# De-Noising Process in Room Impulse Response with Generalized Spectral Subtraction
## 5 Conclusions  
This study examined the possibility of implementing the GBSS algorithm in de-noising RIRs to extend the reverberation decay range of the corresponding EDCs. Furthermore, a detailed analysis of the optimal set factors of the spectral subtraction algorithm, including the over-subtraction factor and the spectral flooring factor that could provide the most significant dynamic range improvement in the EDCs, was performed.  
In regards to the dynamic range improvement in EDCs without distorting the quality of the RIRs, experiments were conducted in measured RIRs with artificial noise and natural ambient noise. The optimal sets of factors for de-noising the RIRs filtered in the octave bands by \(\beta\) 0.001 at SNR \(>=0\), and 0.05 at SNR \(<0\), while the over-subtraction factor \(\alpha\) was calculated from Equation (2). Furthermore, the factor \(\alpha_{0}\) in Equation (2) depends on the estimated SNR of the RIRs filtered in the octave band, given in Figure 7c. The results showed that the improved dynamic range strictly depends on factor \(\alpha_{0}\). If the \(\alpha_{0}\) values are lower than the optimum, a smaller dynamic range improvement compared to the best results is provided; in this case, the level is acceptable because no degradation occurs to the reverberation decay rate. On the other hand, if the value is too high, a loss of the original signals that appears in the RIRs will distort the reverberation decay rates. Therefore, it is essential to find the optimal \(\alpha_{0}\) to prevent the signal over-subtraction in the de-noising processing and minimize degradation on the reverberation decay.  
The GBSS algorithm showed excellent significance in de-noising the RIRs when the noise levels were lower than \(-40\) dB. The optimal \(\alpha_{0}\) was suggested in the range of 3.75 to 4.25 for different SNRs greater than 10. As a result, the mean dynamic ranges were improved by approximately 13 dB and even by 20 dB. Moreover, the noise levels were reduced by around 8 dB. When the estimated SNRs were lower than 10, the improved dynamic range was less than 8 dB using the optimal \(\alpha_{0}\) higher than 4.5, causing the EDC estimation decay range to be less than 10 dB, which contributes fewer effects to de-noising the RIRs regarding the dynamic range improvement. In applying the optimal sets of the factors to real measured noisy RIRs, the estimated RTs and EDT gave a somewhat more stable result in some cases compared to the compensation method.  
Overall, the GBSS algorithm is simple to implement with substantial flexibility to improve the dynamic range of EDCs automated by adjusting the over-subtraction factors of \(\alpha_{0}\), based on the different SNRs, instead of subtracting noise levels with a constant estimated noise level for the entire RIRs. Moreover, the GBSS algorithm using optimal factors has significant effects on de-noising the RIRs to extend the dynamic range of the EDCs and decrease the estimation errors in RTs caused by the noise levels.  
Further work on de-noising the RIRs addresses two aspects. First, because the GBSS algorithm required noise to be stationary or a slowly varying process, a development of the algorithm must be considered for real-world cases with non-stationary background noise. Second, improving the algorithm to render musical noise perceptually inaudible by taking into account the properties of human auditory systems should be studied.  
C.-[PERSON] gave academic guidance to this research work and revised the manuscript. [PERSON] designed the core methodology of this study, programmed the algorithms, carried out the experiments, and drafted the manuscript. Both authors have read and agreed to the published version of the manuscript. This research received no external funding.  
Not applicable.  
The authors declare no conflict of interest.