On widely linear Wiener and tradeoff filters for noise reduction

Noise reduction is often formulated as a linear filtering problem in the frequency domain. With this formulation, the core issue of noise reduction becomes how to design an optimal frequency-domain filter that can significantly suppress noise without introducing perceptually noticeable speech distortion. While higher-order information can be used, most existing approaches use only second-order statistics to design the noise-reduction filter because they are relatively easier to estimate and are more reliable. When we transform non-stationary speech signals into the frequency domain and work with the short-time discrete Fourier transform coefficients, there are two types of second-order statistics, i.e., the variance and the so-called pseudo-variance due to the noncircularity of the signal. So far, only the variance information has been exploited in designing different noise-reduction filters while the pseudo-variance has been neglected. In this paper, we attempt to shed some light on how to use noncircularity in the context of noise reduction. We will discuss the design of optimal and suboptimal noise reduction filters using both the variance and pseudo-variance and answer the basic question whether noncircularity can be used to improve the noise-reduction performance.