## 4 Experimental Results
### Discussion  
In general, by the underestimation of noise power spectral density (PSD), one would expect less reduction of noise and hence lower SegSNR improvement while more preservation of speech i.e., a better PESQ quality. The reason why the proposed method can obtain higher SegSNR improvement than the MCRA method 1 is discussed as follows. The spectral estimate of speech \(\hat{S}(\eta,\Omega)\) can be obtained by multiplying a gain factor with the spectrum of noisy speech \(Y(\eta,\Omega)\) as given in (28). Decomposing (28) can obtain  
\[ \begin{array}{ll}\hat{S}(\eta,\Omega)&=g(\eta,\Omega)\cdot\left[S(\eta,\Omega )+D(\eta,\Omega)\right]\\ &=g(\eta,\Omega)\cdot S(\eta,\Omega)+g(\eta,\Omega)\cdot D(\eta,\Omega)\end{array}  \tag{42}\]  
By assuming that the speech and noise signals are uncorrelated and the noise is zero-mean, the distortion PSD between speech and noise can be expressed as  
\[ \begin{array}{ll}e_{T}=E\big{\{}\big{|}S(\eta,\Omega)-\hat{S}(\eta,\Omega) \big{|}_{2}\big{\}}\\ =E\big{\{}g^{2}(\eta,\Omega)\cdot\big{|}D(\eta,\Omega)\big{|}_{2}+\big{[}1-g( \eta,\Omega)\big{]}\cdot\big{|}S(\eta,\Omega)\big{|}_{2}\big{\}}\\ =E\big{\{}g^{2}(\eta,\Omega)\cdot\big{|}D(\eta,\Omega)\big{|}_{2}\big{\}}+E \big{\{}\big{[}1-g(\eta,\Omega)\big{]}\cdot\big{|}S(\eta,\Omega)\big{|}_{2} \big{\}}\\ =e_{D}+e_{S}\end{array}  \tag{43}\]  
where \(e_{D}\) and \(e_{S}\) denote the PSD of residual noise and speech distortion, respectively. In the case of a strong vowel, the PSD of speech (\(E\{|S(\eta,\Omega)|_{2}\}\)) is much greater than that of background noise (\(E\{|D(\eta,\Omega)|_{2}\}\)), i.e., \(E\{|S(\eta,\Omega)|_{2}\}>>E\{|D(\eta,\Omega)|_{2}\}\). An underestimate of background noise obtains small gain factor. Thus the gain factor using the proposed noise estimator (\(g^{\text{Proposed}}(\eta,\Omega)\)) is smaller than that using the MCRA method (\(g^{\text{MCRA}}(\eta,\Omega)\)), i.e., \(g^{\text{Proposed}}(\eta,\Omega)<g^{\text{MCRA}}(\eta,\Omega)\). This fact enables the PSD of speech distortion for the proposed method (\(e_{S}^{\text{Proposed}}\)) to be much less than that of the MCRA method (\(e_{S}^{\text{MCRA}}\)), i.e., \(e_{S}^{\text{Proposed}}<<e_{S}^{\text{MCRA}}\); meanwhile the PSD of residual noise for the proposed method is greater than that of the MCRA method, i.e., \(e_{D}^{\text{Proposed}}>e_{D}^{\text{MCRA}}\). The total distortion PSD given in (43) (\(e_{T}^{\text{Proposed}}=e_{S}^{\text{Proposed}}+e_{D}^{\text{Proposed}}\)) is less than that of the MCRA method (\(e_{T}^{\text{MCRA}}=e_{S}^{\text{MCRA}}+e_{D}^{\text{MCRA}}\)), i.e., \(e_{T}^{\text{Proposed}}<e_{T}^{\text{MCRA}}\). Accordingly, the \(\textit{Avg\_SegSNR}\) given in (38) of the proposed method is larger than that of the MCRA method. A better \(\textit{Avg\_SegSNR}\) improvement achieves in the proposed method. In the case of a weak vowel, the PSD of speech (\(E\{|S(\eta,\Omega)|_{2}\}\)) is slightly greater than that of residual noise (\(E\{|D(\eta,\Omega)|_{2}\}\)), i.e., \(E\{|S(\eta,\Omega)|_{2}\}>E\{|D(\eta,\Omega)|_{2}\}\). An underestimate of background noise also obtains small gain factor. Thus the gain factor using the proposed noise estimator (\(g^{\text{Proposed}}(\eta,\Omega)\)) is smaller than that using the MCRA method (\(g^{\text{MCRA}}(\eta,\Omega)\)), i.e., \(g^{\text{Proposed}}(\eta,\Omega)<g^{\text{MCRA}}(\eta,\Omega)\). This fact enables the PSD of speech distortion for the proposed method (\(e_{S}^{\text{Proposed}}\)) to be less than that using the MCRA method (\(e_{S}^{\text{MCRA}}\)), i.e., \(e_{S}^{\text{Proposed}}<e_{S}^{\text{MCRA}}\); meanwhile the PSD of residual noise of the proposed method is greater than that of the MCRA method, i.e., \(e_{D}^{\text{Proposed}}>e_{D}^{\text{MCRA}}\). The total distortion (\(e_{T}^{\text{Proposed}}\)) may be slightly greater or comparable to that of the MCRA method