Constrained Wiener gains and filters for single-channel and multichannel noise reduction

Noise reduction has long been an active research topic in signal processing and many algorithms have been developed over the last four decades. These algorithms were proved to be successful in some degree to improve the signal-to-noise ratio (SNR) and speech quality. However, there is one problem common to all these algorithms: the volume of the enhanced signal after noise reduction is often perceived lower than that of the original signal. This phenomenon is particularly serious when SNR is low. In this paper, we develop two constrained Wiener gains and filters for noise reduction in the short-time Fourier transform (STFT) domain. These Wiener gains and filters are deduced by minimizing the mean-squared error (MSE) between the clean speech and the speech estimate with the constraint that the sum of the variances of the filtered speech and residual noise is equal to the variance of the noisy observation.