SDW-SWF: Speech Distortion Weighted Single-Channel Wiener Filter for Noise Reduction

Speech enhancement shows an important necessity in many audio applications, particularly in noisy environments, where the speech quality needs to be improved. In this work, we consider the single-channel noise reduction (NR) problem from the conventional signal processing perspective. As conventional single-channel NR filters suffer from a serious speech distortion (SD) problem, we propose an SD weighted single-channel Wiener filter (SDW-SWF) in the short-time Fourier transform domain, which is obtained by minimizing the mean-square error (MSE) of the clean speech plus a
$\mu$
-weighted residual noise variance. Based on the generalized eigenvalue decomposition (GEVD) and rank-
$r$
approximation of the speech correlation matrix, the SDW-SWF can be written as a linear combination of eigenpairs, from which some special cases reduce to existing single-channel NR filters. As such, the proposed SDW-SWF has two parameters (i.e.,
$\mu$
and
$r$
) to tradeoff the MSE and SD. Then we theoretically analyze the impacts of the tradeoff parameters on the NR performance in SD, residual noise variance and the output signal-to-noise ratio (SNR). In addition, it is shown that the STFT-domain SDW-SWF can be further extended to the time domain, where the derived theorems still hold. Numerical results from several perspectives validate the effectiveness of the proposed method.