# Speaker-Independent Spectral Enhancement for Bone-Conducted Speech
## 4 Experiment
### Objective Evaluation  
The short-time objective intelligibility (STOI) [37], P.563 [38] and log-spectral distortion (LSD) [39] was used to objectively evaluate the quality of the enhanced BC speech to evaluate the effectiveness of the proposed BSEGAN-SI method. In STOI and LSD, the distortion value of some aspects of speech before and after enhancement is calculated to judge whether it is good or bad. Short-time objective intelligence (STOI) is a digital measurement method based on the frequency domain, which aims to evaluate the intelligibility of enhanced BC speech. The evaluation score range is 0-1. The larger the score, the higher the enhanced speech intelligibility. In the objective evaluation index of speech enhancement system, logarithmic spectral distance is widely used because of its high degree of objectivity. The core idea of the LSD algorithm is to evaluate the approximation of two speech signals by calculating the logarithmic spectrum distance of clean AC speech and enhanced BC speech. In this paper, LSD between BC speech and normal speech is used as the objective evaluation index of the BC speech enhancement system. LSD is defined as follows:  
\[\text{LSD}=\frac{1}{N}\sum_{i=1}^{N}\sqrt{\frac{1}{M/2+1}\sum_{j=0}^{M/2} \left(10\log_{10}\abs{S_{i,j}}-10\log_{10}\abs{X_{i,j}}\right)^{2}} \tag{14}\]  
where \(N\) is the number of speech frames, \(M\) is the number of DFT sample points, and \(X_{i,j}\) and \(S_{i,j}\) represent the STFT cepstrum of pure speech and enhanced speech in the \(i\)th and \(j\)th frames, respectively. STFT cepstrum is a description of the relationship between spectrum  
Figure 8: Enhanced BC speech spectrogram by BSEGAN-SI. Figure 7: (**a**) Enhanced BC speech spectrogram by CycleGAN. (**b**) Enhanced BC speech spectrogram by StarGAN. and time. By comparing the spectrum of two kinds of speech, we can clearly see the effect of the speech enhancement algorithm. The smaller the LSD value is, the more similar the log spectrum between the enhanced BC speech and its corresponding pure AC speech is, and the closer the enhanced BC speech quality is to the pure AC speech quality. P.563 is a single-ended speech quality objective evaluation standard proposed by ITU-T [38]. The measurement process of p.563 consists of three stages: the preprocessing stage, the distortion estimation stage, and the perceptual mapping stage. It does not need to use pure speech as a condition when evaluating BC speech quality. It can directly output the smoothness score of the signal [40], which has higher usability. The grades at which the bothersome or perceptual focus was found by analyzing the auditory experiments are presented in Table 3. It can be seen from Figure 9 that we have conducted a P.563 evaluation to enhance the effectiveness of the proposed BSEGAN-SI method. Considering the difference between BC and clean AC speech, the single-ended indicator P.563 is particularly suitable for objective evaluation of BC speech quality obtained in BC speech enhancement tasks. As shown in Table 4, the STOI values of the enhanced BC speech obtained by the comparison model GMM, BLSTM, StarGAN, CycleGAN, and the BSEGAN-SI method proposed in this paper are listed. It can be seen that the STOI score of the enhanced BC speech obtained by our method is the highest, indicating that the enhanced BC has better quality and higher clarity. Table 5 lists the LSDs of the enhanced BC speech obtained by different methods. The spectral distortion of the enhanced BC speech obtained by our method is the lowest, which indicates that the logarithmic spectral similarity between the enhanced BC speech and the clean AC speech is higher, and the information component of the enhanced BC speech spectrum is closer to the target AC speech spectrum. Table 6 lists the P.563. The method we proposed has the highest score, indicating that the voice quality is the best.