audio quality.