The singular value decomposition (SVD)-based method for single-channel speech enhancement has been shown to be very useful when the additive noise is white. For colored noise, with this approach, one needs to whiten the noise spectrum prior to SVD-based approach and perform the inverse whitening processing afterwards. A truncated quotient SVD (QSVD)-based approach has been proposed to handle this problem and found very useful. In this paper, a generalized SVD (GSVD)-based subspace approach for speech enhancement is first extended from the concept of the truncated QSVD-based approach, in which the dimension of the signal subspace can be precisely and automatically determined for each frame of the noisy signal. But with this new approach some residual noise is still perceivable under lower signal-to-noise ratio conditions. Therefore a perceptually constrained GSVD (PCGSVD)-based approach is further proposed to incorporate the masking properties of human auditory system to make sure the undesired residual noise to be nearly un-perceivable. Closed-form solutions are obtained for both the GSVD- and PCGSVD-based enhancement approaches. Very carefully performed objective evaluations and subjective listening tests show that the PCGSVD-based approach proposed here can offer improved speech quality, intelligibility and recognition accuracy, whether the noise is stationary or nonstationary, especially when the additive noise is nonwhite

In previous studies, the signal subspace technique for speech enhancement was extended and a perceptually constrained generalized singular value decomposition (PCGSVD)-based algorithm [1] was developed which properly integrated the auditory masking effect and the GSVD algorithm. Both objective measures and subjective tests verified that this approach can offer better performance than the GSVD-based approach and the conventional spectral subtraction (SS) algorithm. But very high computational complexity is required in the PCGSVD-based method when performing the matrices decomposition via the GSVD algoruthm. In this paper, we properly utilize the time-shift property of DFT and the special structure of Hankel matrices to perform similar functions previously offered by GSVD, and a perceptually constrained minimum variance estimation algorithm is developed. By replacing GSVD algorithm with DFT, the computation complexity is significantly reduced, almost the same as the conventional SS algorithm. Experiments showed that comparable performance to that of the PCGSVD-based approach can be achieved, regardless of whether the additive noise is stationary or not, specially when it is non-white.

In a previous work, we have successfully integrated the transformation-based signal subspace technique with the generalized singular value decomposition (GSVD) algorithm to develop an improved speech enhancement framework [1]. In this paper, we further incorporate the perceptual masking effect of the psychoacoustics model as extra constraints of the previously proposed GSVD-based algorithm to obtain improved sound feature, and furthermore make sure the undesired residual noise to be nearly unperceivable. Both subjective listening tests and spectrogram-plot comparison showed that the closed-form solution developed here can offer significantly better speech quality than either the conventional spectral subtraction algorithm or the previously proposed GSVD-based technique, regardless of whether the additive noise is white or not. 1.