SDW-SWF: Speech Distortion Weighted Single-Channel Wiener Filter for Noise Reduction
Jie Zhang, Rui Tao, Jun Juan Du, Li-Rong Dai · IEEE/ACM Transactions on Audio Speech and Language Processing · 2023
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.