## 3 Reversible Watermarking Based on intDCT
### Extracting Embedded Information and Reconstructing Original Data
coefficients located, the smaller the data overflow. No overflow occurred when expanding [9 th, 16 th] blocks (\(M_{b}=9\)), indicating from 1025 th to 2048 th coefficients. Thus, selecting DCT coefficients at a higher frequency can avoid overflow. ### Evaluation of Audio Quality

#### 4.3.1 Evaluation Criterion

To evaluate the audio quality of the stego data, we mainly use Perceptual Evaluation of Speech Quality (PESQ) and Segmental Signal-to-Noise Ratio (segSNR) in this paper, which have been extensively used to evaluate sound quality objectively [20; 22]. PESQ is a standard comprising a test methodology for objective assessment of speech quality. Mean Opinion Score--Listening Quality Objective (MOS-LQO) scores are used to evaluate the audio quality. SegSNR [dB] is a method of checking the distortion caused by differences in the time domain by comparing original and stego data sample by sample, which is a time-domain-based measurement. The higher the MOS-LQO and segSNR scores are, the better the audio quality is. To evaluate the listening quality of the speech data, we used MOS-LQO, which is an objective technique defined by ITU-T Recommendation P.862.1. MOS-LQO scores are obtained by mapping the distortion to MOS scores in the range from 1.02 (lowest quality) to 4.56 (highest quality). For the objective evaluation using MOS-LQO scores, we used PESQ version 1.2 [39]. We used AFsp package version 9.0 to assess the segSNR, defined as the average SNR value over segments. #### 4.3.2 Audio Quality Results with Different Hiding Locations

Basically, frame lengths and hiding capacities affect quality. Expanded blocks, which indicate the hiding locations, also affect audio quality. The number of DCT blocks \(M_{emb}\) determines the capacity. The segSNRs between stego data and original data are shown in Figure 6, where the stego data are generated by expanding different blocks. Each frame is divided into \(M\) blocks, and the coefficients in the lowest frequency domain are specified as the first block. Different blocks from \(M_{b}\) to \(M_{b}+M_{emb}-1\) with \(M_{emb}=8\) are selected to explore the most suitable blocks for hiding. Figure 7 plots an example of the difference between stego data and original data in DCT coefficients due to different expansion block positions, including an example with overflow. This clearly illustrates the expanded blocks. According to the segSNRs in Figure 6, audio quality generally improves if higher coefficients are expanded, and [9 th, 16 th] are the most suitable locations for expansion. Figure 8 plots a graphic about the original sound, as shown in File Ja_m5.wav in Supplementary Materials and stego sound, as shown in File Ja_m5.9-16.wav in Supplementary Materials of some samples to compare how they change. When [9 th, 16 th] coefficients are expanded for embedding, by comparing the stego data and original data, the boundary for expansion and embedding might be visible. Figure 5: Number of overflowed audio samples with different \(M_{b}\). ### Comparison of Different Frame Lengths and Embedding Capacity

Frame length is supposed to affect both the precision of localizing the tampered positions and audio quality. To determine which frame length is the best, we investigated

Figure 8: Log of DCT coefficient difference between original data and stego data with a red mark on samples to compare how they change: Ja_m5.wav (\(N=2048\)). Figure 6: Segmental signal-to-noise (segSNRs, [dB]) ratio between stego data and original data according to different expanding blocks of 112 data. Figure 7: Log of DCT coefficient difference: expanding different blocks: Ja_m5.wav (\(N=2048\)). the quality of stego signals with different frame lengths, 2048, 1024, and 512. Here, the capacity is 8000 bps (\(M=16,M_{emb}=8\), and \(M_{b}=9\)). We also compared the audio quality of the information-hiding method based on LPC [20]. Note that since the LPC-based method is not a blind watermark method, the LPC-based method is not an alternative to the proposed method.