# A Psychoacoustic-Based Multiple Audio Object Coding Approach via Intra-Object Sparsity
## 3 Performance Evaluation
### Objective Evaluations  
The first experiment is performed in the lossless transmission case, it means that both the downmix signal and the side information are compressed using lossless techniques. The Sparsity Analysis (SPA) multiple audio objects compression technique proposed in our previous work is served as reference approach [19] (named \"SPA-STFT\") because of its superior performance. Meanwhile, the intermediate step given by SPA that uses the MDCT (named 'SPA-MDCT') is also compared in this test. The Objective Difference Grade (ODG) score calculated by the PEAQ of ITU-R BS.1387 is chosen as the evaluation criterion, which reflect the perceptual difference between the compressed signal and the original one. The ODG values vary from 0 to \(-4\) with 0 being imperceptible loss in quality and \(-4\) being a very annoying degradation in quality. What needs to be emphasized is that ODG scores cannot be treated as an absolute criterion because it only provide a relative reference value of the perceptual quality. Condition 'Pro' represents the objects encoded by our proposed encoding framework while condition 'SPA-STFT' and 'SPA-MDCT' are the reference approaches. Note that 'SPA-STFT' encoding approach exploits a 2048-points Short Time Fourier Transform (STFT) with 50% overlapping.  
Statistical results are shown in Figure 3 where each subfigure corresponds to an eight-track audio file. From each subfigure, it can be observed that the decoded signals through our proposed encoding framework has the highest ODG score compared to both the SPA and the MDCT-based SPA approach, which indicates that the proposed framework can cause less damage to audio quality compared to these two reference approaches.  
In addition, the performance of the MDCT-based SPA approach is better than the SPA, which prove that the selection of MDCT as time-frequency transform is efficient. Furthermore, in order to observe the quality differences of decoded objects, the standard deviation of each file is given as follow:  
As illustrated in Figure 4, our proposed encoding framework has a lower standard deviation than the reference algorithms for each multi-track audio file. Hence, it proves that a more balanced quality of decoded objects can be maintained compared to the reference approaches. In general, this test validates that the proposed approach is robust to different kinds of audio objects.  
In the lossy transmission case, the downlink signal which generated by encoder is further compressed using the SQVH at 105.14 kbps, 112.53 kbps and 120.7 kbps, respectively. Each sub-band  
Figure 4: The standard deviation of ODG score of four multi-track audio files.  
Figure 3: ODG (Objective Difference Grade) Score for the proposed audio object encoding approach and the SPA (Sparsity Analysis) framework (both in the STFT (Short Time Fourier Transform) and MDCT domain). (**a–d**) represent the results for 4 multi-track audio files.  
corresponds to a group of certain \(q_{\textit{stepsize}}\), whose allocation for three types of bitrates can be calculated as shown in Table 2.  
The ODG score in three types of bitrates are presented in Figure 5. Condition 'Pro-105', 'Pro-112', 'Pro-120' correspond to compress downmix signal at 105.14 kbps, 112.53 kbps and 120.7 kbps, respectively. It can be observed that the higher quantization precision leads to the better quality of decoded objects but the total bitrates increase as well. Therefore, we cannot pursuit a single factor such as high audio quality or low bitrate for transmission [25]. In consequence, we need to make a trade-off between audio quality and total bitrates in practical application scenarios.