Wheezing Sound Separation Based on Informed Inter-Segment Non-Negative Matrix Partial Co-Factorization

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. 2020 May 8;20(9):2679. doi: 10.3390/s20092679

Algorithm 1 Wheezing sound separation using IIS-NMPCF.

Require: $x [n]$ , $y [n]$ , $K_{R}$ , $K_{W}$ , $λ_{R}^{0}$ , $λ_{R}^{1}$ , $λ_{W}$ , $α$ and M.

1)
Compute the normalized magnitude spectrogram $X$ of the mixture $x [n]$ .
2)
Compute the normalized magnitude spectrogram $Y$ of the training $y [n]$ .
3)
Divide the spectrogram $X$ into L-segments $X^{(1)}$ , $X^{(2)}$ , …, $X^{(L)}$ using AMIE_SEG [53].
4)
Classify the L-segments into wheezing ( $C^{(l)} = 1$ ) and non-wheezing ( $C^{(l)} = 0$ ) using a wheezing detection algorithm [54].
5)
Initialize each activation and basis matrix $U_{R}$ , $U_{W}^{(l)}$ , $V_{R}^{(l)}$ , $V_{W}^{(l)}$ , $H_{R}$ with random non-negative values.
6)
Update each activation and basis matrix $U_{R}$ , $U_{W}^{(l)}$ , $V_{R}^{(l)}$ , $V_{W}^{(l)}$ , $H_{R}$ using Equations (9)–(13) for the predefined number of iterations M. At each iteration, normalize each activation and basis matrix $U_{R}$ , $U_{W}^{(l)}$ , $V_{R}^{(l)}$ , $V_{W}^{(l)}$ , $H_{R}$ and update the terms $D x_{R}$ , $D x_{W}$ and $D y_{R}$ using Equations (14) and (15).
7)
Compute the estimated magnitude spectrograms ${\hat{X}}_{R}^{(l)}$ and ${\hat{X}}_{W}^{(l)}$ .
8)
Denormalize the estimated magnitude spectrograms ${\hat{X}}_{R}^{(l)}$ and ${\hat{X}}_{W}^{(l)}$ .
9)
Apply a Wiener filtering [32] on ${\hat{X}}_{R}^{(l)}$ and ${\hat{X}}_{W}^{(l)}$ .
10)
Concatenate all the estimated complex respiratory spectrograms: ${\hat{X}}_{R} = [{\hat{X}}_{R}^{(1)}, {\hat{X}}_{R}^{(2)}, \dots, {\hat{X}}_{R}^{(L)}]$ .
11)
Concatenate all the estimated complex wheezing spectrograms: ${\hat{X}}_{W} = [{\hat{X}}_{W}^{(1)}, {\hat{X}}_{W}^{(2)}, \dots, {\hat{X}}_{W}^{(L)}]$ .
12)
Synthesize $\hat{r} [n]$ .
13)
Synthesize $\hat{w} [n]$ .

return $\hat{r} [n]$ and $\hat{w} [n]$