Study of the Wiener Filter for Noise Reduction

Abstract

The problem of noise reduction has attracted a considerable amount of research attention over the past several decades. Numerous techniques were developed, and among them is the optimal Wiener filter, which is the most fundamental approach, and has been delineated in different forms and adopted in diversified applications. It is not a secret that the Wiener filter achieves noise reduction with some integrity loss of the speech signal. However, few efforts have been reported to show the inherent relationship between noise reduction and speech distortion. By defining a speech-distortion index and a noise-reduction factor, this chapter studies the quantitative performance behavior of the Wiener filter in the context of noise reduction. We show that for a single-channel Wiener filter, the amount of noise attenuation is in general proportionate to the amount of speech degradation. In other words, the more the noise is reduced, the more the speech is distorted. This may seem discouraging as we always expect an algorithm to have maximal noise attenuation without much speech distortion. Fortunately, we show that the speech distortion can be better managed by properly manipulating the Wiener filter, or by considering some knowledge of the speech signal. The former leads to a sub-optimal Wiener filter where a parameter is introduced to control the tradeoff between speech distortion and noise reduction, and the latter leads to the well-known parametric-model-based noise reduction technique. We also show that speech distortion can even be avoided if we have multiple realizations of the speech signal.