Spectral subtraction

$$y[n]=x[n]+b[n]$$

Boll [1] proposes a magnitude based subtraction:

$$\vert\hat{X}(\omega)\vert= \vert Y(\omega)\vert-E\{\vert B(\omega)\vert\}\\$$

Berouti et al [5] use power subtraction instead:

$$\vert\hat{X}(\omega)\vert^2=\left\{ \begin{array}{ll} \v... ... \textrm{otherwise (Spectral floor)}\\ \end{array} \right.$$

where

$$\vert D(\omega)\vert^2=\vert Y(\omega)\vert^2-\alpha S_b(\omega) \quad \textrm{(Oversubtraction since $\alpha \ge 1$)}$$